Theoretical Foundations of $\max$@$k$ Reinforcement Learning
arXiv:2607. 17823v1 Announce Type: new Abstract: Reinforcement Learning is a cornerstone technique for modern large reasoning models.
arXiv:2606. 00367v1 Announce Type: cross Abstract: Reinforcement learning problems typically define the goal as maximizing the expected value of a scalar reward function.
arXiv:2607. 17823v1 Announce Type: new Abstract: Reinforcement Learning is a cornerstone technique for modern large reasoning models.
arXiv:2606. 19328v1 Announce Type: cross Abstract: Preference-based RL provides an approach to learning reward models from pairwise comparisons of behaviors, bypassing the need for explicit reward design.
arXiv:2603. 23461v2 Announce Type: replace Abstract: We study reinforcement learning (RL) with linear function approximation in Markov Decision Processes (MDPs) satisfying \emph{linear Bellman completeness} -- a fundamental setting where the Bellman backup of any linear value function remains linear.
arXiv:2512. 14617v2 Announce Type: replace-cross Abstract: Many practical decision-making problems involve tasks whose success depends on the entire system history, rather than on achieving a state with desired properties.
arXiv:2608. 01151v1 Announce Type: cross Abstract: In this paper, we consider stochastic optimal control problems with infinite-horizon joint chance constraints.
The paper introduces a framework for optimal policy improvement in reinforcement learning, defining it as the best single update under given constraints. It shows that restricting improvement to a subset of states is equivalent to solving an induced Markov Decision Process, linking planning with explicit or implicit models to optimal policy improvement. The authors develop a novel operator for greedification under approximate evaluation, demonstrating empirical gains across several RL algorithms and settings.
The paper investigates learning Nash equilibria in partially observable Markov games (POMGs) where agents cannot fully observe the state. By focusing on a subclass with independent state transitions and a Markov potential game structure, the authors propose an independent learning algorithm that allows agents to converge to an approximate Nash equilibrium using only their own observations and actions, without communication. Under a filter stability assumption, finite‑history policies are shown to approximate the POMG sufficiently, enabling a surrogate near‑potential Markov game and yielding quasi‑polynomial sample and computational complexity.
We study infinite-horizon average-reward constrained Markov decision processes (CMDPs) under the weakly communicating assumption. Existing high-probability guarantees for this setting either require c...
The paper introduces BUMEX, a reinforcement learning exploration strategy that leverages a set of prior models containing the true transition kernel and reward function. By optimizing over this model set, the method derives upper and lower bounds on the Q‑function to guide exploration, providing theoretical guarantees of convergence to the optimal policy. When the model set follows a bounded‑parameter MDP structure, the optimization becomes convex, enabling finite‑time convergence under mild assumptions and demonstrating accelerated learning in simulations.
arXiv:2608. 09389v1 Announce Type: cross Abstract: This note aims to serve as an entry point to the literature on learning in games, a topic with significant theoretical appeal and a wide range of applications -- from machine learning and data science to economics and beyond.
arXiv:2606. 10979v1 Announce Type: new Abstract: Many Markov decision processes (MDPs) in operations research have feasible actions that are state dependent and defined implicitly by various operational constraints.
arXiv:2606. 26397v1 Announce Type: cross Abstract: Real-world decision-making often requires balancing multiple conflicting objectives, a challenge that standard Reinforcement Learning (RL) frequently addresses by aggregating rewards into a single scalar signal.