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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. 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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3. Federated Learning over Wireless Networks: A Band-limited Coordinated Descent Approach

   https://doi.org/10.1109/INFOCOM42981.2021.9488818  

   Zhang, Junshan ; Li, Na ; Dedeoglu, Mehmet ( May 2021 , IEEE INFOCOM 2021 - IEEE Conference on Computer Communications)

   null (Ed.)

   We consider a many-to-one wireless architecture for federated learning at the network edge, where multiple edge devices collaboratively train a model using local data. The unreliable nature of wireless connectivity, together with constraints in computing resources at edge devices, dictates that the local updates at edge devices should be carefully crafted and compressed to match the wireless communication resources available and should work in concert with the receiver. Thus motivated, we propose SGD-based bandlimited coordinate descent algorithms for such settings. Specifically, for the wireless edge employing over-the-air computing, a common subset of k-coordinates of the gradient updates across edge devices are selected by the receiver in each iteration, and then transmitted simultaneously over k sub-carriers, each experiencing time-varying channel conditions. We characterize the impact of communication error and compression, in terms of the resulting gradient bias and mean squared error, on the convergence of the proposed algorithms. We then study learning-driven communication error minimization via joint optimization of power allocation and learning rates. Our findings reveal that optimal power allocation across different sub-carriers should take into account both the gradient values and channel conditions, thus generalizing the widely used water-filling policy. We also develop sub-optimal distributed solutions amenable to implementation. 

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4. 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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5. Distributed Q-Learning with State Tracking for Multi-agent Networked Control

   Wang, Hang ; Lin, Sen ; Jafarkhani, Hamid ; Zhang, Junshan ( May 2021 , AAMAS '21: Proceedings of the 20th International Conference on Autonomous Agents and MultiAgent SystemsMay 2021)

   This paper studies distributed Q-learning for Linear Quadratic Regulator (LQR) in a multi-agent network. The existing results often assume that agents can observe the global system state, which may be infeasible in large-scale systems due to privacy concerns or communication constraints. In this work, we consider a setting with unknown system models and no centralized coordinator. We devise a state tracking (ST) based Q-learning algorithm to design optimal controllers for agents. Specifically, we assume that agents maintain local estimates of the global state based on their local information and communications with neighbors. At each step, every agent updates its local global state estimation, based on which it solves an approximate Q-factor locally through policy iteration. Assuming a decaying injected excitation noise during the policy evaluation, we prove that the local estimation converges to the true global state, and establish the convergence of the proposed distributed ST-based Q-learning algorithm. The experimental studies corroborate our theoretical results by showing that our proposed method achieves comparable performance with the centralized case. 

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