The paper introduces a vector Bellman theory for multichain robust average‑reward Markov decision processes, addressing the state‑dependent optimal long‑run rewards that arise under uncertainty. It develops a gain‑first, bias‑second optimization principle for finite models with compact, post‑action $(s,a)$‑rectangular ambiguity, yielding a coupled vector gain‑bias system and stationary saddle strategies from all initial states. The authors also characterize solvability conditions, provide certificates for asymptotically affine trajectories of the robust Bellman operator, and design a robust approximately shifted Halpern planning algorithm that converges to the optimal gain vector and produces average‑optimal greedy controllers.
arXiv:2506. 07040v4 Announce Type: replace-cross Abstract: We study model-free methods for distributionally robust infinite-horizon average-reward Markov decision processes (MDPs).
arXiv:2609.39093v1 Announce Type: new Abstract: We study infinite-horizon average-reward constrained Markov decision processes (CMDPs) under the weakly communicating assumption. Existing high-probabi...
arXiv:2602. 03778v2 Announce Type: replace-cross Abstract: Tail-end risk measures such as static conditional value-at-risk (CVaR) are used in safety-critical applications to prevent rare, yet catastrophic events.
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...
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:2607. 16858v1 Announce Type: cross Abstract: Across environments with mixed sources of uncertainty, unsupervised reinforcement learning requires intrinsic motivation that does not precommit to a particular direction of surprise.
The paper introduces a new approach to learning chance-constrained Markov decision processes (CCMDPs) using a Bellman distributional certificate. It provides both model-based and model-free algorithms with theoretical guarantees, including matching upper and lower bounds for tabular discounted CCMDPs with bounded successor support. Numerical experiments on synthetic CCMDPs and an IEEE 14-bus energy storage benchmark demonstrate the safety and effectiveness of the proposed methods.
The paper investigates model‑free robust Q‑learning with χ² uncertainty sets and linear function approximation, using data from a single trajectory of an unknown nominal MDP. It introduces a variational reformulation of the robust Bellman target and a blockwise frozen‑target scheme to overcome estimation and non‑contractivity challenges, and proves a finite‑time error bound for every discount factor γ in (0,1). A neural‑network experiment demonstrates the practical use of the variational target in a continuous‑state nonlinear‑control task.
arXiv:2511.08097v2 Announce Type: replace-cross Abstract: We consider a general infinite horizon Heterogeneous Restless multi-armed Bandit (RMAB). Heterogeneity is a fundamental problem for many real...
arXiv:2608. 07725v1 Announce Type: new Abstract: Average-reward reinforcement-learning regret is known up to logarithmic factors, but the numerical content of published guarantees is difficult to compare because probability mode, structural parameter, logarithmic normalization, prior information, and planning assumptions differ.
arXiv:2609.39837v1 Announce Type: new Abstract: Policy mirror descent (PMD) enjoys fast convergence in regularized Markov decision processes (MDPs), but existing guarantees often rely on exact or inc...
arXiv:2607. 22982v1 Announce Type: new Abstract: Natural Policy Gradient (NPG) is a well-established Reinforcement Learning algorithm that underlies widely used methods such as Trust Region Policy Optimization and Proximal Policy Optimization, both of which have demonstrated strong empirical success.