The paper addresses the exponential complexity of Decentralised Partially Observable Markov Decision Processes (DecPOMDPs) by shifting focus from counting agents to counting policies. By exploiting symmetry among agents, it introduces a compact encoding that reduces model complexity and evaluation cost to polynomial dependence. The authors further develop a policy‑counted dynamic programming algorithm that efficiently solves these policy‑counted DecPOMDPs.
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
arXiv:2403. 19883v2 Announce Type: replace Abstract: Fully-observable non-deterministic (FOND) planning is at the core of artificial intelligence planning with uncertainty.
By Frederico Messa, Andr\'e Grahl Pereira
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.
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...
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
arXiv:2511. 19849v2 Announce Type: replace-cross Abstract: Recurrence objectives, where a target region must be visited infinitely often, are a fundamental class of specifications for Markov decision processes (MDPs) and form the core of $\omega$-regular and linear temporal logic (LTL) objectives.
By Dominik Wagner, Leon Witzman, Luke Ong
arXiv:2609.00504v1 Announce Type: cross
Abstract: In this work, we study radically uncoupled learning in discounted general-sum Markov games. Assuming ``$\mathsf{ETH}$ for $\mathsf{PPAD}$", we show t...
By Asrin Efe Yorulmaz, Ugur Aydin, Tamer Basar
arXiv:2601. 23229v2 Announce Type: replace Abstract: Markov decision processes (MDPs) are a fundamental model in sequential decision making.
By Ali Asadi, Krishnendu Chatterjee, Ehsan Goharshady, Mehrdad Karrabi, Alipasha Montaseri, Carlo Pagano
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.
By Philip Jordan, Maryam Kamgarpour
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
The paper develops a geometric theory of decision boundaries for structured Markov Decision Processes, treating the geometry induced by optimal policies as the key analytical object. It shows that, under structural regularity, this geometry yields the minimal representation needed for policy reconstruction and dictates the statistical and computational complexity of the reconstruction problem. The authors introduce intrinsic notions of boundary and decision complexity, derive information-theoretic measures of decision compression, and provide statistical guarantees for boundary estimation and policy reconstruction from black-box queries, supported by controlled numerical experiments.
By Fredy Pokou (MRE, INOCS)