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Overcoming the diffraction limit, meaning focusing waves on a sub-wavelength scale, has received considerable attention for applications involving light and acoustics. Indeed, the intense focusing achieved enhances the interactions between waves and matter, and the improved spatial resolution opens up possibilities in fields such as imaging, detection and communication. In optics, a passive sink may be obtained if the incident light couples to localized surface plasmon (LSP) resonances, resulting in Coherent Perfect Absorption condition. The presence of optical surface plasmons at metal interfaces is due to the angular frequency of metals, which lies in the optical regime due to their high density of free electrons. Plasmas, which consists of ionized gazes with a lower electron density, can support surface plasmons in the microwave regime. Hence, we demonstrate in this paper that sub-wavelength plasmas behave as a passive microwave sink by exciting LSP resonance inside the plasma.

We consider risk-averse contextual optimization problems where the decision maker (DM) faces two types of uncertainties: problem data uncertainty (PDU) and contextual uncertainty (CU) associated with PDU, the DM makes an optimal decision by minimizing the risk arising from PDU based on the present observation of CU and then assesses the risk of the optimal policy against the CU. A natural question arises as to whether the nested risk minimization/assessment process is equivalent to joint risk minimization/assessment against CU and PDU simultaneously. First, we demonstrate that the equivalence can be established by appropriate choices of the risk measures and give counter examples where such equivalence may fail. One of the interesting findings is that the optimal policies are independent of the choice of the risk measure against the CU under certain conditions. Second, by using the equivalence, we propose computational method for solving the risk-averse contextual optimization problem by solving a one-stage risk minimization problem. The latter is particularly helpful in data-driven environments. We consider a number of risk measures/metrics to characterize the DM's risk preference for PDU and discuss the computational tractability for the resulting risk-averse contextual optimization problem. Third, when the risk-averse contextual optimization problem is defined in the reproducing kernel Hilbert space, we show consistency of the optimal values obtained from solving sample average approximation problems. Some numerical tests, in newsvendor problem and portfolio selection problem, are performed to validate the theoretical results.

Reinforcement learning (RL) has shown promise in solving various combinatorial optimization problems. However, conventional RL faces challenges when dealing with real-world constraints, especially when action space feasibility is explicit and dependent on the corresponding state or trajectory. In this work, we focus on using RL in container shipping, often considered the cornerstone of global trade, by dealing with the critical challenge of master stowage planning. The main objective is to maximize cargo revenue and minimize operational costs while navigating demand uncertainty and various complex operational constraints, namely vessel capacity and stability, which must be dynamically updated along the vessel's voyage. To address this problem, we implement a deep reinforcement learning framework with feasibility projection to solve the master stowage planning problem (MPP) under demand uncertainty. The experimental results show that our architecture efficiently finds adaptive, feasible solutions for this multi-stage stochastic optimization problem, outperforming traditional mixed-integer programming and RL with feasibility regularization. Our AI-driven decision-support policy enables adaptive and feasible planning under uncertainty, optimizing operational efficiency and capacity utilization while contributing to sustainable and resilient global supply chains., Comment: This paper is currently under review for IJCAI 2025

We consider fair resource allocation in sequential decision-making environments modeled as weakly coupled Markov decision processes, where resource constraints couple the action spaces of $N$ sub-Markov decision processes (sub-MDPs) that would otherwise operate independently. We adopt a fairness definition using the generalized Gini function instead of the traditional utilitarian (total-sum) objective. After introducing a general but computationally prohibitive solution scheme based on linear programming, we focus on the homogeneous case where all sub-MDPs are identical. For this case, we show for the first time that the problem reduces to optimizing the utilitarian objective over the class of "permutation invariant" policies. This result is particularly useful as we can exploit Whittle index policies in the restless bandits setting while, for the more general setting, we introduce a count-proportion-based deep reinforcement learning approach. Finally, we validate our theoretical findings with comprehensive experiments, confirming the effectiveness of our proposed method in achieving fairness.

