Deep Q-Learning on H\"older Spaces
arXiv:2606. 16846v1 Announce Type: cross Abstract: We study the operator-theoretic core of Q-learning in continuous-time stochastic control with continuous states and actions.
arXiv:2606. 16846v1 Announce Type: cross Abstract: We study the operator-theoretic core of Q-learning in continuous-time stochastic control with continuous states and actions.
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:2506. 13862v2 Announce Type: replace-cross Abstract: In Reinforcement Learning (RL), regularization with a Kullback-Leibler divergence that penalizes large deviations between successive policies has emerged as a popular tool both in theory and practice.
Limiting‑Kernel Q(λ) (LKQL) is an off‑policy value estimator that blends n‑step truncation with a long‑horizon approximation based on the limiting kernel. It maintains the computational efficiency of n‑step methods while improving policy evaluation accuracy, especially for long‑horizon tasks. The authors prove faster convergence of LKQL’s operator under aperiodicity and near‑on‑policy conditions, and demonstrate empirical gains on MuJoCo continuous‑control benchmarks.
In value-based reinforcement learning, improving the accuracy of policy evaluation has been shown to improve downstream policy optimization performance. The widely adopted family of approximations rel...
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:2506. 07040v4 Announce Type: replace-cross Abstract: We study model-free methods for distributionally robust infinite-horizon average-reward Markov decision processes (MDPs).
The paper introduces Dually Regularized AIL, a model‑free algorithm for adversarial imitation learning that jointly applies KL policy regularization and a quadratic reward penalty based on expert and learner occupancies. It proves fast convergence rates, achieving a ×O(1/K+1/N) bound on the regularized imitation gap in finite‑horizon MDPs with general function approximation, and establishes the first algorithm to attain ×O(1/ε) sample complexity in both expert demonstrations and online interactions for this regularized objective.
arXiv:2607. 28916v1 Announce Type: cross Abstract: Multistep credit assignment is critical for sample-efficient reinforcement learning, yet managing off-policy bias in Q-learning remains a fundamental challenge.
The paper introduces state abstractions that preserve the difference of Q‑functions for offline reinforcement learning, aiming to exclude irrelevant dynamics from rich state data. It proposes a dynamic generalization of the R‑learner that uses orthogonal estimation and sparse learning to estimate the Q‑function contrast, achieving faster convergence and consistency under a margin condition. Experiments on simulated and simulator‑augmented real data show variance reductions and demonstrate that the necessary information for sequential decision‑making can be smaller than that required for full state prediction.
arXiv:2310. 07211v2 Announce Type: replace Abstract: Regularization is a cornerstone of modern reinforcement learning.
The paper introduces Fast Regularized Policy Mirror Descent (PMD) that pairs policy updates with a single temporal-difference (TD) critic step. It proves global linear convergence for finite discounted MDPs using exact coordinate-wise Bellman updates and any positive actor stepsize, regardless of critic initialization. For stochastic TD-PMD with strongly convex mirror maps, the authors achieve an expected value gap of ε after “~O(1/((1-γ)^5 σ_b ε))” transitions, without requiring trajectory resets, generative models, or nested policy evaluation loops.