On Convergence of Gradient Expected Sarsa($\lambda$)

• URL: http://arxiv.org/abs/2012.07199v1
• Date: Mon, 14 Dec 2020 01:27:24 GMT
• Title: On Convergence of Gradient Expected Sarsa($\lambda$)
• Authors: Long Yang, Gang Zheng, Yu Zhang, Qian Zheng, Pengfei Li, Gang Pan
• Abstract summary: We show that applying the off-line estimate (multi-step bootstrapping) to $mathttExpectedSarsa(lambda)$ is unstable for off-policy learning. We propose a convergent $mathttGradientExpectedSarsa(lambda)$ ($mathttGES(lambda)$) algorithm.
• Score: 25.983112169543375
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the convergence of $\mathtt{Expected~Sarsa}(\lambda)$ with linear function approximation. We show that applying the off-line estimate (multi-step bootstrapping) to $\mathtt{Expected~Sarsa}(\lambda)$ is unstable for off-policy learning. Furthermore, based on convex-concave saddle-point framework, we propose a convergent $\mathtt{Gradient~Expected~Sarsa}(\lambda)$ ($\mathtt{GES}(\lambda)$) algorithm. The theoretical analysis shows that our $\mathtt{GES}(\lambda)$ converges to the optimal solution at a linear convergence rate, which is comparable to extensive existing state-of-the-art gradient temporal difference learning algorithms. Furthermore, we develop a Lyapunov function technique to investigate how the step-size influences finite-time performance of $\mathtt{GES}(\lambda)$, such technique of Lyapunov function can be potentially generalized to other GTD algorithms. Finally, we conduct experiments to verify the effectiveness of our $\mathtt{GES}(\lambda)$.

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