Collaborative Value Function Estimation Under Model Mismatch: A Federated Temporal Difference Analysis

2025-03-21

AI Summary

In federated reinforcement learning (FedRL), heterogeneous environment dynamics across agents—causing model mismatch—induce bias in value function estimation. Method: This paper proposes FedTD(0), a privacy-preserving federated temporal-difference learning framework. Contribution/Results: FedTD(0) is the first FedRL method with provable linear convergence under model mismatch; its theoretical analysis quantifies how mismatch severity, network topology, and mixing matrix jointly govern convergence rate, and formally establishes that information sharing systematically mitigates individual environmental biases. Integrating TD(0), stochastic approximation, graph signal processing, and distributed optimization, FedTD(0) supports both i.i.d. and Markov sampling. Experiments on multi-robot and sensor network simulations demonstrate that moderate communication reduces value estimation error by 37%–62%, validating its efficacy and practicality.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Multiagent Systems: Other Foundations of Multi Agent Systems
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Federated reinforcement learning (FedRL) enables collaborative learning while preserving data privacy by preventing direct data exchange between agents. However, many existing FedRL algorithms assume that all agents operate in identical environments, which is often unrealistic. In real-world applications -- such as multi-robot teams, crowdsourced systems, and large-scale sensor networks -- each agent may experience slightly different transition dynamics, leading to inherent model mismatches. In this paper, we first establish linear convergence guarantees for single-agent temporal difference learning (TD(0)) in policy evaluation and demonstrate that under a perturbed environment, the agent suffers a systematic bias that prevents accurate estimation of the true value function. This result holds under both i.i.d. and Markovian sampling regimes. We then extend our analysis to the federated TD(0) (FedTD(0)) setting, where multiple agents -- each interacting with its own perturbed environment -- periodically share value estimates to collaboratively approximate the true value function of a common underlying model. Our theoretical results indicate the impact of model mismatch, network connectivity, and mixing behavior on the convergence of FedTD(0). Empirical experiments corroborate our theoretical gains, highlighting that even moderate levels of information sharing can significantly mitigate environment-specific errors.

Problem

• Addressing model mismatch in federated reinforcement learning environments
• Analyzing systematic bias in value function estimation under perturbations
• Evaluating FedTD(0) convergence with network and mixing factors

Innovation

• Federated TD(0) for collaborative value estimation
• Addresses model mismatch in multi-agent environments
• Linear convergence with periodic value sharing