Minimax-Optimal Multi-Agent Robust Reinforcement Learning

• URL: http://arxiv.org/abs/2412.19873v1
• Date: Fri, 27 Dec 2024 16:37:33 GMT
• Title: Minimax-Optimal Multi-Agent Robust Reinforcement Learning
• Authors: Yuchen Jiao, Gen Li,
• Abstract summary: We extend the Q-FTRL algorithm citepli2022minimax to the RMGs in finite-horizon setting, assuming access to a generative model. We prove that the proposed algorithm achieves an $varepsilon$-robust coarse correlated equilibrium (CCE) with a sample complexity (up to log factors) of $widetildeOleft(H3Ssum_i=1mA_iminleftH,1/Rright/varepsilon2right), where $S$ denotes the
• Score: 7.237817437521988
• License:
• Abstract: Multi-agent robust reinforcement learning, also known as multi-player robust Markov games (RMGs), is a crucial framework for modeling competitive interactions under environmental uncertainties, with wide applications in multi-agent systems. However, existing results on sample complexity in RMGs suffer from at least one of three obstacles: restrictive range of uncertainty level or accuracy, the curse of multiple agents, and the barrier of long horizons, all of which cause existing results to significantly exceed the information-theoretic lower bound. To close this gap, we extend the Q-FTRL algorithm \citep{li2022minimax} to the RMGs in finite-horizon setting, assuming access to a generative model. We prove that the proposed algorithm achieves an $\varepsilon$-robust coarse correlated equilibrium (CCE) with a sample complexity (up to log factors) of $\widetilde{O}\left(H^3S\sum_{i=1}^mA_i\min\left\{H,1/R\right\}/\varepsilon^2\right)$, where $S$ denotes the number of states, $A_i$ is the number of actions of the $i$-th agent, $H$ is the finite horizon length, and $R$ is uncertainty level. We also show that this sample compelxity is minimax optimal by combining an information-theoretic lower bound. Additionally, in the special case of two-player zero-sum RMGs, the algorithm achieves an $\varepsilon$-robust Nash equilibrium (NE) with the same sample complexity.

Related papers

• Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPs [56.237917407785545]
  We consider the problem of learning an $varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Key to our solution is a novel projection technique based on ideas from harmonic analysis. Our result bridges the gap between two popular but conflicting perspectives on continuous-space MDPs.
  arXiv  Detail & Related papers  (2024-05-10T09:58:47Z)
• Contextual Combinatorial Bandits with Probabilistically Triggered Arms [55.9237004478033]
  We study contextual bandits with probabilistically triggered arms (C$2$MAB-T) under a variety of smoothness conditions. Under the triggering modulated (TPM) condition, we devise the C$2$-UC-T algorithm and derive a regret bound $tildeO(dsqrtT)$.
  arXiv  Detail & Related papers  (2023-03-30T02:51:00Z)
• Bridging Distributional and Risk-sensitive Reinforcement Learning with Provable Regret Bounds [24.571530193140916]
  We consider finite episodic Markov decision processes whose objective is the entropic risk measure (EntRM) of return. We propose two novel DRL algorithms that implement optimism through two different schemes, including a model-free one and a model-based one. We prove that they both attain $tildemathcalO(fracexp(|beta| H)-1|beta|HsqrtS2AK)$ regret upper bound, where $S$, $A$, $K$, and $H$ represent the number
  arXiv  Detail & Related papers  (2022-10-25T14:30:48Z)
• Minimax-Optimal Multi-Agent RL in Zero-Sum Markov Games With a Generative Model [50.38446482252857]
  Two-player zero-sum Markov games are arguably the most basic setting in multi-agent reinforcement learning. We develop a learning algorithm that learns an $varepsilon$-approximate Markov NE policy using $$ widetildeObigg. We derive a refined regret bound for FTRL that makes explicit the role of variance-type quantities.
  arXiv  Detail & Related papers  (2022-08-22T17:24:55Z)
• Settling the Sample Complexity of Model-Based Offline Reinforcement Learning [50.5790774201146]
  offline reinforcement learning (RL) learns using pre-collected data without further exploration. Prior algorithms or analyses either suffer from suboptimal sample complexities or incur high burn-in cost to reach sample optimality. We demonstrate that the model-based (or "plug-in") approach achieves minimax-optimal sample complexity without burn-in cost.
  arXiv  Detail & Related papers  (2022-04-11T17:26:19Z)
• Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity [67.02490430380415]
  We show that model-based MARL achieves a sample complexity of $tilde O(|S||B|(gamma)-3epsilon-2)$ for finding the Nash equilibrium (NE) value up to some $epsilon$ error. We also show that such a sample bound is minimax-optimal (up to logarithmic factors) if the algorithm is reward-agnostic, where the algorithm queries state transition samples without reward knowledge.
  arXiv  Detail & Related papers  (2020-07-15T03:25:24Z)
• Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model [50.38446482252857]
  This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator) We first consider $gamma$-discounted infinite-horizon Markov decision processes (MDPs) with state space $mathcalS$ and action space $mathcalA$. We prove that a plain model-based planning algorithm suffices to achieve minimax-optimal sample complexity given any target accuracy level.
  arXiv  Detail & Related papers  (2020-05-26T17:53:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.