The paper presents linear programming formulations and strongly polynomial algorithms for robust Markov decision processes (RMDPs) with rational polyhedral state-action rectangular uncertainty in rewards and transitions. By encoding a finite sequence of robust policy-iteration steps, a single LP is constructed whose optimal solutions recover the robust optimal value and all optimal stationary randomized policies. The authors provide a general complexity analysis of robust policy iteration, improving known bounds for α1 and α1∞ RMDPs and establishing new strongly polynomial bounds for general interval, weighted α1, and Wasserstein RMDPs, as well as turn‑based stochastic games with these uncertainty sets.
By Han Zhong, Yinyu Ye
Robust Markov Decision Processes (RMDPs) generalize classical MDPs by allowing uncertainty in transition probabilities and optimizing against their worst-case realization. We consider $(s,a)$-rectangu...
arXiv:2608.24986v2 Announce Type: replace
Abstract: Robust POMDPs (RPOMDPs) generalize classical POMDPs to the setting where exact transition probabilities are not known -- rather, they are only know...
By Durgam Latha, Dion Reji, S. Akshay, {\DJ}or{\dj}e \v{Z}ikeli\'c, Shankaranarayanan Krishna
The paper presents an exponential lower bound on the number of iterations required by Howard's policy iteration algorithm for deterministic discounted Markov decision processes with at most two actions per state, when the discount factor is part of the input. This result shows that Howard's method cannot be strongly polynomial in this setting and establishes an exponential gap compared to the simplex method with Dantzig's pivoting rule, which remains strongly polynomial. Even with rewards limited to logarithmic bit length, a stretched‑exponential lower bound is achieved, highlighting a fundamental difference between decentralized, simultaneous improvements and Dantzig's coordinated single‑action selection.
By Han Zhong, Yinyu Ye
Sequential decision-making in real-world applications often involves uncertainty about the environment's model. Uncertain Markov decision processes (UMDPs) represent the possible environments as a set of MDPs with shared states and actions but potentially different transition probabilities and rewards.
arXiv:2608. 02509v1 Announce Type: cross Abstract: Sequential decision-making in real-world applications often involves uncertainty about the environment's model.
By Sterre Lutz, Dani\"el Vos, Matthijs T. J. Spaan, Anna Lukina
The paper investigates adaptive policy portfolios for Robust Markov Decision Processes (RMDPs), proposing finite sets of memoryless randomized policies generated offline and selected online. It introduces robust regret as a metric for portfolio quality, comparing each portfolio member’s performance to the optimal policy for each plausible environment. The authors provide complexity-theoretic results showing that certifying and synthesizing such portfolios is highly intractable, and they present an offline construction method that can be specialized at runtime.
The paper introduces adaptive policy portfolios for robust Markov decision processes, where a finite set of memoryless randomized policies is synthesized offline and paired with an online selector. It defines robust regret as a measure of portfolio quality, comparing each portfolio member to the optimal policy for each plausible environment. The authors provide a complexity-theoretic analysis of portfolio certification and synthesis, showing that even deterministic portfolios in simple settings are highly complex, and present an offline construction method that can be specialized at runtime.
By Kasper Engelen, Sebastian Junges, Guillermo A. P\'{e}rez, Marnix Suilen
The paper investigates reinforcement learning with multi‑step transition look‑ahead, where an agent can foresee the states resulting from any sequence of λ actions before choosing its next move. It proves that exact planning remains NP‑hard for every fixed rational discount factor γ in (0,1), and introduces a randomized polynomial‑time approximation scheme that works for any fixed look‑ahead depth. Extending this to unknown transitions and stochastic rewards, the authors develop an algorithm with cumulative regret matching classical tabular discounted RL up to logarithmic factors, showing that efficient near‑optimal planning and learning are achievable despite the NP‑hardness of exact planning.
By Corentin Pla, Hugo Richard, Marc Abeille, Vianney Perchet
arXiv:2606. 14095v1 Announce Type: new Abstract: We study the sample complexity of learning in average-reward weakly-coupled Markov decision processes (WCMDPs) and Restless Bandits (RBs) under a generative model.
By Tianhao Wu, Matthew Zurek, Weina Wang, Qiaomin Xie
The paper presents the first PAC learning framework for general-sum concurrent stochastic games with uncertain transitions, addressing the challenge of Nash equilibrium existence. It introduces data‑driven L¹ confidence sets over transition kernels and a robust CSG solver that computes a social‑welfare optimal ε‑NE, or provides a certificate that no exact NE exists. The algorithm achieves polynomial sample complexity under a minimum reachability condition and is validated on benchmark CSGs with near‑optimal performance.
By Angel Y. He, David Parker
We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a robust CSG to compute a social-welfare optimal $\varepsilon$-NE, using a robust MDP-based exploration mechanism to drive joint state-action coverage.