In Markov decision processes (MDPs), quantile risk measures such as Value-at-Risk are a standard metric for modeling RL agents' preferences for certain outcomes. This paper proposes a new Q-learning algorithm for quantile optimization in MDPs with strong convergence and performance guarantees. The algorithm leverages a new, simple dynamic program (DP) decomposition for quantile MDPs. Compared with prior work, our DP decomposition requires neither known transition probabilities nor solving complex saddle point equations and serves as a suitable foundation for other model-free RL algorithms. Our numerical results in tabular domains show that our Q-learning algorithm converges to its DP variant and outperforms earlier algorithms.

In restless multi-arm bandits, a central agent is tasked with optimally distributing limited resources across several bandits (arms), with each arm being a Markov decision process. In this work, we generalize the traditional restless multi-arm bandit problem with a risk-neutral objective by incorporating risk-awareness. We establish indexability conditions for the case of a risk-aware objective and provide a solution based on Whittle index. In addition, we address the learning problem when the true transition probabilities are unknown by proposing a Thompson sampling approach and show that it achieves bounded regret that scales sublinearly with the number of episodes and quadratically with the number of arms. The efficacy of our method in reducing risk exposure in restless multi-arm bandits is illustrated through a set of numerical experiments.

The entropic risk measure is widely used in high-stakes decision making to account for tail risks associated with an uncertain loss. With limited data, the empirical entropic risk estimator, i.e. replacing the expectation in the entropic risk measure with a sample average, underestimates the true risk. To mitigate the bias in the empirical entropic risk estimator, we propose a strongly asymptotically consistent bootstrapping procedure. The first step of the procedure involves fitting a distribution to the data, whereas the second step estimates the bias of the empirical entropic risk estimator using bootstrapping, and corrects for it. Two methods are proposed to fit a Gaussian Mixture Model to the data, a computationally intensive one that fits the distribution of empirical entropic risk, and a simpler one with a component that fits the tail of the empirical distribution. As an application of our approach, we study distributionally robust entropic risk minimization problems with type-$\infty$ Wasserstein ambiguity set and apply our bias correction to debias validation performance. Furthermore, we propose a distributionally robust optimization model for an insurance contract design problem that takes into account the correlations of losses across households. We show that choosing regularization parameters based on the cross validation methods can result in significantly higher out-of-sample risk for the insurer if the bias in validation performance is not corrected for. This improvement in performance can be explained from the observation that our methods suggest a higher (and more accurate) premium to homeowners.

This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating with a version of {\L}ojasiewicz's inequality. The geometry is further developed for the case of dimension 2, where it can be shown that there exist many of the usual correspondences between the algebra and geometry of these functions that one expects from complex algebraic geometry and from other classes of functions in real algebraic geometry such as regulous functions., Comment: 24 pages

The centralized training for decentralized execution paradigm emerged as the state-of-the-art approach to $\epsilon$-optimally solving decentralized partially observable Markov decision processes. However, scalability remains a significant issue. This paper presents a novel and more scalable alternative, namely the sequential-move centralized training for decentralized execution. This paradigm further pushes the applicability of the Bellman's principle of optimality, raising three new properties. First, it allows a central planner to reason upon sufficient sequential-move statistics instead of prior simultaneous-move ones. Next, it proves that $\epsilon$-optimal value functions are piecewise linear and convex in such sufficient sequential-move statistics. Finally, it drops the complexity of the backup operators from double exponential to polynomial at the expense of longer planning horizons. Besides, it makes it easy to use single-agent methods, e.g., SARSA algorithm enhanced with these findings, while still preserving convergence guarantees. Experiments on two- as well as many-agent domains from the literature against $\epsilon$-optimal simultaneous-move solvers confirm the superiority of our novel approach. This paradigm opens the door for efficient planning and reinforcement learning methods for multi-agent systems.

