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