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Understanding the variation of the optimal value with respect to change in the data is an old problem of mathematical optimisation. This paper focuses on the linear problem $f(\lambda) = \min c^t x$ such that $(A+\lambda D)x \leq b$, where $\lambda$ is an unknown parameter that varies within an interval and $D$ is a matrix modifying the coefficients of the constraint matrix $A$. This problem is used to analyse the impact of multiple affine changes in the constraint matrix on the objective function. The function $f(\lambda)$ can have an erratic behaviour and computing it for a large number of points is computationally heavy while not providing any guarantees in between the computed points. As a new approach to the problem, we derive several bounding methods that provide guarantees on the objective function's behaviour. Those guarantees can be exploited to avoid recomputing the problem for numerous $\lambda$. The bounding methods are based on approaches from robust optimisation or Lagrangian relaxations. For each approach, we derive three methods of increasing complexity and precision, one that provides constant bounds, one that provides $\lambda$-dependant bounds and envelope bounds. We assess each bounding method in terms of precision, availability and timing. We show that for a large number of problems, the bound approach outperforms the naive sampling approach considered with 100 points while still providing a good precision and stronger guarantees on a large dataset of problems. We also introduce an iterative algorithm that uses these bounds to compute an approximation of the original function within a given error threshold and discuss its performances.

This paper introduces a systematic approach to address the topological path identification (TPI) problem in power distribution networks. Our approach starts by listing the DSO's raw information coming from several sources. The raw information undergoes a transformation process using a set of transformation functions. This process converts the raw information into well-defined information exploitable by an algorithm. Then a set of hypothetical paths is generated, considering any potential connections between the elements of the power distribution system. This set of hypothetical paths is processed by the algorithm that identifies the hypothetical paths that are compatible with the well-defined information. This procedure operates iteratively, adapting the set of transformation functions based on the result obtained: if the identified paths fail to meet the DSO's expectations, new data is collected, and/or the transformation functions found to be responsible for the discrepancies are modified. The systematic procedure offers practical advantages for DSOs, including improved accuracy in path identification and high adaptability to diverse network configurations, even with incomplete or inaccurate data. Consequently, it emerges as a useful tool for the construction of digital twins of power distribution networks that aligns with DSO expectations.

A customer topological path represents the sequence of network elements connecting an MV/LV transformer to a customer. Accurate knowledge of these paths is crucial for distribution system operators (DSOs) in digitalization, analysis, and network planning. This paper introduces an innovative approach to address the challenge of customer topological path identification (TPI) using only the limited and often inaccurate data available to DSOs. Specifically, our method relies only on geographic information system (GIS) data of network elements and the customer to MV/LV transformers connection information. We introduce an integer linear programming (ILP) optimization algorithm designed to identify customer topological paths that closely approximate the real electricity paths. The effectiveness of the proposed approach is demonstrated through its application to both an academic and a real-world electrical distribution network. Results show that the method effectively addresses data inaccuracies and successfully identifies customer topological paths, providing a valuable tool for DSOs in developing accurate digital twins of their distribution networks.

The increasing adoption of distributed energy resources, particularly photovoltaic (PV) panels, has presented new and complex challenges for power network control. With the significant energy production from PV panels, voltage issues in the network have become a problem. Currently, PV smart inverters (SIs) are used to mitigate the voltage problems by controlling their active power generation and reactive power injection or absorption. However, reducing the active power output of PV panels can be perceived as unfair to some customers, discouraging future installations. To solve this issue, in this paper, a reinforcement learning technique is proposed to address voltage issues in a distribution network, while considering fairness in active power curtailment among customers. The feasibility of the proposed approach is explored through experiments, demonstrating its ability to effectively control voltage in a fair and efficient manner.

The Unit Commitment (UC) problem is a key optimization task in power systems to forecast the generation schedules of power units over a finite time period by minimizing costs while meeting demand and technical constraints. However, many parameters required by the UC problem are unknown, such as the costs. In this work, we estimate these unknown costs using simulation-based inference on an illustrative UC problem, which provides an approximated posterior distribution of the parameters given observed generation schedules and demands. Our results highlight that the learned posterior distribution effectively captures the underlying distribution of the data, providing a range of possible values for the unknown parameters given a past observation. This posterior allows for the estimation of past costs using observed past generation schedules, enabling operators to better forecast future costs and make more robust generation scheduling forecasts. We present avenues for future research to address overconfidence in posterior estimation, enhance the scalability of the methodology and apply it to more complex UC problems modeling the network constraints and renewable energy sources.

Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM)., Comment: 4 pages, 11 pages total, 3 figures

This study proposes a novel approach based on reinforcement learning (RL) to enhance the sorting efficiency of scrap metal using delta robots and a Pick-and-Place (PaP) process, widely used in the industry. We use three classical model-free RL algorithms (TD3, SAC and PPO) to reduce the time to sort metal scraps. We learn the release position and speed needed to throw an object in a bin instead of moving to the exact bin location, as with the classical PaP technique. Our contribution is threefold. First, we provide a new simulation environment for learning RL-based Pick-and-Throw (PaT) strategies for parallel grippers. Second, we use RL algorithms for learning this task in this environment resulting in 89% accuracy while speeding up the throughput by 51% in simulation. Third, we evaluate the performances of RL algorithms and compare them to a PaP and a state-of-the-art PaT method both in simulation and reality, learning only from simulation with domain randomisation and without fine tuning in reality to transfer our policies. This work shows the benefits of RL-based PaT compared to PaP or classical optimization PaT techniques used in the industry.

Policy-gradient algorithms are effective reinforcement learning methods for solving control problems with continuous state and action spaces. To compute near-optimal policies, it is essential in practice to include exploration terms in the learning objective. Although the effectiveness of these terms is usually justified by an intrinsic need to explore environments, we propose a novel analysis and distinguish two different implications of these techniques. First, they make it possible to smooth the learning objective and to eliminate local optima while preserving the global maximum. Second, they modify the gradient estimates, increasing the probability that the stochastic parameter update eventually provides an optimal policy. In light of these effects, we discuss and illustrate empirically exploration strategies based on entropy bonuses, highlighting their limitations and opening avenues for future works in the design and analysis of such strategies.

