Sampling in discrete spaces, with critical applications in simulation and optimization, has recently been boosted by significant advances in gradient-based approaches that exploit modern accelerators like GPUs. However, two key challenges are hindering further advancement in research on discrete sampling.

Thompson sampling (TS) has attracted a lot of interest in the bandit area. It was introduced in the 1930s but has not been theoretically proven until recent years. All of its analysis in the combinatorial multi-armed bandit (CMAB) setting requires an exact oracle to provide optimal solutions with any input. However, such an oracle is usually not feasible since many combinatorial optimization problems are NP-hard and only approximation oracles are available. An example \cite{WangC18} has shown the failure of TS to learn with an approximation oracle. However, this oracle is uncommon and is designed only for a specific problem instance.

Learning heuristics for combinatorial optimization problems through graph neural networks have recently shown promising results on some classic NP-hard problems. These are single-level optimization problems with only one player. Multilevel combinatorial optimization problems are their generalization, encompassing situations with multiple players taking decisions sequentially. By framing them in a multi-agent reinforcement learning setting, we devise a value-based method to learn to solve multilevel budgeted combinatorial problems involving two players in a zero-sum game over a graph. Our framework is based on a simple curriculum: if an agent knows how to estimate the value of instances with budgets up to $B$, then solving instances with budget $B+1$ can be done in polynomial time regardless of the direction of the optimization by checking the value of every possible afterstate. Thus, in a bottom-up approach, we generate datasets of heuristically solved instances with increasingly larger budgets to train our agent. We report results close to optimality on graphs up to $100$ nodes and a $185 \times$ speedup on average compared to the quickest exact solver known for the Multilevel Critical Node problem, a max-min-max trilevel problem that has been shown to be at least $\Sigma_2^p$-hard.

Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is unknown and thus has to be debunked using empirical evidence. In contrast to the common practice that relies on a learning-and-optimization strategy, we consider the regression between combinatorial spaces, aiming to infer high-quality optimization solutions from samples of input-solution pairs -- without the need to learn the objective function. Our main deliverable is a universal solver that is able to handle abstract undetermined stochastic combinatorial optimization problems.

Abstract--The rapid adoption of electric vehicles (EVs) introduces major challenges for decentralized charging control. Existing decentralized approaches efficiently coordinate a large number of EVs to select charging stations while reducing energy costs, preventing power peak and preserving driver privacy. These situations create competition for limited charging slots, resulting in long queues and reduced driver comfort. T o address these limitations, we propose a novel collective learning-based coordination framework that allows EVs to balance individual comfort on their selections against system-wide efficiency, i.e., the overall queues across all stations. In the framework, EVs are recommended for adaptive charging behaviors that shift priority between comfort and efficiency, achieving Pareto-optimal trade-offs under varying station capacities and dynamic spatiotemporal EV distribution. Experiments using real-world data from EVs and charging stations show that the proposed approach outperforms baseline methods, significantly reducing travel and queuing time. The results reveal that, under uncertain charging conditions, EV drivers that behave selfishly or altruistically at the right moments achieve shorter waiting time than those maintaining moderate behavior throughout. Our findings under high fractions of station outages and adversarial EVs further demonstrate improved resilience and trustworthiness of decentralized EV charging infrastructure. LECTRIC vehicles (EVs) are becoming a preferred option in intelligent transportation systems due to their energy efficiency and reduced emissions, critical in addressing environmental concerns and fuel shortages. According to recent global market reports, EV sales are projected to surpass 17 million units in 2024 (over 20% market share), with over 20 million expected in 2025 [1]. As governments expand public charging infrastructure to meet soaring demand, centralized charging management faces limitations in scalability, cost, and resilience (e.g., single points of failure) [2], [3]. A promising alternative lies in decentralized charging control among EVs. It aims to allow EVs to manage their charging based on local conditions, user preference and grid/station needs without a central authority.

We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show that the sleeping versions of these problems are at least as hard as P AC learning DNF expressions, a long standing open problem.

We present an end-to-end framework for solving the V ehicle Routing Problem (VRP) using reinforcement learning.

To overcome this challenge, diverging from conventional efforts of expanding the solver's search scope, we focus on enabling information to actively propagate to the solver through heat diffusion.

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