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An optimal randomized strategy for design of balanced, normalized mass transport plans is developed. It replaces -- but specializes to -- the deterministic, regularized optimal transport (OT) strategy, which yields only a certainty-equivalent plan. The incompletely specified -- and therefore uncertain -- transport plan is acknowledged to be a random process. Therefore, hierarchical fully probabilistic design (HFPD) is adopted, yielding an optimal hyperprior supported on the set of possible transport plans, and consistent with prior mean constraints on the marginals of the uncertain plan. This Bayesian resetting of the design problem for transport plans -- which we call HFPD-OT -- confers new opportunities. These include (i) a strategy for the generation of a random sample of joint transport plans; (ii) randomized marginal contracts for individual source-target pairs; and (iii) consistent measures of uncertainty in the plan and its contracts. An application in algorithmic fairness is outlined, where HFPD-OT enables the recruitment of a more diverse subset of contracts -- than is possible in classical OT -- into the delivery of an expected plan. Also, it permits fairness proxies to be endowed with uncertainty quantifiers., Comment: 27 pages, 26 figures

As consumer flexibility becomes expected, it is important that the market mechanisms which attain that flexibility are perceived as fair. We set out fairness issues in energy markets today, and propose a market design to address them. Consumption is categorised as either essential or flexible with different prices and reliability levels for each. Prices are generated by an Automatic Market Maker (AMM) based on instantaneous scarcity and resource is allocated using a novel Fair Play algorithm. We empirically show the performance of the system over 1 year for 101 UK households and benchmark its performance against more classical approaches., Comment: Under review for inclusion in Special Issue of Applied Energy on `(R)Evolution of Electricity Markets: Designing Smart Electricity Markets for a Decarbonized World'

Controlled charging of electric vehicles, EVs, is a major potential source of flexibility to facilitate the integration of variable renewable energy and reduce the need for stationary energy storage. To offer system services from EVs, fleet aggregators must address the uncertainty of individual driving and charging behaviour. This paper introduces a means of forecasting the service volume available from EVs by considering several EV batteries as one conceptual battery with aggregate power and energy boundaries. This avoids the impossible task of predicting individual driving behaviour by taking advantage of the law of large numbers. The forecastability of the boundaries is demonstrated in a multiple linear regression model which achieves an $R^2$ of 0.7 for a fleet of 1,000 EVs. A two-stage stochastic model predictive control algorithm is used to schedule reserve services on a day-ahead basis addressing risk trade-offs by including Conditional Value-at-Risk in the objective function. A case study with 1.2 million domestic EV charge records from Great Britain shows that increasing fleet size improves prediction accuracy, thereby increasing reserve revenues and decreasing effective charging costs. For fleet sizes of 400 or above, charging cost reductions plateau at 60\%, with an average of 1.8kW of reserve provided per vehicle.

We present a novel class of proof-of-position algorithms: Tree-Proof-of-Position (T-PoP). This algorithm is decentralised, collaborative and can be computed in a privacy preserving manner, such that agents do not need to reveal their position publicly. We make no assumptions of honest behaviour in the system, and consider varying ways in which agents may misbehave. Our algorithm is therefore resilient to highly adversarial scenarios. This makes it suitable for a wide class of applications, namely those in which trust in a centralised infrastructure may not be assumed, or high security risk scenarios. Our algorithm has a worst case quadratic runtime, making it suitable for hardware constrained IoT applications. We also provide a mathematical model that summarises T-PoP's performance for varying operating conditions. We then simulate T-PoP's behaviour with a large number of agent-based simulations, which are in complete agreement with our mathematical model, thus demonstrating its validity. T-PoP can achieve high levels of reliability and security by tuning its operating conditions, both in high and low density environments. Finally, we also present a mathematical model to probabilistically detect platooning attacks.

Vaccination campaigns have both direct and indirect effects that act to control an infectious disease as it spreads through a population. Indirect effects arise when vaccinated individuals block disease transmission in any infection chains they are part of, and this in turn can benefit both vaccinated and unvaccinated individuals. Indirect effects are difficult to quantify in practice, but here, working with the Susceptible-Infected-Recovered (SIR) model, they are analytically calculated in important cases, through pivoting on the Final Size formula for epidemics. Their relationship to herd immunity is also clarified. Furthermore, we identify the important distinction between quantifying indirect effects of vaccination at the "population level" versus the "per capita" individual level, which often results in radically different conclusions. As an important example, the analysis unpacks why population-level indirect effect can appear significantly larger than its per capita analogue. In addition, we consider a recently proposed epidemiological non-pharamaceutical intervention used over COVID-19, referred to as "shielding", and study its impact in our mathematical analysis. The shielding scheme is extended by inclusion of limited vaccination.