We propose in this paper an optimal control framework for renewable energy communities (RECs) equipped with controllable assets. Such RECs allow its members to exchange production surplus through an internal market. The objective is to control their assets in order to minimise the sum of individual electricity bills. These bills account for the electricity exchanged through the REC and with the retailers. Typically, for large companies, another important part of the bills are the costs related to the power peaks; in our framework, they are determined from the energy exchanges with the retailers. We compare rule-based control strategies with the two following control algorithms. The first one is derived from model predictive control techniques, and the second one is built with reinforcement learning techniques. We also compare variants of these algorithms that neglect the peak power costs. Results confirm that using policies accounting for the power peaks lead to a significantly lower sum of electricity bills and thus better control strategies at the cost of higher computation time. Furthermore, policies trained with reinforcement learning approaches appear promising for real-time control of the communities, where model predictive control policies may be computationally expensive in practice. These findings encourage pursuing the efforts toward development of scalable control algorithms, operating from a centralised standpoint, for renewable energy communities equipped with controllable assets., Comment: 13 pages (excl. appendices and references), 14 pages of appendix. 10 figures and 10 tables. To be reviewed as a journal paper

Achieving carbon neutrality is probably one of the most important challenges of the 21st century for our societies. Part of the solution to this challenge is to leverage renewable energies. However, these energy sources are often located far away from places that need the energy, and their availability is intermittent, which makes them challenging to work with. In this paper, we build upon the concept of Remote Renewable Energy Hubs (RREHs), which are hubs located at remote places with abundant renewable energy sources whose purpose is to produce carbon-neutral synthetic fuels. More precisely, we model and study the Energy Supply Chain (ESC) that would be required to provide a constant source of carbon-neutral synthetic methane, also called e-NG (electric Natural Gas) or e-methane (electric methane), in Belgium from an RREH located in Morocco. To be carbon neutral, a synthetic fuel has to be produced from existing carbon dioxide (CO2) that needs to be captured using either Direct Air Capture (DAC) or Post Combustion Carbon Capture (PCCC). In this work, we detail the impact of three different carbon sourcing configurations on the price of the e-methane delivered in Belgium. Our results show that sourcing CO2 through a combination of DAC and PCCC is more cost-effective, resulting in a cost of 146 e/MWh for e-methane delivered in Belgium, as opposed to relying solely on DAC, which leads to a cost of 158 e/MWh. Moreover, these scenarios are compared to a scenario where CO2 is captured in Morocco from a CO2 emitting asset that allows to deliver e-methane for a cost of 136 e/MWh.

We introduce IMP-MARL, an open-source suite of multi-agent reinforcement learning (MARL) environments for large-scale Infrastructure Management Planning (IMP), offering a platform for benchmarking the scalability of cooperative MARL methods in real-world engineering applications. In IMP, a multi-component engineering system is subject to a risk of failure due to its components' damage condition. Specifically, each agent plans inspections and repairs for a specific system component, aiming to minimise maintenance costs while cooperating to minimise system failure risk. With IMP-MARL, we release several environments including one related to offshore wind structural systems, in an effort to meet today's needs to improve management strategies to support sustainable and reliable energy systems. Supported by IMP practical engineering environments featuring up to 100 agents, we conduct a benchmark campaign, where the scalability and performance of state-of-the-art cooperative MARL methods are compared against expert-based heuristic policies. The results reveal that centralised training with decentralised execution methods scale better with the number of agents than fully centralised or decentralised RL approaches, while also outperforming expert-based heuristic policies in most IMP environments. Based on our findings, we additionally outline remaining cooperation and scalability challenges that future MARL methods should still address. Through IMP-MARL, we encourage the implementation of new environments and the further development of MARL methods.

In this work, we generalize the problem of learning through interaction in a POMDP by accounting for eventual additional information available at training time. First, we introduce the informed POMDP, a new learning paradigm offering a clear distinction between the information at training and the observation at execution. Next, we propose an objective that leverages this information for learning a sufficient statistic of the history for the optimal control. We then adapt this informed objective to learn a world model able to sample latent trajectories. Finally, we empirically show a learning speed improvement in several environments using this informed world model in the Dreamer algorithm. These results and the simplicity of the proposed adaptation advocate for a systematic consideration of eventual additional information when learning in a POMDP using model-based RL., Comment: In Reinforcement Learning Conference, 2024. 10 pages, 22 pages total, 10 figures

Spiking neural networks are a type of artificial neural networks in which communication between neurons is only made of events, also called spikes. This property allows neural networks to make asynchronous and sparse computations and therefore drastically decrease energy consumption when run on specialised hardware. However, training such networks is known to be difficult, mainly due to the non-differentiability of the spike activation, which prevents the use of classical backpropagation. This is because state-of-the-art spiking neural networks are usually derived from biologically-inspired neuron models, to which are applied machine learning methods for training. Nowadays, research about spiking neural networks focuses on the design of training algorithms whose goal is to obtain networks that compete with their non-spiking version on specific tasks. In this paper, we attempt the symmetrical approach: we modify the dynamics of a well-known, easily trainable type of recurrent neural network to make it event-based. This new RNN cell, called the Spiking Recurrent Cell, therefore communicates using events, i.e. spikes, while being completely differentiable. Vanilla backpropagation can thus be used to train any network made of such RNN cell. We show that this new network can achieve performance comparable to other types of spiking networks in the MNIST benchmark and its variants, the Fashion-MNIST and the Neuromorphic-MNIST. Moreover, we show that this new cell makes the training of deep spiking networks achievable., Comment: 17 pages, 8 figures

