[Paper Review] Finite-Sample Analysis For Decentralized Batch Multi-Agent Reinforcement Learning With Networked Agents

Kaiqing Zhang, Zhuoran Yang+3 more|arXiv (Cornell University)|Dec 6, 2018

Distributed Control Multi-Agent Systems69 references4 citations

TL;DR

This paper presents the first finite-sample analysis for decentralized batch multi-agent reinforcement learning (MARL) in cooperative and competitive settings with time-varying communication networks. It proposes decentralized fitted Q-iteration algorithms using distributed optimization (e.g., DIGing), and establishes error bounds that quantify the impact of function class, sample size, and computation iterations on statistical accuracy, with additional error terms due to decentralized computation.

ABSTRACT

Despite the increasing interest in multi-agent reinforcement learning (MARL) in multiple communities, understanding its theoretical foundation has long been recognized as a challenging problem. In this work, we address this problem by providing a finite-sample analysis for decentralized batch MARL with networked agents. Specifically, we consider two decentralized MARL settings, where teams of agents are connected by time-varying communication networks, and either collaborate or compete in a zero-sum game setting, without any central controller. These settings cover many conventional MARL settings in the literature. For both settings, we develop batch MARL algorithms that can be implemented in a decentralized fashion, and quantify the finite-sample errors of the estimated action-value functions. Our error analysis captures how the function class, the number of samples within each iteration, and the number of iterations determine the statistical accuracy of the proposed algorithms. Our results, compared to the finite-sample bounds for single-agent RL, involve additional error terms caused by decentralized computation, which is inherent in our decentralized MARL setting. This work appears to be the first finite-sample analysis for batch MARL, a step towards rigorous theoretical understanding of general MARL algorithms in the finite-sample regime.

Motivation & Objective

• Address the lack of finite-sample theoretical guarantees in multi-agent reinforcement learning (MARL), especially in decentralized settings without central coordination.
• Provide a rigorous finite-sample error analysis for batch MARL algorithms in both cooperative and competitive (zero-sum) settings with time-varying communication networks.
• Characterize how function class complexity, number of samples per iteration, and number of iterations affect the statistical accuracy of decentralized MARL algorithms.
• Establish performance bounds that isolate and quantify decentralized computation errors, which are inherent in decentralized MARL but absent in single-agent or centralized settings.
• Bridge the gap between empirical MARL advances and theoretical understanding by offering non-asymptotic, finite-sample convergence guarantees for batch MARL with linear function approximation.

Proposed method

• Propose decentralized fitted Q-iteration algorithms for both cooperative and competitive MARL settings, where agents operate without a central controller and communicate via time-varying networks.
• Use the DIGing algorithm (a decentralized gradient descent method) to solve the value function fitting problem in each iteration, enabling distributed computation across agents.
• Introduce a batch learning framework using a single trajectory of data, allowing off-policy evaluation and handling large state-action spaces via function approximation.
• Apply statistical learning theory tools to bound the estimation error of the action-value function after a finite number of iterations and samples.
• Derive finite-sample error bounds that decompose into three components: estimation error (from data), decentralized computation error (from networked agents), and approximation error (from function class).
• For linear function approximation, derive explicit bounds on the error in terms of the feature dimension, number of samples, and number of inner-loop iterations in the decentralized computation.

Experimental results

Research questions

• RQ1 How does the finite-sample performance of decentralized batch MARL depend on the number of samples, function class complexity, and number of iterations?
• RQ2 What is the role of decentralized computation in introducing additional error terms beyond standard single-agent RL bounds?
• RQ3 Can finite-sample convergence guarantees be established for cooperative MARL with heterogeneous rewards and no central controller?
• RQ4 How does the performance of the algorithm scale with the dimension of the function class (e.g., feature dimension) in the linear approximation setting?
• RQ5 To what extent can the decentralized computation error be reduced by increasing the number of inner-loop iterations in the distributed optimization procedure?

Key findings

• The proposed batch MARL algorithms achieve finite-sample convergence with error bounds that include estimation, decentralized computation, and approximation error terms.
• The estimation error decreases with more samples (larger T), as shown by the convergence of the outer loop in simulations for increasing T.
• The decentralized computation error decreases with more inner-loop iterations (L), but diminishes significantly after L ≈ 100, indicating diminishing returns beyond a certain threshold.
• Larger feature dimension (d) leads to smaller approximation error, as richer function classes better represent the true value function, corroborated by improved performance in simulations.
• Even with relatively small L (e.g., L=10), the algorithm still converges, indicating robustness to initial decentralized computation errors.
• The theoretical bounds are the first of their kind for batch MARL, providing a foundational step toward understanding the statistical efficiency of decentralized MARL algorithms.