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1. 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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2. Federated Reinforcement Learning: Linear Speedup Under Markovian Sampling

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

   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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3. 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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4. Momentum for the Win: Collaborative Federated Reinforcement Learning across Heterogeneous Environments

   Wang, Han; He, Shone; Zhang, Zhili; Miao, Fei; Anderson, James (May 2024, Proceedings of Machine Learning Research)

   We explore a Federated Reinforcement Learning (FRL) problem where agents collaboratively learn a common policy without sharing their trajectory data. To date, existing FRL work has primarily focused on agents operating in the same or ``similar" environments. In contrast, our problem setup allows for arbitrarily large levels of environment heterogeneity. To obtain the optimal policy which maximizes the average performance across all potentially completely different environments, we propose two algorithms: FedSVRPG-M and FedHAPG-M. In contrast to existing results, we demonstrate that both FedSVRPG-M and FedHAPG-M, both of which leverage momentum mechanisms, can exactly converge to a stationary point of the average performance function, regardless of the magnitude of environment heterogeneity. Furthermore, by incorporating the benefits of variance-reduction techniques or Hessian approximation, both algorithms achieve state-of-the-art convergence results, characterized by a sample complexity of $$O(\epsilon^{-\frac{3}{2}}/N)$$. Notably, our algorithms enjoy linear convergence speedups with respect to the number of agents, highlighting the benefit of collaboration among agents in finding a common policy. 

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5. Model-free Learning with Heterogeneous Dynamical Systems: A Federated LQR Approach

   Wang, H.; Toso, L.F.; Mitra, A.; Anderson, J (August 2023, arXivorg)

   We study a model-free federated linear quadratic regulator (LQR) problem where M agents with unknown, distinct yet similar dynamics collaboratively learn an optimal policy to minimize an average quadratic cost while keeping their data private. To exploit the similarity of the agents' dynamics, we propose to use federated learning (FL) to allow the agents to periodically communicate with a central server to train policies by leveraging a larger dataset from all the agents. With this setup, we seek to understand the following questions: (i) Is the learned common policy stabilizing for all agents? (ii) How close is the learned common policy to each agent's own optimal policy? (iii) Can each agent learn its own optimal policy faster by leveraging data from all agents? To answer these questions, we propose a federated and model-free algorithm named FedLQR. Our analysis overcomes numerous technical challenges, such as heterogeneity in the agents' dynamics, multiple local updates, and stability concerns. We show that FedLQR produces a common policy that, at each iteration, is stabilizing for all agents. We provide bounds on the distance between the common policy and each agent's local optimal policy. Furthermore, we prove that when learning each agent's optimal policy, FedLQR achieves a sample complexity reduction proportional to the number of agents M in a low-heterogeneity regime, compared to the single-agent setting. 

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