With the integration of renewable sources in electricity distribution networks, the need to develop intelligent mechanisms for balancing the energy market has arisen. In the absence of such mechanisms, the energy market may face imbalances that can lead to power outages, financial losses or instability at the grid level. In this context, the grouping of microgrids into optimal coalitions that can absorb energy from the market during periods of surplus or supply energy to the market during periods of is a key aspect in the efficient management of distribution networks. In this article, we propose a method that identify an optimal microgrids coalition capable of addressing the dynamics of the energy market. The proposed method models the problem of identifying the optimal coalition as an optimization problem that it solves by combining a strategy inspired by cooperative game theory with a memetic algorithm. An individual is represented as a coalition of microgrids and the evolution of population of individuals over generations is assured by recombination and mutation. The fitness function is defined as the difference between the total value generated by the coalition and a penalty applied to the coalition when the energy traded by coalition exceeds the energy available/demanded on/by the energy market. The value generated by the coalition is calculated based on the profit obtained by the collation if it sells energy on the market during periods of deficit or the savings obtained by the coalition if it buys energy on the market during periods of surplus and the costs associated with the trading process. This value is divided equitably among the coalition members, according to the Shapley value, which considers the contribution of each one to the formation of collective value.

Standard uncertainty estimation techniques, such as dropout, often struggle to clearly distinguish reliable predictions from unreliable ones. We attribute this limitation to noisy classifier weights, which, while not impairing overall class-level predictions, render finer-level statistics less informative. To address this, we propose a novel test-time optimization method that accounts for the impact of such noise to produce more reliable confidence estimates. This score defines a monotonic subset-selection function, where population accuracy consistently increases as samples with lower scores are removed, and it demonstrates superior performance in standard risk-based metrics such as AUSE and AURC. Additionally, our method effectively identifies discrepancies between training and test distributions, reliably differentiates in-distribution from out-of-distribution samples, and elucidates key differences between CNN and ViT classifiers across various vision datasets.

Constrained Reinforcement Learning (CRL) addresses sequential decision-making problems where agents are required to achieve goals by maximizing the expected return while meeting domain-specific constraints. In this setting, policy-based methods are widely used thanks to their advantages when dealing with continuous-control problems. These methods search in the policy space with an action-based or a parameter-based exploration strategy, depending on whether they learn the parameters of a stochastic policy or those of a stochastic hyperpolicy. We introduce an exploration-agnostic algorithm, called C-PG, which enjoys global last-iterate convergence guarantees under gradient domination assumptions. Furthermore, under specific noise models where the (hyper)policy is expressed as a stochastic perturbation of the actions or of the parameters of an underlying deterministic policy, we additionally establish global last-iterate convergence guarantees of C-PG to the optimal deterministic policy . This holds when learning a stochastic (hyper)policy and subsequently switching off the stochasticity at the end of training, thereby deploying a deterministic policy. Finally, we empirically validate both the action-based ( C-PGAE) and parameter-based ( C-PGPE) variants of C-PG on constrained control tasks, and compare them against state-of-the-art baselines, demonstrating their effectiveness, in particular when deploying deterministic policies after training.

Accurately estimating the impact of road maintenance schedules on traffic conditions is important because maintenance operations can substantially worsen congestion if not carefully planned. Reliable estimates allow planners to avoid excessive delays during periods of roadwork. Since the exact increase in congestion is difficult to predict analytically, traffic simulations are commonly used to assess the redistribution of the flow of traffic. However, when applied to long-term maintenance planning involving many overlapping projects and scheduling alternatives, these simulations must be run thousands of times, resulting in a significant computational burden. This paper investigates the use of machine learning-based surrogate models to predict network-wide congestion caused by simultaneous road renovations. We frame the problem as a supervised learning task, using one-hot encodings, engineered traffic features, and heuristic approximations. A range of linear, ensemble-based, probabilistic, and neural regression models is evaluated under an online learning framework in which data progressively becomes available. The experimental results show that the Costliest Subset Heuristic provides a reasonable approximation when limited training data is available, and that most regression models fail to outperform it, with the exception of XGBoost, which achieves substantially better accuracy. In overall performance, XGBoost significantly outperforms alternatives in a range of metrics, most strikingly Mean Absolute Percentage Error (MAPE) and Pinball loss, where it achieves a MAPE of 11% and outperforms the next-best model by 20% and 38% respectively. This modeling approach has the potential to reduce the computational burden of large-scale traffic assignment problems in maintenance planning.