Reinforcement Learning (RL) is a powerful method for controlling dynamic systems, but its learning mechanism can lead to unpredictable actions that undermine the safety of critical systems. Here, we propose RL with Adaptive Control Regularization (RL-ACR), an algorithm that enables safe RL exploration by combining the RL policy with a policy regularizer that hard-codes safety constraints. We perform policy combination via a "focus network," which determines the appropriate combination depending on the state -- relying more on the safe policy regularizer for less-exploited states while allowing unbiased convergence for well-exploited states. In a series of critical control applications, we demonstrate that RL-ACR ensures safety during training while achieving the performance standards of model-free RL approaches that disregard safety.

With the advent of the AI Act and other regulations, there is now an urgent need for algorithms that repair unfairness in training data. In this paper, we define fairness in terms of conditional independence between protected attributes ($S$) and features ($X$), given unprotected attributes ($U$). We address the important setting in which torrents of archival data need to be repaired, using only a small proportion of these data, which are $S|U$-labelled (the research data). We use the latter to design optimal transport (OT)-based repair plans on interpolated supports. This allows {\em off-sample}, labelled, archival data to be repaired, subject to stationarity assumptions. It also significantly reduces the size of the supports of the OT plans, with correspondingly large savings in the cost of their design and of their {\em sequential\/} application to the off-sample data. We provide detailed experimental results with simulated and benchmark real data (the Adult data set). Our performance figures demonstrate effective repair -- in the sense of quenching conditional dependence -- of large quantities of off-sample, labelled (archival) data.

We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove asymptotic convergence of our algorithms to a unique optimal solution. New insights obtained from the convergence proof are highlighted. An example from electrical vehicle charging in a smart city context is outlined, in which the prior zero-constraints prevent energy from being transported from some providers to some vehicles., Comment: Submitted for publication

This paper discusses congestion control and inconsistency problems in DAG-based distributed ledgers and proposes an additional filter to mitigate these issues. Unlike traditional blockchains, DAG-based DLTs use a directed acyclic graph structure to organize transactions, allowing higher scalability and efficiency. However, this also introduces challenges in controlling the rate at which blocks are added to the network and preventing the influence of spam attacks. To address these challenges, we propose a filter to limit the tip pool size and to avoid referencing old blocks. Furthermore, we present experimental results to demonstrate the effectiveness of this filter in reducing the negative impacts of various attacks. Our approach offers a lightweight and efficient solution for managing the flow of blocks in DAG-based DLTs, which can enhance the consistency and reliability of these systems. Index

We present a decentralised class of algorithms called Tree-Proof-of-Position (T-PoP). T-PoP algorithms rely on the web of interconnected devices in a smart city to establish how likely it is that an agent is in the position they claim to be. T-PoP operates under adversarial assumptions, by which some agents are incentivised to be dishonest. We present a theoretical formulation for T-PoP and its security properties, and we validate this model through a large number of Monte-Carlo simulations. We specifically focus on two instances of T-PoP and analyse their security and reliability properties under a range of adversarial conditions. Use-cases and applications are discussed towards the end of this paper.

The goal of this paper is to introduce a new theoretical framework for Optimal Transport (OT), using the terminology and techniques of Fully Probabilistic Design (FPD). Optimal Transport is the canonical method for comparing probability measures and has been successfully applied in a wide range of areas (computer vision Rubner et al. [2004], computer graphics Solomon et al. [2015], natural language processing Kusner et al. [2015], etc.). However, we argue that the current OT framework suffers from two shortcomings: first, it is hard to induce generic constraints and probabilistic knowledge in the OT problem; second, the current formalism does not address the question of uncertainty in the marginals, lacking therefore the mechanisms to design robust solutions. By viewing the OT problem as the optimal design of a probability density function with marginal constraints, we prove that OT is an instance of the more generic FPD framework. In this new setting, we can furnish the OT framework with the necessary mechanisms for processing probabilistic constraints and deriving uncertainty quantifiers, hence establishing a new extended framework, called FPD-OT. Our main contribution in this paper is to establish the connection between OT and FPD, providing new theoretical insights for both. This will lay the foundations for the application of FPD-OT in a subsequent work, notably in processing more sophisticated knowledge constraints, as well as in designing robust solutions in the case of uncertain marginals., Comment: Keywords: Optimal Transport, Fully Probabilistic Design, Convex optimization

The AIMD algorithm, which underpins the Transmission Control Protocol (TCP) for transporting data packets in communication networks, is perhaps the most successful control algorithm ever deployed. Recently, its use has been extended beyond communication networks, and successful applications of the AIMD algorithm have been reported in transportation, energy, and mathematical biology. A very recent development in the use of AIMD is its application in solving large-scale optimization and distributed control problems without the need for inter-agent communication. In this context, an interesting problem arises when multiple AIMD networks that are coupled in some sense (usually through a nonlinearity). The purpose of this note is to prove that such systems in certain settings inherit the ergodic properties of individual AIMD networks. This result has important consequences for the convergence of the aforementioned optimization algorithms. The arguments in the paper also correct conceptual and technical errors in [1].

