Given a previously generated plan, how do we effectively regenerate a new plan?

One of the fundamental cognitive abilities of humans is to quickly resolve uncertainty by generating hypotheses and testing them via active trials.

Reinforcement learning (RL) aims to learn and evaluate a sequential decision rule, often referred to as a "policy", that maximizes expected discounted cumulative rewards to optimize the population-level benefit in an environment across possibly infinitely many time steps. RL has gained popularity in fields such as healthcare, banking, autonomous driving, and, more recently, large language model fine-tuning. However, the sequential decisions made by an RL algorithm, while optimized to maximize overall population benefits, may disadvantage certain individuals who are in minority or socioeconomically disadvantaged groups. A fairness-unaware RL algorithm learns an optimal policy that makes decisions based on the observed state variables. However, if certain values of the sensitive attribute influence the state variables and lead the policy to systematically withhold certain actions from an individual, unfairness will result. For example, Hispanics may under-report their pain levels due to cultural factors, misleading a fairness-unaware RL agent to assign less therapist time to these individuals (Piette et al., 2023). Deployment of RL algorithms without careful fairness considerations can raise concerns and erode public trust in high-stakes settings. To formally define and address the fairness problem in the novel sequential decision-making settings, Wang et al. (2025) extended the concept of single-stage counterfactual

We study fine-grained gap-dependent regret bounds for model-free reinforcement learning in episodic tabular Markov Decision Processes. Existing model-free algorithms achieve minimax worst-case regret, but their gap-dependent bounds remain coarse and fail to fully capture the structure of suboptimality gaps. We address this limitation by establishing fine-grained gap-dependent regret bounds for both UCB-based and non-UCB-based algorithms. In the UCB-based setting, we develop a novel analytical framework that explicitly separates the analysis of optimal and suboptimal state-action pairs, yielding the first fine-grained regret upper bound for UCB-Hoeffding (Jin et al., 2018). To highlight the generality of this framework, we introduce ULCB-Hoeffding, a new UCB-based algorithm inspired by AMB (Xu et al.,2021) but with a simplified structure, which enjoys fine-grained regret guarantees and empirically outperforms AMB. In the non-UCB-based setting, we revisit the only known algorithm AMB, and identify two key issues in its algorithm design and analysis: improper truncation in the $Q$-updates and violation of the martingale difference condition in its concentration argument. We propose a refined version of AMB that addresses these issues, establishing the first rigorous fine-grained gap-dependent regret for a non-UCB-based method, with experiments demonstrating improved performance over AMB.

The continuous nature of belief states in POMDPs presents significant computational challenges in learning the optimal policy. In this paper, we consider an approach that solves a Partially Observable Reinforcement Learning (PORL) problem by approximating the corresponding POMDP model into a finite-state Markov Decision Process (MDP) (called Superstate MDP). We first derive theoretical guarantees that improve upon prior work that relate the optimal value function of the transformed Superstate MDP to the optimal value function of the original POMDP. Next, we propose a policy-based learning approach with linear function approximation to learn the optimal policy for the Superstate MDP. Consequently, our approach shows that a POMDP can be approximately solved using TD-learning followed by Policy Optimization by treating it as an MDP, where the MDP state corresponds to a finite history. We show that the approximation error decreases exponentially with the length of this history. To the best of our knowledge, our finite-time bounds are the first to explicitly quantify the error introduced when applying standard TD learning to a setting where the true dynamics are not Markovian.

Online matching problems arise in many complex systems, from cloud services and online marketplaces to organ exchange networks, where timely, principled decisions are critical for maintaining high system performance. Traditional heuristics in these settings are simple and interpretable but typically tailored to specific operating regimes, which can lead to inefficiencies when conditions change. We propose a reinforcement learning (RL) approach that learns to orchestrate a set of such expert policies, leveraging their complementary strengths in a data-driven, adaptive manner. Building on the Adv2 framework (Jonckheere et al., 2024), our method combines expert decisions through advantage-based weight updates and extends naturally to settings where only estimated value functions are available. We establish both expectation and high-probability regret guarantees and derive a novel finite-time bias bound for temporal-difference learning, enabling reliable advantage estimation even under constant step size and non-stationary dynamics. To support scalability, we introduce a neural actor-critic architecture that generalizes across large state spaces while preserving interpretability. Simulations on stochastic matching models, including an organ exchange scenario, show that the orchestrated policy converges faster and yields higher system level efficiency than both individual experts and conventional RL baselines. Our results highlight how structured, adaptive learning can improve the modeling and management of complex resource allocation and decision-making processes.

Preventing collisions in multi-robot navigation is crucial for deployment. This requirement hinders the use of learning-based approaches, such as multi-agent reinforcement learning (MARL), on their own due to their lack of safety guarantees. Traditional control methods, such as reachability and control barrier functions, can provide rigorous safety guarantees when interactions are limited only to a small number of robots. However, conflicts between the constraints faced by different agents pose a challenge to safe multi-agent coordination. To overcome this challenge, we propose a method that integrates multiple layers of safety by combining MARL with safety filters. First, MARL is used to learn strategies that minimize multiple agent interactions, where multiple indicates more than two. Particularly, we focus on interactions likely to result in conflicting constraints within the engagement distance. Next, for agents that enter the engagement distance, we prioritize pairs requiring the most urgent corrective actions. Finally, a dedicated safety filter provides tactical corrective actions to resolve these conflicts. Crucially, the design decisions for all layers of this framework are grounded in reachability analysis and a control barrier-value function-based filtering mechanism. We validate our Layered Safe MARL framework in 1) hardware experiments using Crazyflie drones and 2) high-density advanced aerial mobility (AAM) operation scenarios, where agents navigate to designated waypoints while avoiding collisions. The results show that our method significantly reduces conflict while maintaining safety without sacrificing much efficiency (i.e., shorter travel time and distance) compared to baselines that do not incorporate layered safety. The project website is available at https://dinamo-mit.github.io/Layered-Safe-MARL/