Soil properties, such as wetting collapse behavior and permeability, are strongly correlated to the soil microstructure. To date, several techniques including mercury intrusion porosimetry (MIP), can be used to characterize the microstructure of soil, but all techniques have their own limitations. In this study, the features of mercury that penetrated and has been entrapped in the pore network of the specimens through MIP testing were investigated by X-Ray microtomography (X-$\mu$CT), in order to give an insight into the geometry of macropores and possible ink-bottle geometry. Two conditions of water content and density were selected for the compacted Maryland clay. The distribution and geometry features of mercury entrapped in the microstructure after MIP were characterized and pore size distributions were also reconstructed. The results suggest that, for the two conditions studied in this paper, macropores were evenly distributed within the specimens, and most of them with a non-spherical shape, and with aspect ratio (ratio between the maximum and minimum thickness along a given segment) smaller than three. Different dominant entrance pore size of macropore was obtained from MIP and X-$\mu$CT, due to the specific experimental protocol used in tests and the effect of ink-bottle geometry. Only the large pore bodies with high aspect ratio were imaged in X-$\mu$CT, due to the extrusion of mercury during the process of depressurization and subsequent sample preparation for X- $\mu$CT. But entire pore space was accessible in MIP. The difference in dominant entrance pore size was more significant for specimens with lower void ratio due to a more pronounced aspect ratio.

The field of Contextual Optimization (CO) integrates machine learning and optimization to solve decision making problems under uncertainty. Recently, a risk sensitive variant of CO, known as Conditional Robust Optimization (CRO), combines uncertainty quantification with robust optimization in order to promote safety and reliability in high stake applications. Exploiting modern differentiable optimization methods, we propose a novel end-to-end approach to train a CRO model in a way that accounts for both the empirical risk of the prescribed decisions and the quality of conditional coverage of the contextual uncertainty set that supports them. While guarantees of success for the latter objective are impossible to obtain from the point of view of conformal prediction theory, high quality conditional coverage is achieved empirically by ingeniously employing a logistic regression differentiable layer within the calculation of coverage quality in our training loss. We show that the proposed training algorithms produce decisions that outperform the traditional estimate then optimize approaches.

A recent theory shows that a multi-player decentralized partially observable Markov decision process can be transformed into an equivalent single-player game, enabling the application of \citeauthor{bellman}'s principle of optimality to solve the single-player game by breaking it down into single-stage subgames. However, this approach entangles the decision variables of all players at each single-stage subgame, resulting in backups with a double-exponential complexity. This paper demonstrates how to disentangle these decision variables while maintaining optimality under hierarchical information sharing, a prominent management style in our society. To achieve this, we apply the principle of optimality to solve any single-stage subgame by breaking it down further into smaller subgames, enabling us to make single-player decisions at a time. Our approach reveals that extensive-form games always exist with solutions to a single-stage subgame, significantly reducing time complexity. Our experimental results show that the algorithms leveraging these findings can scale up to much larger multi-player games without compromising optimality.

Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters are used to prescribe new decisions. The prescribed decisions may be low-quality and misaligned with human intuition and thus are unlikely to be adopted. To tackle this challenge, we propose conformal inverse optimization, which seeks to learn an uncertainty set for the unknown parameters and then solve a robust optimization model to prescribe new decisions. Under mild assumptions, we show that our method enjoys provable guarantees on solution quality, as evaluated using both the ground-truth parameters and the decision maker's perception of the unknown parameters. Our method demonstrates strong empirical performance compared to classic inverse optimization.

Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty. This gave rise to the field of contextual optimization, under which data-driven procedures are developed to prescribe actions to the decision-maker that make the best use of the most recently updated information. A large variety of models and methods have been presented in both OR and ML literature under a variety of names, including data-driven optimization, prescriptive optimization, predictive stochastic programming, policy optimization, (smart) predict/estimate-then-optimize, decision-focused learning, (task-based) end-to-end learning/forecasting/optimization, etc. Focusing on single and two-stage stochastic programming problems, this review article identifies three main frameworks for learning policies from data and discusses their strengths and limitations. We present the existing models and methods under a uniform notation and terminology and classify them according to the three main frameworks identified. Our objective with this survey is to both strengthen the general understanding of this active field of research and stimulate further theoretical and algorithmic advancements in integrating ML and stochastic programming.