Direct policy optimization in reinforcement learning is usually solved with policy-gradient algorithms, which optimize policy parameters via stochastic gradient ascent. This paper provides a new theoretical interpretation and justification of these algorithms. First, we formulate direct policy optimization in the optimization by continuation framework. The latter is a framework for optimizing nonconvex functions where a sequence of surrogate objective functions, called continuations, are locally optimized. Second, we show that optimizing affine Gaussian policies and performing entropy regularization can be interpreted as implicitly optimizing deterministic policies by continuation. Based on these theoretical results, we argue that exploration in policy-gradient algorithms consists in computing a continuation of the return of the policy at hand, and that the variance of policies should be history-dependent functions adapted to avoid local extrema rather than to maximize the return of the policy., Comment: In Transactions on Machine Learning Research (2023)

In this paper, we propose a multi-RREH (Remote Renewable Energy Hub) based optimization framework. This framework allows a valorization of CO2 using carbon capture technologies. This valorization is grounded on the idea that CO2 gathered from the atmosphere or post combustion can be combined with hydrogen to produce synthetic methane. The hydrogen is obtained from water electrolysis using renewable energy (RE). Such renewable energy is generated in RREHs, which are locations where RE is cheap and abundant (e.g., solar PV in the Sahara Desert, or wind in Greenland). We instantiate our framework on a case study focusing on Belgium and 2 RREHs, and we conduct a techno-economic analysis. This analysis highlights the key role played by the cost of the two main carbon capture technologies: Post Combustion Carbon Capture (PCCC) and Direct Air Capture (DAC). In addition, we use our framework to derive a carbon price threshold above which carbon capture technologies may start playing a pivotal role in the decarbonation process of our industries. For example, this price threshold may give relevant information for calibrating the EU Emission Trading System so as to trigger the emergence of the multi-RREH.

This paper extends the concepts of epsilon-optimal spaces and necessary conditions for near-optimality from single-objective to multi-objective optimisation. These notions are first presented for single-objective optimisation, and the mathematical formulation is adapted to address the multi-objective framework. Afterwards, we illustrate the newly developed methodology by conducting multi-sectoral planning of the Belgian energy system with an open-source model called EnergyScope TD. The cost and energy invested in the system are used as objectives. Optimal and efficient solutions for these two objectives are computed and analysed. These results are then used to obtain necessary conditions corresponding to the minimum amount of energy from different sets of resources, including endogenous and exogenous resources. This case study highlights the high dependence of Belgium on imported energy while demonstrating that no individual resource is essential on its own., Comment: 20 pages, 8 figures, submitted to Elsevier

The energy transition is expected to significantly increase the share of renewable energy sources whose production is intermittent in the electricity mix. Apart from key benefits, this development has the major drawback of generating a mismatch between power supply and demand. The innovative dynamic pricing approach may significantly contribute to mitigating that critical problem by taking advantage of the flexibility offered by the demand side. At its core, this idea consists in providing the consumer with a price signal which is evolving over time, in order to influence its consumption. This novel approach involves a challenging decision-making problem that can be summarised as follows: how to determine a price signal maximising the synchronisation between power supply and demand under the constraints of maintaining the producer/retailer's profitability and benefiting the final consumer at the same time? As a contribution, this research work presents a detailed formalisation of this particular decision-making problem. Moreover, the paper discusses the diverse algorithmic components required to efficiently design a dynamic pricing policy: different forecasting models together with an accurate statistical modelling of the demand response to dynamic prices., Comment: Research paper accepted for publication in the peer-reviewed journal Energy Reports edited by Elsevier

Classical reinforcement learning (RL) techniques are generally concerned with the design of decision-making policies driven by the maximisation of the expected outcome. Nevertheless, this approach does not take into consideration the potential risk associated with the actions taken, which may be critical in certain applications. To address that issue, the present research work introduces a novel methodology based on distributional RL to derive sequential decision-making policies that are sensitive to the risk, the latter being modelled by the tail of the return probability distribution. The core idea is to replace the $Q$ function generally standing at the core of learning schemes in RL by another function taking into account both the expected return and the risk. Named the risk-based utility function $U$, it can be extracted from the random return distribution $Z$ naturally learnt by any distributional RL algorithm. This enables to span the complete potential trade-off between risk minimisation and expected return maximisation, in contrast to fully risk-averse methodologies. Fundamentally, this research yields a truly practical and accessible solution for learning risk-sensitive policies with minimal modification to the distributional RL algorithm, and with an emphasis on the interpretability of the resulting decision-making process.

In this paper, we identify the best learning scenario to train a team of agents to compete against multiple possible strategies of opposing teams. We evaluate cooperative value-based methods in a mixed cooperative-competitive environment. We restrict ourselves to the case of a symmetric, partially observable, two-team Markov game. We selected three training methods based on the centralised training and decentralised execution (CTDE) paradigm: QMIX, MAVEN and QVMix. For each method, we considered three learning scenarios differentiated by the variety of team policies encountered during training. For our experiments, we modified the StarCraft Multi-Agent Challenge environment to create competitive environments where both teams could learn and compete simultaneously. Our results suggest that training against multiple evolving strategies achieves the best results when, for scoring their performances, teams are faced with several strategies.