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. This behaviour can often be modelled as observations of an unknown dynamical system with an unobserved state. When the training data for the subgroups are not controlled carefully, however, under-representation bias arises. To counter under-representation bias, we introduce two natural notions of fairness in time-series forecasting problems: subgroup fairness and instantaneous fairness. These notions extend predictive parity to the learning of dynamical systems. We also show globally convergent methods for the fairness-constrained learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. We also show that by exploiting sparsity in the convexifications, we can reduce the run time of our methods considerably. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate the efficacy of our methods., Comment: Journal version of Zhou et al. [arXiv:2006.07315, AAAI 2021]

There has been much recent interest in the regulation of AI. We argue for a view based on civil-rights legislation, built on the notions of equal treatment and equal impact. In a closed-loop view of the AI system and its users, the equal treatment concerns one pass through the loop. Equal impact, in our view, concerns the long-run average behaviour across repeated interactions. In order to establish the existence of the average and its properties, one needs to study the ergodic properties of the closed-loop and its unique stationary measure.

Cyclists travelling in urban areas are particularly at risk of harm from particulate emissions due to their increased breathing rate and proximity to vehicles. In this paper we combine human respiratory models with models of particulate inhalation to estimate the pollution risk an individual is experiencing in real time given the local pollution level and their heart rate for the first time. Using this model as a baseline, we learn a policy that simultaneously optimises the route for a large number of cyclists with diverse origins and destinations, to minimise overall pollution risk and account for the detrimental impacts of congestion. We learn this policy using reinforcement learning techniques on simulated data in different environments with varying distributions of cyclist fitness. These findings establish that individualised routing is effective in reducing pollution risk while cycling, improving the net benefits of active commuting.

Over two thirds of women of all ages in the UK have experienced some form of sexual harassment in a public space. Recent tragic incidents involving female pedestrians have highlighted some of the personal safety issues that women still face in cities today. There exist many popular location-based safety applications as a result of this; however, these applications tend to take a reactive approach where action is taken only after an incident has occurred. This paper proposes a preventative approach to the problem by creating safer public environments through societal incentivisation. The proposed system, called "Herd Routes", improves the safety of female pedestrians by generating busier pedestrian routes as a result of route incentivisation. A novel application of distributed ledgers is proposed to provide security and trust, a record of system users' locations and IDs, and a platform for token exchange. A proof-of-concept was developed using the simulation package SUMO (Simulation of Urban Mobility), and a smartphone app. was built in Android Studio so that pedestrian Hardware-in-the-Loop testing could be carried out to validate the technical feasibility and desirability of the system. With positive results from the initial testing of the proof-of-concept, further development could significantly contribute towards creating safer pedestrian routes through cities, and tackle the societal change that is required to improve female pedestrian safety in the long term.

In this paper, we describe an approach to guide drivers searching for a parking space (PS). The proposed system suggests a sequence of routes that drivers should traverse in order to maximise the expected likelihood of finding a PS and minimise the travel distance. This system is built on our recent architecture SPToken, which combines both Distributed Ledger Technology (DLT) and Reinforcement Learning (RL) to realise a system for the estimation of an unknown distribution without disturbing the environment. For this, we use a number of virtual tokens that are passed from vehicle to vehicle to enable a massively parallelised RL system that estimates the best route for a given origin-destination (OD) pair, using crowdsourced information from participant vehicles. Additionally, a moving window with reward memory mechanism is included to better cope with non-stationary environments. Simulation results are given to illustrate the efficacy of our system., Comment: 12 pages, 5 figures, 27th ITS World Congress, Hamburg, Germany, 11-15 October 2021

We describe an architecture for a decentralised data market for applications in which agents are incentivised to collaborate to crowd-source their data. The architecture is designed to reward data that furthers the market's collective goal, and distributes reward fairly to all those that contribute with their data. We show that the architecture is resilient to Sybil, wormhole, and data poisoning attacks. In order to evaluate the resilience of the architecture, we characterise its breakdown points for various adversarial threat models in an automotive use case., Comment: 13 pages, 7 figures

As Covid-19 remains a cause of concern, especially due to its mutations, wearing masks correctly and efficiently remains a priority in order to limit the spread of the disease. In this paper we present a wearable smart-mask prototype using concepts from Internet of Things, Control Theory and Distributed Ledger Technologies. Its purpose is to encourage people to comply with social distancing norms, through the use of incentives. The smart mask is designed to monitor Carbon Dioxide and Total Volatile Organic Compounds concentrations. The detected data is appended to a DAG-based DLT, named the IOTA Tangle. The IOTA Tangle ensures that the data is secure and immutable and acts as a communication backbone for the incentive mechanism. A hardware-in-the-loop simulation, based on indoor positioning, is developed to validate the effectiveness of the designed prototype.