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating such games while capturing heterogeneity among players. In this paper, we propose and analyze a policy optimization framework for continuous-time, finite-horizon linear-quadratic GMFGs. Exploiting the structural properties of GMFGs, we design an efficient policy parameterization in which each player's policy is represented as an affine function of their private state, with a shared slope function and player-specific intercepts. We develop a bilevel optimization algorithm that alternates between policy gradient updates for best-response computation under a fixed population distribution, and distribution updates using the resulting policies. We prove linear convergence of the policy gradient steps to best-response policies and establish global convergence of the overall algorithm to the Nash equilibrium. The analysis relies on novel landscape characterizations over infinite-dimensional policy spaces. Numerical experiments demonstrate the convergence and robustness of the proposed algorithm under varying graphon structures, noise levels, and action frequencies.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

Reducing communication complexity is critical for efficient decentralized optimization. The proximal decentralized optimization (PDO) framework is particularly appealing, as methods within this framework can exploit functional similarity among nodes to reduce communication rounds. Specifically, when local functions at different nodes are similar, these methods achieve faster convergence with fewer communication steps. However, existing PDO methods often require highly accurate solutions to subproblems associated with the proximal operator, resulting in significant computational overhead. In this work, we propose the Stabilized Proximal Decentralized Optimization (SPDO) method, which achieves state-of-the-art communication and computational complexities within the PDO framework. Additionally, we refine the analysis of existing PDO methods by relaxing subproblem accuracy requirements and leveraging average functional similarity. Experimental results demonstrate that SPDO significantly outperforms existing methods.

Quality-Diversity (QD) algorithms have shown remarkable success in discovering diverse, high-performing solutions, but rely heavily on hand-crafted behavioral descriptors that constrain exploration to predefined notions of diversity. Leveraging the equivalence between policies and occupancy measures, we present a theoretically grounded approach to automatically generate behavioral descriptors by embedding the occupancy measures of policies in Markov Decision Processes. Our method, AutoQD, leverages random Fourier features to approximate the Maximum Mean Discrepancy (MMD) between policy occupancy measures, creating embeddings whose distances reflect meaningful behavioral differences. A low-dimensional projection of these embeddings that captures the most behaviorally significant dimensions is then used as behavioral descriptors for off-the-shelf QD methods. We prove that our embeddings converge to true MMD distances between occupancy measures as the number of sampled trajectories and embedding dimensions increase. Through experiments in multiple continuous control tasks we demonstrate AutoQD's ability in discovering diverse policies without predefined behavioral descriptors, presenting a well-motivated alternative to prior methods in unsupervised Reinforcement Learning and QD optimization. Our approach opens new possibilities for open-ended learning and automated behavior discovery in sequential decision making settings without requiring domain-specific knowledge.

Quantified Integer Programming (QIP) bridges multiple domains by extending Quantified Boolean Formulas (QBF) to incorporate general integer variables and linear constraints while also generalizing Integer Programming through variable quantification. As a special case of Quantified Constraint Satisfaction Problems (QCSP), QIP provides a versatile framework for addressing complex decision-making scenarios. Additionally, the inclusion of a linear objective function enables QIP to effectively model multistage robust discrete linear optimization problems, making it a powerful tool for tackling uncertainty in optimization. While two primary solution paradigms exist for QBF -- search-based and expansion-based approaches -- only search-based methods have been explored for QIP and QCSP. We introduce an expansion-based approach for QIP using Counterexample-Guided Abstraction Refinement (CEGAR), adapting techniques from QBF. We extend this methodology to tackle multistage robust discrete optimization problems with linear constraints and further embed it in an optimization framework, enhancing its applicability. Our experimental results highlight the advantages of this approach, demonstrating superior performance over existing search-based solvers for QIP in specific instances. Furthermore, the ability to model problems using linear constraints enables notable performance gains over state-of-the-art expansion-based solvers for QBF.

--Training with huge datasets and a large number of participating devices leads to bottlenecks in federated learning (FL). Furthermore, the challenges of heterogeneity between multiple FL clients affect the overall performance of the system. In a quantum federated learning (QFL) context, we address these three main challenges: i) training bottlenecks from massive datasets, ii) the involvement of a substantial number of devices, and iii) non-IID data distributions. We introduce a model-driven quantum federated learning algorithm (mdQFL) to tackle these challenges. Our proposed approach is efficient and adaptable to various factors, including different numbers of devices. T o the best of our knowledge, it is the first to explore training and update personalization, as well as test generalization within a QFL setting, which can be applied to other FL scenarios. We evaluated the efficiency of the proposed mdQFL framework through extensive experiments under diverse non-IID data heterogeneity conditions using various datasets within the Qiskit environment. Our results demonstrate a nearly 50% decrease in total communication costs while maintaining or, in some cases, exceeding the accuracy of the final model and consistently improving local model training compared to the standard QFL baseline. Moreover, our experimental evaluation thoroughly explores the QFL and mdQFL algorithms, along with several influencing factors. In addition, we present a theoretical analysis to clarify the complexities of the proposed algorithm. Federated Learning (FL) has emerged as a pivotal technique to address the challenges of privacy and security in distributed machine learning [1], [2].