Reinforcement learning aims to learn optimal policies from interaction with environments whose dynamics are unknown. Many methods rely on the approximation of a value function to derive near-optimal policies. In partially observable environments, these functions depend on the complete sequence of observations and past actions, called the history. In this work, we show empirically that recurrent neural networks trained to approximate such value functions internally filter the posterior probability distribution of the current state given the history, called the belief. More precisely, we show that, as a recurrent neural network learns the Q-function, its hidden states become more and more correlated with the beliefs of state variables that are relevant to optimal control. This correlation is measured through their mutual information. In addition, we show that the expected return of an agent increases with the ability of its recurrent architecture to reach a high mutual information between its hidden states and the beliefs. Finally, we show that the mutual information between the hidden states and the beliefs of variables that are irrelevant for optimal control decreases through the learning process. In summary, this work shows that in its hidden states, a recurrent neural network approximating the Q-function of a partially observable environment reproduces a sufficient statistic from the history that is correlated to the relevant part of the belief for taking optimal actions., Comment: 12 pages, 28 pages total, 20 figures. Transactions on Machine Learning Research (2022)

The recent major increase in decentralized energy resources (DERs) such as photovoltaic (PV) panels alters the loading profile of distribution systems (DS) and impacts higher voltage levels. Distribution system operators (DSOs) try to manage the deployment of new DERs to decrease the operational costs. However, DER location and size are factors beyond any DSO's reach. This paper presents a practical method to minimize the DS operational costs due to new DER deployments, through optimal selection of their connection phase. The impact of such distribution grid management efforts on aggregated demand for higher voltage levels is also evaluated and discussed in this paper. Simulation results on a real-life Belgian network show the effectiveness of optimal connection phase selection in decreasing DS operational costs, and the considerable impact of such simple DS management efforts on the aggregated demand., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

In business retention, churn prevention has always been a major concern. This work contributes to this domain by formalizing the problem of churn prediction in the context of online gambling as a binary classification task. We also propose an algorithmic answer to this problem based on recurrent neural network. This algorithm is tested with online gambling data that have the form of time series, which can be efficiently processed by recurrent neural networks. To evaluate the performances of the trained models, standard machine learning metrics were used, such as accuracy, precision and recall. For this problem in particular, the conducted experiments allowed to assess that the choice of a specific architecture depends on the metric which is given the greatest importance. Architectures using nBRC favour precision, those using LSTM give better recall, while GRU-based architectures allow a higher accuracy and balance two other metrics. Moreover, further experiments showed that using only the more recent time-series histories to train the networks decreases the quality of the results. We also study the performances of models learned at a specific instant $t$, at other times $t^{\prime} > t$. The results show that the performances of the models learned at time $t$ remain good at the following instants $t^{\prime} > t$, suggesting that there is no need to refresh the models at a high rate. However, the performances of the models were subject to noticeable variance due to one-off events impacting the data., Comment: 14 pages, 3 figures Submitted to Expert Systems with Applications

In power systems, large-scale optimisation problems are extensively used to plan for capacity expansion at the supra-national level. However, their cost-optimal solutions are often not exploitable by decision-makers who are preferably looking for features of solutions that can accommodate their different requirements. This paper proposes a generic framework for addressing this problem. It is based on the concept of the epsilon-optimal feasible space of a given optimisation problem and the identification of necessary conditions over this space. This framework has been developed in a generic case, and an approach for solving this problem is subsequently described for a specific case where conditions are constrained sums of variables. The approach is tested on a case study about capacity expansion planning of the European electricity network to determine necessary conditions on the minimal investments in transmission, storage and generation capacity., Comment: 8 pages, 10 figures, 1 table, accepted at PSCC2022

The distributional reinforcement learning (RL) approach advocates for representing the complete probability distribution of the random return instead of only modelling its expectation. A distributional RL algorithm may be characterised by two main components, namely the representation of the distribution together with its parameterisation and the probability metric defining the loss. The present research work considers the unconstrained monotonic neural network (UMNN) architecture, a universal approximator of continuous monotonic functions which is particularly well suited for modelling different representations of a distribution. This property enables the efficient decoupling of the effect of the function approximator class from that of the probability metric. The research paper firstly introduces a methodology for learning different representations of the random return distribution (PDF, CDF and QF). Secondly, a novel distributional RL algorithm named unconstrained monotonic deep Q-network (UMDQN) is presented. To the authors' knowledge, it is the first distributional RL method supporting the learning of three, valid and continuous representations of the random return distribution. Lastly, in light of this new algorithm, an empirical comparison is performed between three probability quasi-metrics, namely the Kullback-Leibler divergence, Cramer distance, and Wasserstein distance. The results highlight the main strengths and weaknesses associated with each probability metric together with an important limitation of the Wasserstein distance., Comment: Research paper accepted for publication in the peer-reviewed Neurocomputing journal edited by Elsevier

Training recurrent neural networks is known to be difficult when time dependencies become long. In this work, we show that most standard cells only have one stable equilibrium at initialisation, and that learning on tasks with long time dependencies generally occurs once the number of network stable equilibria increases; a property known as multistability. Multistability is often not easily attained by initially monostable networks, making learning of long time dependencies between inputs and outputs difficult. This insight leads to the design of a novel way to initialise any recurrent cell connectivity through a procedure called "warmup" to improve its capability to learn arbitrarily long time dependencies. This initialisation procedure is designed to maximise network reachable multistability, i.e., the number of equilibria within the network that can be reached through relevant input trajectories, in few gradient steps. We show on several information restitution, sequence classification, and reinforcement learning benchmarks that warming up greatly improves learning speed and performance, for multiple recurrent cells, but sometimes impedes precision. We therefore introduce a double-layer architecture initialised with a partial warmup that is shown to greatly improve learning of long time dependencies while maintaining high levels of precision. This approach provides a general framework for improving learning abilities of any recurrent cell when long time dependencies are present. We also show empirically that other initialisation and pretraining procedures from the literature implicitly foster reachable multistability of recurrent cells., Comment: 20 pages, 35 pages total, 38 figures

Estimating the distance to objects is crucial for autonomous vehicles when using depth sensors is not possible. In this case, the distance has to be estimated from on-board mounted RGB cameras, which is a complex task especially in environments such as natural outdoor landscapes. In this paper, we present a new method named M4Depth for depth estimation. First, we establish a bijective relationship between depth and the visual disparity of two consecutive frames and show how to exploit it to perform motion-invariant pixel-wise depth estimation. Then, we detail M4Depth which is based on a pyramidal convolutional neural network architecture where each level refines an input disparity map estimate by using two customized cost volumes. We use these cost volumes to leverage the visual spatio-temporal constraints imposed by motion and to make the network robust for varied scenes. We benchmarked our approach both in test and generalization modes on public datasets featuring synthetic camera trajectories recorded in a wide variety of outdoor scenes. Results show that our network outperforms the state of the art on these datasets, while also performing well on a standard depth estimation benchmark. The code of our method is publicly available at https://github.com/michael-fonder/M4Depth., Comment: Main paper: 9 pages, Appendix: 4 pages, References: 2 pages. Code available on GitHub: https://github.com/michael-fonder/M4Depth

