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1. 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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2. 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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3. 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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4. The Blessing of Heterogeneity in Federated Q-Learning: Linear Speedup and Beyond

   Woo, Jiin ; Joshi, Gauri ; Chi, Yuejie ( July 2023 , International Conference on Machine Learning (ICML))

   In this paper, we consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. Focusing on infinite-horizon tabular Markov decision processes, we provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning. In both cases, our bounds exhibit a linear speedup with respect to the number of agents and sharper dependencies on other salient problem parameters. Moreover, existing approaches to federated Q-learning adopt an equally-weighted averaging of local Q-estimates, which can be highly sub-optimal in the asynchronous setting since the local trajectories can be highly heterogeneous due to different local behavior policies. Existing sample complexity scales inverse proportionally to the minimum entry of the stationary state-action occupancy distributions over all agents, requiring that every agent covers the entire state-action space. Instead, we propose a novel importance averaging algorithm, giving larger weights to more frequently visited state-action pairs. The improved sample complexity scales inverse proportionally to the minimum entry of the average stationary state-action occupancy distribution of all agents, thus only requiring the agents collectively cover the entire state-action space, unveiling the blessing of heterogeneity. 

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5. Decentralized graph-based multi-agent reinforcement learning using reward machines

   https://doi.org/10.1016/j.neucom.2023.126974  

   Hu, Jueming ; Xu, Zhe ; Wang, Weichang ; Qu, Guannan ; Pang, Yutian ; Liu, Yongming ( January 2024 , Neurocomputing)

   In multi-agent reinforcement learning (MARL), it is challenging for a collection of agents to learn complex temporally extended tasks. The difficulties lie in computational complexity and how to learn the high-level ideas behind reward functions. We study the graph-based Markov Decision Process (MDP), where the dynamics of neighboring agents are coupled. To learn complex temporally extended tasks, we use a reward machine (RM) to encode each agent’s task and expose reward function internal structures. RM has the capacity to describe high-level knowledge and encode non-Markovian reward functions. We propose a decentralized learning algorithm to tackle computational complexity, called decentralized graph-based reinforcement learning using reward machines (DGRM), that equips each agent with a localized policy, allowing agents to make decisions independently based on the information available to the agents. DGRM uses the actor-critic structure, and we introduce the tabular Q-function for discrete state problems. We show that the dependency of the Q-function on other agents decreases exponentially as the distance between them increases. To further improve efficiency, we also propose the deep DGRM algorithm, using deep neural networks to approximate the Q-function and policy function to solve large-scale or continuous state problems. The effectiveness of the proposed DGRM algorithm is evaluated by three case studies, two wireless communication case studies with independent and dependent reward functions, respectively, and COVID-19 pandemic mitigation. Experimental results show that local information is sufficient for DGRM and agents can accomplish complex tasks with the help of RM. DGRM improves the global accumulated reward by 119% compared to the baseline in the case of COVID-19 pandemic mitigation. 

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