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arXiv · 2012.07199

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

Long Yang·Gang Zheng·Yu Zhang·Qian Zheng·Pengfei Li·Gang Pan
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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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Long Yang, Gang Zheng, Yu Zhang, Qian Zheng, Pengfei Li, Gang Pan. 2020-12-14. On Convergence of Gradient Expected Sarsa($\lambda$). https://arxiv.org/abs/2012.07199

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