Gym-ANM is a Python package that facilitates the design of reinforcement learning (RL) environments that model active network management (ANM) tasks in electricity networks. Here, we describe how to implement new environments and how to write code to interact with pre-existing ones. We also provide an overview of ANM6-Easy, an environment designed to highlight common ANM challenges. Finally, we discuss the potential impact of Gym-ANM on the scientific community, both in terms of research and education. We hope this package will facilitate collaboration between the power system and RL communities in the search for algorithms to control future energy systems., Comment: 5 pages, 2 figures, 2 code samples

The accurate representation of variable renewable generation (RES, e.g., wind, solar PV) assets in capacity expansion planning (CEP) studies is paramount to capture spatial and temporal correlations that may exist between sites and impact both power system design and operation. However, it typically has a high computational cost. This paper proposes a method to reduce the spatial dimension of CEP problems while preserving an accurate representation of renewable energy sources. A two-stage approach is proposed to this end. In the first stage, relevant sites are identified via a screening routine that discards the locations with little impact on system design. In the second stage, the subset of relevant RES sites previously identified is used in a CEP problem to determine the optimal configuration of the power system. The proposed method is tested on a realistic EU case study and its performance is benchmarked against a CEP set-up in which the entire set of candidate RES sites is available. The method shows great promise, with the screening stage consistently identifying 90% of the optimal RES sites while discarding up to 54% of the total number of candidate locations. This leads to a peak memory reduction of up to 41% and solver runtime gains between 31% and 46%, depending on the weather year considered., Comment: Accepted to PowerTech2021, Madrid, Spain

Active network management (ANM) of electricity distribution networks include many complex stochastic sequential optimization problems. These problems need to be solved for integrating renewable energies and distributed storage into future electrical grids. In this work, we introduce Gym-ANM, a framework for designing reinforcement learning (RL) environments that model ANM tasks in electricity distribution networks. These environments provide new playgrounds for RL research in the management of electricity networks that do not require an extensive knowledge of the underlying dynamics of such systems. Along with this work, we are releasing an implementation of an introductory toy-environment, ANM6-Easy, designed to emphasize common challenges in ANM. We also show that state-of-the-art RL algorithms can already achieve good performance on ANM6-Easy when compared against a model predictive control (MPC) approach. Finally, we provide guidelines to create new Gym-ANM environments differing in terms of (a) the distribution network topology and parameters, (b) the observation space, (c) the modelling of the stochastic processes present in the system, and (d) a set of hyperparameters influencing the reward signal. Gym-ANM can be downloaded at https://github.com/robinhenry/gym-anm., Comment: 15 main pages, 17 pages of appendix, 10 figures, GitHub repository: https://github.com/robinhenry/gym-anm

A fundamental task for artificial intelligence is learning. Deep Neural Networks have proven to cope perfectly with all learning paradigms, i.e. supervised, unsupervised, and reinforcement learning. Nevertheless, traditional deep learning approaches make use of cloud computing facilities and do not scale well to autonomous agents with low computational resources. Even in the cloud, they suffer from computational and memory limitations, and they cannot be used to model adequately large physical worlds for agents which assume networks with billions of neurons. These issues are addressed in the last few years by the emerging topic of sparse training, which trains sparse networks from scratch. This paper discusses sparse training state-of-the-art, its challenges and limitations while introducing a couple of new theoretical research directions which has the potential of alleviating sparse training limitations to push deep learning scalability well beyond its current boundaries. Nevertheless, the theoretical advancements impact in complex multi-agents settings is discussed from a real-world perspective, using the smart grid case study.

This paper studies the economics of carbon-neutral synthetic fuel production from renewable electricity in remote areas where high-quality renewable resources are abundant. To this end, a graph-based optimisation modelling framework directly applicable to the strategic planning of remote renewable energy supply chains is proposed. More precisely, a hypergraph abstraction of planning problems is introduced, wherein nodes can be viewed as optimisation subproblems with their own parameters, variables, constraints and local objective. Nodes typically represent a subsystem such as a technology, a plant or a process. Hyperedges, on the other hand, express the connectivity between subsystems. The framework is leveraged to study the economics of carbon-neutral synthetic methane production from solar and wind energy in North Africa and its delivery to Northwestern European markets. The full supply chain is modelled in an integrated fashion, which makes it possible to accurately capture the interaction between various technologies on an hourly time scale. Results suggest that the cost of synthetic methane production and delivery would be slightly under 150 EUR/MWh (higher heating value) by 2030 for a system supplying 10 TWh annually and relying on a combination of solar photovoltaic and wind power plants, assuming a uniform weighted average cost of capital of 7%. A comprehensive sensitivity analysis is also carried out in order to assess the impact of various techno-economic parameters and assumptions on synthetic methane cost, including the availability of wind power plants, the investment costs of electrolysis, methanation and direct air capture plants, their operational flexibility, the energy consumption of direct air capture plants, and financing costs.