In this paper we present a feedback approach to the design of an attack mitigation policy for DAG-based Distributed Ledgers. We develop a model to analyse the behaviour of the ledger under the so called Tips Inflation Attack and we design a control strategy to counteract this attack strategy. The efficacy of this approach is showcased through a theoretical analysis, in the form of two theorems about the stability properties of the ledger with and without the controller, and extensive Monte Carlo simulations of an agent-based model of the distributed ledger.

An outstanding problem in the design of distributed ledgers concerns policies that govern the manner in which users interact with the network. Network usability is crucial to the mainstream adoption of distributed ledgers, particularly for enterprise applications in which most users do not wish to operate full node. For DAG-based ledgers such as IOTA, we propose a user-node interaction mechanism that is designed to ensure the risk of a user experiencing a poor quality of service is low. Our mechanism involves users selecting nodes to issue their transactions to the ledger based on quality of service indicators advertised by the nodes. Simulation results are presented to illustrate the efficacy of the proposed policies.

This is a Masters Thesis completed at University College Dublin, Ireland in 2017 which involved augmenting an off-the-shelf electric bike with sensors to enable new services to be delivered to cyclists in cities. The application of primary interest was to control the cyclist's ventilation rate based on the concentration of local air pollutants. Detailed modelling and system design is presented for our Cyberphysical system which consisted of a modified BTwin e-bike, Cycle Analyst sensors, the cyclist themselves, a Bluetooth connected smartphone and our algorithms. Control algorithms to regulate the proportion of power the cyclist provided as a proxy for their ventilation rate were proposed and validated in a basic way, which were later proven significantly further in Further Work (see IEEE Transactions on Intelligent Transportation Systems paper: https://ieeexplore.ieee.org/abstract/document/8357977). The basic idea was to provide more electrical assistance to cyclists in areas of high air pollution to reduce the cyclist ventilation rate and thereby the amount of air pollutants inhaled. This presents an interesting control challenge due to the human-in-the-loop characteristics and the potential for impactful real life applications. A background literature review is provided on energy as it relates to cycling and some other applications are also discussed. A link to a video which demonstrates the system is provided, and also to a blog published by IBM Research about the system.

We present the observation that the process of stochastic model predictive control can be formulated in the framework of iterated function systems. The latter has a rich ergodic theory that can be applied to study the system's long-run behavior. We show how such a framework can be realized for specific problems and illustrate the required conditions for the application of relevant theoretical guarantees.

In many sharing-economy applications, as well as in conventional economy applications, one wishes to regulate the behaviour of an ensemble of agents with guarantees on both the regulation of the ensemble in aggregate and the revenue or quality of service associated with each agent. Previous work [Automatica, Volume 108, 108483, arXiv:1807.03256 ] has developed guarantees of unique ergodicity when there are linear filters. Here, we extend the guarantees to systems including non-linear elements, such as non-linear filters.

In power systems, one wishes to regulate the aggregate demand of an ensemble of distributed energy resources (DERs), such as controllable loads and battery energy storage systems. We suggest a notion of predictability and fairness, which suggests that the long-term averages of prices or incentives offered should be independent of the initial states of the operators of the DER, the aggregator, and the power grid. We show that this notion cannot be guaranteed with many traditional controllers used by the load aggregator, including the usual proportional-integral (PI) controller. We show that even considering the non-linearity of the alternating-current model, this notion of predictability and fairness can be guaranteed for incrementally input-to-state stable (iISS) controllers, under mild assumptions.

This paper is concerned with the design of a human-in-the-loop system for deployment on a smart pedelec (e-bike). From the control-theoretic perspective, the goal is not only to use the power assistance of the e-bike to reject disturbances along the route but also to manage the possibly competitive interactions between a human and the motor intervention. Managing the competitive/cooperative nature of the interactions is crucial for applications in which we wish to control physical aspects of the cycling behavior (e.g. heart rate and breathing rate). The basis of the control is a pitchfork bifurcation system, modeling the interactions, augmented using ideas from gain-scheduling. In vivo experiments have been conducted, showing the effectiveness of the proposed control strategy., Comment: 7 figures