The abundance of data has led to the emergence of a variety of optimization techniques that attempt to leverage available side information to provide more anticipative decisions. The wide range of methods and contexts of application have motivated the design of a universal unitless measure of performance known as the coefficient of prescriptiveness. This coefficient was designed to quantify both the quality of contextual decisions compared to a reference one and the prescriptive power of side information. To identify policies that maximize the former in a data-driven context, this paper introduces a distributionally robust contextual optimization model where the coefficient of prescriptiveness substitutes for the classical empirical risk minimization objective. We present a bisection algorithm to solve this model, which relies on solving a series of linear programs when the distributional ambiguity set has an appropriate nested form and polyhedral structure. Studying a contextual shortest path problem, we evaluate the robustness of the resulting policies against alternative methods when the out-of-sample dataset is subject to varying amounts of distribution shift.

Plasma ignition is critical in various scientific and industrial applications, demanding an efficient and robust execution mechanism. In this work, we present an innovative approach to plasma ignition by incorporating the analysis of fundamental aspects of light scattering in the complex frequency plane. For the first time, we demonstrate the high-power virtual perfect absorption (VPA) regime, a groundbreaking method for perfectly capturing light within a resonator. By carefully designing the temporal profile of the incident wave, we effectively minimize reflections during the ignition stages, thereby significantly enhancing the efficiency and resilience of the process. Through comprehensive experimental investigations, we validate the viability of this approach, establishing VPA as a powerful tool for reflectionless excitation and optimal control of plasma discharge. By addressing the limitations of conventional plasma ignition methods, this research represents a pivotal step towards transformative advancements in plasma technology, with promising implications for improving the performance and sustainability of numerous applications.

Optimizing static risk-averse objectives in Markov decision processes is difficult because they do not admit standard dynamic programming equations common in Reinforcement Learning (RL) algorithms. Dynamic programming decompositions that augment the state space with discrete risk levels have recently gained popularity in the RL community. Prior work has shown that these decompositions are optimal when the risk level is discretized sufficiently. However, we show that these popular decompositions for Conditional-Value-at-Risk (CVaR) and Entropic-Value-at-Risk (EVaR) are inherently suboptimal regardless of the discretization level. In particular, we show that a saddle point property assumed to hold in prior literature may be violated. However, a decomposition does hold for Value-at-Risk and our proof demonstrates how this risk measure differs from CVaR and EVaR. Our findings are significant because risk-averse algorithms are used in high-stake environments, making their correctness much more critical.

[Abridged] Aims. We provide an important step toward a better understanding of the magnetorotational instability (MRI)-dust coevolution in protoplanetary disks by presenting a proof of concept that dust evolution ultimately plays a crucial role in the MRI activity. Methods. First, we study how a fixed power-law dust size distribution with varying parameters impacts the MRI activity, especially the steady-state MRI-driven accretion, by employing and improving our previous 1+1D MRI-driven turbulence model. Second, we relax the steady-state accretion assumption in this disk accretion model, and partially couple it to a dust evolution model in order to investigate how the evolution of dust (dynamics and grain growth processes combined) and MRI-driven accretion are intertwined on million-year timescales. Results. Dust coagulation and settling lead to a higher gas ionization degree in the protoplanetary disk, resulting in stronger MRI-driven turbulence as well as a more compact dead zone. On the other hand, fragmentation has an opposite effect because it replenishes the disk in small dust particles. Since the dust content of the disk decreases over million years of evolution due to radial drift, the MRI-driven turbulence overall becomes stronger and the dead zone more compact until the disk dust-gas mixture eventually behaves as a grain-free plasma. Furthermore, our results show that dust evolution alone does not lead to a complete reactivation of the dead zone. Conclusions. The MRI activity evolution (hence the temporal evolution of the MRI-induced $\alpha$-parameter) is controlled by dust evolution and occurs on a timescale of local dust growth, as long as there is enough dust particles in the disk to dominate the recombination process for the ionization chemistry. Once it is no longer the case, it is expected to be controlled by gas evolution and occurs on a viscous evolution timescale., Comment: 23 pages, 13 figures, Accepted for publication in A&A