This paper introduces four new algorithms that can be used for tackling multi-agent reinforcement learning (MARL) problems occurring in cooperative settings. All algorithms are based on the Deep Quality-Value (DQV) family of algorithms, a set of techniques that have proven to be successful when dealing with single-agent reinforcement learning problems (SARL). The key idea of DQV algorithms is to jointly learn an approximation of the state-value function $V$, alongside an approximation of the state-action value function $Q$. We follow this principle and generalise these algorithms by introducing two fully decentralised MARL algorithms (IQV and IQV-Max) and two algorithms that are based on the centralised training with decentralised execution training paradigm (QVMix and QVMix-Max). We compare our algorithms with state-of-the-art MARL techniques on the popular StarCraft Multi-Agent Challenge (SMAC) environment. We show competitive results when QVMix and QVMix-Max are compared to well-known MARL techniques such as QMIX and MAVEN and show that QVMix can even outperform them on some of the tested environments, being the algorithm which performs best overall. We hypothesise that this is due to the fact that QVMix suffers less from the overestimation bias of the $Q$ function., Comment: To be published in AAAI-21 Workshop on Reinforcement Learning in Games

This paper provides a detailed account of the impact of different offshore wind siting strategies on the design of the European power system. To this end, a two-stage method is proposed. In the first stage, a highly-granular siting problem identifies a suitable set of sites where offshore wind plants could be deployed according to a pre-specified criterion. Two siting schemes are analysed and compared within a realistic case study. These schemes essentially select a pre-specified number of sites so as to maximise their aggregate power output and their spatiotemporal complementarity, respectively. In addition, two variants of these siting schemes are provided, wherein the number of sites to be selected is specified on a country-by-country basis rather than Europe-wide. In the second stage, the subset of previously identified sites is passed to a capacity expansion planning (CEP) framework that sizes the power generation, transmission and storage assets that should be deployed and operated in order to satisfy pre-specified electricity demand levels at minimum cost. Results show that the complementarity-based siting criterion leads to system designs which are up to 5% cheaper than the ones relying the power output-based criterion when offshore wind plants are deployed with no consideration for country-based deployment targets. On the contrary, the power output-based scheme leads to system designs which are consistently 2% cheaper than the ones leveraging the complementarity-based siting strategy when such constraints are enforced. The robustness of the results is supported by a sensitivity analysis on offshore wind capital expenditure and inter-annual weather variability, respectively., Comment: Submitted to Applied Energy

Local electricity markets represent a way of supplementing traditional retailing contracts for end consumers -- among these markets, the renewable energy community has gained momentum over the last few years. This paper proposes a practical and readily to be adopted modelling solution for these communities, one that allows their members to share the economic benefits derived from them. The proposed solution relies on an \emph{ex-post} allocation of the electricity that is generated within energy communities (i.e., local electricity) based on the optimisation of \emph{repartition keys}. Repartition keys are therefore optimally computed to represent the proportion of total local electricity to be allocated to each community member, and aim to minimise the sum of electricity bills of all community members. Since the optimisation takes place \emph{ex-post} the repartition keys do not modify the actual electricity flows, but rather the financial flows of the community members. Then, the billing process of the community will take these keys into account to correctly send the electricity bills to each member. Building on this concept, we also introduce two additions to the basic algorithm to enhance the stability of the community, which a global bill minimisation may fail to ensure (e.g., very asymmetrical solutions between members may lead to some of them opting out)., Comment: 16 pages, 8 figures, 5 tables, 3 algorithms, submitted to IEEE Access

Retailers and major consumers of electricity generally purchase an important percentage of their estimated electricity needs years ahead in the forward market. This long-term electricity procurement task consists of determining when to buy electricity so that the resulting energy cost is minimised, and the forecast consumption is covered. In this scientific article, the focus is set on a yearly base load product from the Belgian forward market, named calendar (CAL), which is tradable up to three years ahead of the delivery period. This research paper introduces a novel algorithm providing recommendations to either buy electricity now or wait for a future opportunity based on the history of CAL prices. This algorithm relies on deep learning forecasting techniques and on an indicator quantifying the deviation from a perfectly uniform reference procurement policy. On average, the proposed approach surpasses the benchmark procurement policies considered and achieves a reduction in costs of 1.65% with respect to the perfectly uniform reference procurement policy achieving the mean electricity price. Moreover, in addition to automating the complex electricity procurement task, this algorithm demonstrates more consistent results throughout the years. Eventually, the generality of the solution presented makes it well suited for solving other commodity procurement problems., Comment: Scientific article accepted for publication in the Energies journal edited by MDPI

Recurrent neural networks (RNNs) provide state-of-the-art performances in a wide variety of tasks that require memory. These performances can often be achieved thanks to gated recurrent cells such as gated recurrent units (GRU) and long short-term memory (LSTM). Standard gated cells share a layer internal state to store information at the network level, and long term memory is shaped by network-wide recurrent connection weights. Biological neurons on the other hand are capable of holding information at the cellular level for an arbitrary long amount of time through a process called bistability. Through bistability, cells can stabilize to different stable states depending on their own past state and inputs, which permits the durable storing of past information in neuron state. In this work, we take inspiration from biological neuron bistability to embed RNNs with long-lasting memory at the cellular level. This leads to the introduction of a new bistable biologically-inspired recurrent cell that is shown to strongly improves RNN performance on time-series which require very long memory, despite using only cellular connections (all recurrent connections are from neurons to themselves, i.e. a neuron state is not influenced by the state of other neurons). Furthermore, equipping this cell with recurrent neuromodulation permits to link them to standard GRU cells, taking a step towards the biological plausibility of GRU.

We consider the joint design and control of discrete-time stochastic dynamical systems over a finite time horizon. We formulate the problem as a multi-step optimization problem under uncertainty seeking to identify a system design and a control policy that jointly maximize the expected sum of rewards collected over the time horizon considered. The transition function, the reward function and the policy are all parametrized, assumed known and differentiable with respect to their parameters. We then introduce a deep reinforcement learning algorithm combining policy gradient methods with model-based optimization techniques to solve this problem. In essence, our algorithm iteratively approximates the gradient of the expected return via Monte-Carlo sampling and automatic differentiation and takes projected gradient ascent steps in the space of environment and policy parameters. This algorithm is referred to as Direct Environment and Policy Search (DEPS). We assess the performance of our algorithm in three environments concerned with the design and control of a mass-spring-damper system, a small-scale off-grid power system and a drone, respectively. In addition, our algorithm is benchmarked against a state-of-the-art deep reinforcement learning algorithm used to tackle joint design and control problems. We show that DEPS performs at least as well or better in all three environments, consistently yielding solutions with higher returns in fewer iterations. Finally, solutions produced by our algorithm are also compared with solutions produced by an algorithm that does not jointly optimize environment and policy parameters, highlighting the fact that higher returns can be achieved when joint optimization is performed.

