Finite-Time Analysis of Federated On-Policy Reinforcement Learning with Heterogeneous Environments

핵심 개념
Federated reinforcement learning (FRL) can expedite the process of learning near-optimal policies for agents operating in heterogeneous environments by leveraging collaborative information from other agents.
This paper introduces FedSARSA, a novel federated on-policy reinforcement learning algorithm that integrates the classic SARSA algorithm with a federated learning framework. The key contributions are: Heterogeneity in FRL Optimal Policies: The paper formulates an FRL planning problem where agents operate in heterogeneous environments, leading to heterogeneity in their optimal policies. It provides an explicit bound on this heterogeneity, validating the benefits of collaboration. Finite-Time Error Analysis of FedSARSA: The paper establishes a finite-time error bound for FedSARSA, achieving state-of-the-art sample complexity. This is the first provably sample-efficient on-policy algorithm for FRL problems. Convergence Region and Linear Speedups: The paper shows that FedSARSA exponentially converges to a small region containing agents' optimal policies, whose radius tightens as the number of agents grows. For a linearly decaying step-size, the learning process enjoys linear speedups through federated collaboration. The analysis tackles several key challenges, including time-varying behavior policies, environmental heterogeneity, multiple local updates, and continuous state-action spaces with linear function approximation. The theoretical findings are validated through numerical simulations.

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by Chenyu Zhang... 위치 04-16-2024
Finite-Time Analysis of On-Policy Heterogeneous Federated Reinforcement  Learning

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To extend the FedSARSA algorithm to handle more complex reward and transition dynamics, such as partial observability or non-Markovian environments, several modifications and enhancements can be implemented: Partial Observability: Introduce techniques like Partially Observable Markov Decision Processes (POMDPs) to model environments where agents have incomplete information. Incorporate belief states or memory elements in the state representation to account for partial observability. Modify the Q-value function to handle belief states and update the policy accordingly. Non-Markovian Environments: Extend the state representation to include historical information or context to capture non-Markovian dynamics. Utilize memory or recurrent neural networks to capture temporal dependencies in the environment. Adjust the update rules to account for the non-Markovian nature of the environment, possibly by incorporating memory elements in the learning process. Advanced Function Approximation: Use more sophisticated function approximation techniques like deep neural networks to handle complex reward and transition dynamics. Implement techniques like Dueling DQN or distributional RL to capture uncertainty and variability in the environment. Explore ensemble methods or meta-learning approaches to adapt to varying dynamics across agents. By incorporating these enhancements, FedSARSA can be adapted to address a wider range of environments with complex reward and transition dynamics.


The linear function approximation used in this work may have certain limitations, including: Limited Expressiveness: Linear approximations may struggle to capture complex, nonlinear relationships between states and actions, leading to suboptimal performance in environments with intricate dynamics. Curse of Dimensionality: In high-dimensional state spaces, linear approximations may require a large number of features to adequately represent the value function, leading to increased computational complexity. Stability Concerns: Linear function approximation can be prone to issues like overfitting or underfitting, especially in the presence of noise or heterogeneity in the data. To generalize the analysis to other function approximation schemes, one could: Consider non-linear function approximators like neural networks or kernel methods to capture more complex relationships. Incorporate regularization techniques to prevent overfitting and improve generalization. Explore ensemble methods or hybrid approaches combining linear and non-linear approximators for improved performance and stability. By extending the analysis to diverse function approximation schemes, the algorithm's robustness and applicability to a wider range of environments can be enhanced.


The ideas behind FedSARSA can indeed be applied to other on-policy RL algorithms, such as actor-critic methods, to achieve similar theoretical guarantees in federated settings. Here's how: Actor-Critic Adaptation: Modify the actor-critic architecture to incorporate federated learning principles, where the actor represents the policy and the critic evaluates the policy's performance. Implement communication strategies between actors and critics to exchange information and collaborate in a federated manner. Update the policy and value functions using local observations and federated aggregation to achieve convergence to near-optimal solutions. Theoretical Guarantees: Extend the finite-time analysis to actor-critic algorithms in federated settings to provide formal convergence guarantees and performance bounds. Consider the impact of environmental heterogeneity, communication constraints, and non-stationarity on the convergence properties of actor-critic methods in federated reinforcement learning. By applying the principles of federated learning to actor-critic algorithms and conducting a rigorous theoretical analysis, similar guarantees to those achieved by FedSARSA can be established in the context of other on-policy RL algorithms.