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1. Federated Reinforcement Learning: Linear Speedup Under Markovian Sampling

   Khodadadian, Sajad; Sharma, Pranay; Joshi, Gauri; Maguluri Siva Theja (July 2022, International Conference on Machine Learning (ICML))

   Since reinforcement learning algorithms are notoriously data-intensive, the task of sampling observations from the environment is usually split across multiple agents. However, transferring these observations from the agents to a central location can be prohibitively expensive in terms of the communication cost, and it can also compromise the privacy of each agent’s local behavior policy. In this paper, we consider a federated reinforcement learning framework where multiple agents collaboratively learn a global model, without sharing their individual data and policies. Each agent maintains a local copy of the model and updates it using locally sampled data. Although having N agents enables the sampling of N times more data, it is not clear if it leads to proportional convergence speedup. We propose federated versions of on-policy TD, off-policy TD and Q-learning, and analyze their convergence. For all these algorithms, to the best of our knowledge, we are the first to consider Markovian noise and multiple local updates, and prove a linear convergence speedup with respect to the number of agents. To obtain these results, we show that federated TD and Q-learning are special cases of a general framework for federated stochastic approximation with Markovian noise, and we leverage this framework to provide a unified convergence analysis that applies to all the algorithms. 

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2. On the Linear Speedup of Personalized Federated Reinforcement Learning with Shared Representations

   Xiong, Guojun; Wang, Shufan; Jiang, Daniel; Li, Jian (April 2025, The Thirteenth International Conference on Learning Representations (ICLR 2025))

   Federated reinforcement learning (FedRL) enables multiple agents to collaboratively learn a policy without needing to share the local trajectories collected during agent-environment interactions. However, in practice, the environments faced by different agents are often heterogeneous, but since existing FedRL algorithms learn a single policy across all agents, this may lead to poor performance. In this paper, we introduce a \emph{personalized} FedRL framework (PFedRL) by taking advantage of possibly shared common structure among agents in heterogeneous environments. Specifically, we develop a class of PFedRL algorithms named PFedRL-Rep that learns (1) a shared feature representation collaboratively among all agents, and (2) an agent-specific weight vector personalized to its local environment. We analyze the convergence of PFedTD-Rep, a particular instance of the framework with temporal difference (TD) learning and linear representations. To the best of our knowledge, we are the first to prove a linear convergence speedup with respect to the number of agents in the PFedRL setting. To achieve this, we show that PFedTD-Rep is an example of federated two-timescale stochastic approximation with Markovian noise. Experimental results demonstrate that PFedTD-Rep, along with an extension to the control setting based on deep Q-networks (DQN), not only improve learning in heterogeneous settings, but also provide better generalization to new environments. 

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3. Federated Temporal Difference Learning with Linear Function Approximation Under Environmental Heterogeneity

   Wang, H.; Mitra, A.; Hassani, H; Pappas, G.; Anderson, J (February 2023, arXivorg)

   We initiate the study of federated reinforcement learning under environmental heterogeneity by considering a policy evaluation problem. Our setup involves agents interacting with environments that share the same state and action space but differ in their reward functions and state transition kernels. Assuming agents can communicate via a central server, we ask: Does exchanging information expedite the process of evaluating a common policy? To answer this question, we provide the first comprehensive finite-time analysis of a federated temporal difference (TD) learning algorithm with linear function approximation, while accounting for Markovian sampling, heterogeneity in the agents' environments, and multiple local updates to save communication. Our analysis crucially relies on several novel ingredients: (i) deriving perturbation bounds on TD fixed points as a function of the heterogeneity in the agents' underlying Markov decision processes (MDPs); (ii) introducing a virtual MDP to closely approximate the dynamics of the federated TD algorithm; and (iii) using the virtual MDP to make explicit connections to federated optimization. Putting these pieces together, we rigorously prove that in a low-heterogeneity regime, exchanging model estimates leads to linear convergence speedups in the number of agents. 

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4. Single-Loop Federated Actor-Critic across Heterogeneous Environments

   https://doi.org/10.1609/aaai.v39i21.34469  

   Zhu, Ye; Gong, Xiaowen (April 2025, Proceedings of the AAAI Conference on Artificial Intelligence)

   Federated reinforcement learning (FRL) has emerged as a promising paradigm, enabling multiple agents to collaborate and learn a shared policy adaptable across heterogeneous environments. Among the various reinforcement learning (RL) algorithms, the actor-critic (AC) algorithm stands out for its low variance and high sample efficiency. However, little to nothing is known theoretically about AC in a federated manner, especially each agent interacts with a potentially different environment. The lack of such results is attributed to various technical challenges: a two-level structure illustrating the coupling effect between the actor and the critic, heterogeneous environments, Markovian sampling and multiple local updates. In response, we study Single-Loop Federated Actor Critic (SFAC) where agents perform AC learning in a two-level federated manner while interacting with heterogeneous environments. We then provide bounds on the convergence error of SFAC. The results show that the convergence error asymptotically converges to a near-stationary point, with the extent proportional to environment heterogeneity. Moreover, the sample complexity exhibits a linear speed-up through the federation of agents. We evaluate the performance of SFAC through numerical experiments using common RL benchmarks, which demonstrate its effectiveness. 

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5. Finite-Time Analysis of On-Policy Heterogeneous Federated Reinforcement Learning

   Zhanh, Chenyu; Wang, Han; Mitra, Aritra; Anderson, James (January 2024, The Twelfth International Conference on Learning Representations (ICLR))

   Federated reinforcement learning (FRL) has emerged as a promising paradigm for reducing the sample complexity of reinforcement learning tasks by exploiting information from different agents. However, when each agent interacts with a po- tentially different environment, little to nothing is known theoretically about the non-asymptotic performance of FRL algorithms. The lack of such results can be attributed to various technical challenges and their intricate interplay: Markovian sampling, linear function approximation, multiple local updates to save communi- cation, heterogeneity in the reward functions and transition kernels of the agents’ MDPs, and continuous state-action spaces. Moreover, in the on-policy setting, the behavior policies vary with time, further complicating the analysis. In response, we introduce FedSARSA, a novel federated on-policy reinforcement learning scheme, equipped with linear function approximation, to address these challenges and provide a comprehensive finite-time error analysis. Notably, we establish that FedSARSA converges to a policy that is near-optimal for all agents, with the ex- tent of near-optimality proportional to the level of heterogeneity. Furthermore, we prove that FedSARSA leverages agent collaboration to enable linear speedups as the number of agents increases, which holds for both fixed and adaptive step-size configurations. 

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