The large integration of variable energy resources is expected to shift a large part of the energy exchanges closer to real-time, where more accurate forecasts are available. In this context, the short-term electricity markets and in particular the intraday market are considered a suitable trading floor for these exchanges to occur. A key component for the successful renewable energy sources integration is the usage of energy storage. In this paper, we propose a novel modelling framework for the strategic participation of energy storage in the European continuous intraday market where exchanges occur through a centralized order book. The goal of the storage device operator is the maximization of the profits received over the entire trading horizon, while taking into account the operational constraints of the unit. The sequential decision-making problem of trading in the intraday market is modelled as a Markov Decision Process. An asynchronous distributed version of the fitted Q iteration algorithm is chosen for solving this problem due to its sample efficiency. The large and variable number of the existing orders in the order book motivates the use of high-level actions and an alternative state representation. Historical data are used for the generation of a large number of artificial trajectories in order to address exploration issues during the learning process. The resulting policy is back-tested and compared against a benchmark strategy that is the current industrial standard. Results indicate that the agent converges to a policy that achieves in average higher total revenues than the benchmark strategy.

This scientific research paper presents an innovative approach based on deep reinforcement learning (DRL) to solve the algorithmic trading problem of determining the optimal trading position at any point in time during a trading activity in stock markets. It proposes a novel DRL trading strategy so as to maximise the resulting Sharpe ratio performance indicator on a broad range of stock markets. Denominated the Trading Deep Q-Network algorithm (TDQN), this new trading strategy is inspired from the popular DQN algorithm and significantly adapted to the specific algorithmic trading problem at hand. The training of the resulting reinforcement learning (RL) agent is entirely based on the generation of artificial trajectories from a limited set of stock market historical data. In order to objectively assess the performance of trading strategies, the research paper also proposes a novel, more rigorous performance assessment methodology. Following this new performance assessment approach, promising results are reported for the TDQN strategy., Comment: Preprint submitted to Elsevier journal "Expert Systems with Applications"

Animals excel at adapting their intentions, attention, and actions to the environment, making them remarkably efficient at interacting with a rich, unpredictable and ever-changing external world, a property that intelligent machines currently lack. Such an adaptation property relies heavily on cellular neuromodulation, the biological mechanism that dynamically controls intrinsic properties of neurons and their response to external stimuli in a context-dependent manner. In this paper, we take inspiration from cellular neuromodulation to construct a new deep neural network architecture that is specifically designed to learn adaptive behaviours. The network adaptation capabilities are tested on navigation benchmarks in a meta-reinforcement learning context and compared with state-of-the-art approaches. Results show that neuromodulation is capable of adapting an agent to different tasks and that neuromodulation-based approaches provide a promising way of improving adaptation of artificial systems.

Current global environmental challenges require vigorous and diverse actions in the energy sector. One solution that has recently attracted interest consists in harnessing high-quality variable renewable energy resources in remote locations, while using transmission links to transport the power to end users. In this context, a comparison of western European and Greenland wind regimes is proposed. By leveraging a regional atmospheric model specifically designed to accurately capture polar phenomena, local climatic features of southern Greenland are identified to be particularly conducive to extensive renewable electricity generation from wind. A methodology to assess how connecting remote locations to major demand centres would benefit the latter from a resource availability standpoint is introduced and applied to the aforementioned Europe-Greenland case study, showing superior and complementary wind generation potential in the considered region of Greenland with respect to selected European sites., Comment: Published in Elsevier Energy

This paper proposes a systematic framework to assess the complementarity of renewable resources over arbitrary geographical scopes and temporal scales which is particularly well-suited to exploit very large data sets of climatological data. The concept of critical time windows is introduced, and a spatio-temporal criticality indicator is proposed, consisting in a parametrised family of scalar indicators quantifying the complementarity between renewable resources in both space and time. The criticality indicator is leveraged to devise a family of optimisation problems identifying sets of locations with maximum complementarity under arbitrary geographical deployment constraints. The applicability of the framework is shown in a case study investigating the complementarity between the wind regimes in continental western Europe and southern Greenland, and its usefulness in a power system planning context is demonstrated. Besides showing that the occurrence of low wind power production events can be significantly reduced on a regional scale by exploiting diversity in local wind patterns, results highlight the fact that aggregating wind power production sites located on different continents may result in a lower occurrence of system-wide low wind power production events and indicate potential benefits of intercontinental electrical interconnections.

This paper provides an analysis of the tradeoff between asymptotic bias (suboptimality with unlimited data) and overfitting (additional suboptimality due to limited data) in the context of reinforcement learning with partial observability. Our theoretical analysis formally characterizes that while potentially increasing the asymptotic bias, a smaller state representation decreases the risk of overfitting. This analysis relies on expressing the quality of a state representation by bounding L1 error terms of the associated belief states. Theoretical results are empirically illustrated when the state representation is a truncated history of observations, both on synthetic POMDPs and on a large-scale POMDP in the context of smartgrids, with real-world data. Finally, similarly to known results in the fully observable setting, we also briefly discuss and empirically illustrate how using function approximators and adapting the discount factor may enhance the tradeoff between asymptotic bias and overfitting in the partially observable context., Comment: Accepted at the Journal of Artificial Intelligence Research (JAIR) - 31 pages

In applications, such as biomedicine and systems/synthetic biology, technical limitations in actuation complicate implementation of time-varying control signals. In order to alleviate some of these limitations, it may be desirable to derive simple control policies, such as step functions with fixed magnitude and length (or temporal pulses). In this technical note, we further develop a recently proposed pulse-based solution to the convergence problem, i.e., minimizing the convergence time to the target exponentially stable equilibrium, for monotone systems. In particular, we extend this solution to monotone systems with parametric uncertainty. Our solutions also provide worst-case estimates on convergence times. Furthermore, we indicate how our tools can be used for a class of non-monotone systems, and more importantly how these tools can be extended to other control problems. We illustrate our approach on switching under parametric uncertainty and regulation around a saddle point problems in a genetic toggle switch system.

In many applications, and in systems/synthetic biology, in particular, it is desirable to compute control policies that force the trajectory of a bistable system from one equilibrium (the initial point) to another equilibrium (the target point), or in other words to solve the switching problem. It was recently shown that, for monotone bistable systems, this problem admits easy-to-implement open-loop solutions in terms of temporal pulses (i.e., step functions of fixed length and fixed magnitude). In this paper, we develop this idea further and formulate a problem of convergence to an equilibrium from an arbitrary initial point. We show that this problem can be solved using a static optimization problem in the case of monotone systems. Changing the initial point to an arbitrary state allows to build closed-loop, event-based or open-loop policies for the switching/convergence problems. In our derivations we exploit the Koopman operator, which offers a linear infinite-dimensional representation of an autonomous nonlinear system. One of the main advantages of using the Koopman operator is the powerful computational tools developed for this framework. Besides the presence of numerical solutions, the switching/convergence problem can also serve as a building block for solving more complicated control problems and can potentially be applied to non-monotone systems. We illustrate this argument on the problem of synchronizing cardiac cells by defibrillation. Potentially, our approach can be extended to problems with different parametrizations of control signals since the only fundamental limitation is the finite time application of the control signal., Comment: corrected typos

Using deep neural nets as function approximator for reinforcement learning tasks have recently been shown to be very powerful for solving problems approaching real-world complexity. Using these results as a benchmark, we discuss the role that the discount factor may play in the quality of the learning process of a deep Q-network (DQN). When the discount factor progressively increases up to its final value, we empirically show that it is possible to significantly reduce the number of learning steps. When used in conjunction with a varying learning rate, we empirically show that it outperforms original DQN on several experiments. We relate this phenomenon with the instabilities of neural networks when they are used in an approximate Dynamic Programming setting. We also describe the possibility to fall within a local optimum during the learning process, thus connecting our discussion with the exploration/exploitation dilemma., Comment: NIPS 2015 Deep Reinforcement Learning Workshop

In the Bayesian Reinforcement Learning (BRL) setting, agents try to maximise the collected rewards while interacting with their environment while using some prior knowledge that is accessed beforehand. Many BRL algorithms have already been proposed, but even though a few toy examples exist in the literature, there are still no extensive or rigorous benchmarks to compare them. The paper addresses this problem, and provides a new BRL comparison methodology along with the corresponding open source library. In this methodology, a comparison criterion that measures the performance of algorithms on large sets of Markov Decision Processes (MDPs) drawn from some probability distributions is defined. In order to enable the comparison of non-anytime algorithms, our methodology also includes a detailed analysis of the computation time requirement of each algorithm. Our library is released with all source code and documentation: it includes three test problems, each of which has two different prior distributions, and seven state-of-the-art RL algorithms. Finally, our library is illustrated by comparing all the available algorithms and the results are discussed., Comment: 37 pages

In this work, we propose a simple yet effective solution to the problem of connectome inference in calcium imaging data. The proposed algorithm consists of two steps. First, processing the raw signals to detect neural peak activities. Second, inferring the degree of association between neurons from partial correlation statistics. This paper summarises the methodology that led us to win the Connectomics Challenge, proposes a simplified version of our method, and finally compares our results with respect to other inference methods.

With the increasing share of renewable and distributed generation in electrical distribution systems, Active Network Management (ANM) becomes a valuable option for a distribution system operator to operate his system in a secure and cost-effective way without relying solely on network reinforcement. ANM strategies are short-term policies that control the power injected by generators and/or taken off by loads in order to avoid congestion or voltage issues. Advanced ANM strategies imply that the system operator has to solve large-scale optimal sequential decision-making problems under uncertainty. For example, decisions taken at a given moment constrain the future decisions that can be taken and uncertainty must be explicitly accounted for because neither demand nor generation can be accurately forecasted. We first formulate the ANM problem, which in addition to be sequential and uncertain, has a nonlinear nature stemming from the power flow equations and a discrete nature arising from the activation of power modulation signals. This ANM problem is then cast as a stochastic mixed-integer nonlinear program, as well as second-order cone and linear counterparts, for which we provide quantitative results using state of the art solvers and perform a sensitivity analysis over the size of the system, the amount of available flexibility, and the number of scenarios considered in the deterministic equivalent of the stochastic program. To foster further research on this problem, we make available at http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution networks of 5, 33, and 77 buses. These test beds contain a simulator of the distribution system, with stochastic models for the generation and consumption devices, and callbacks to implement and test various ANM strategies.

We propose and analyze a day-ahead reserve market model that handles bids from flexible loads. This pool market model takes into account the fact that a load modulation in one direction must usually be compensated later by a modulation of the same magnitude in the opposite direction. Our analysis takes into account the gaming possibilities of producers and retailers, controlling load flexibility, in the day-ahead energy and reserve markets, and in imbalance settlement. This analysis is carried out by an agent-based approach where, for every round, each actor uses linear programs to maximize its profit according to forecasts of the prices. The procurement of a reserve is assumed to be determined, for each period, as a fixed percentage of the total consumption cleared in the energy market for the same period. The results show that the provision of reserves by flexible loads has a negligible impact on the energy market prices but markedly decreases the cost of reserve procurement. However, as the rate of flexible loads increases, the system operator has to rely more and more on non-contracted reserves, which may cancel out the benefits made in the procurement of reserves.