Learning Stochastic Shortest Path with Linear Function Approximation

• URL: http://arxiv.org/abs/2110.12727v1
• Date: Mon, 25 Oct 2021 08:34:00 GMT
• Title: Learning Stochastic Shortest Path with Linear Function Approximation
• Authors: Yifei Min and Jiafan He and Tianhao Wang and Quanquan Gu
• Abstract summary: We study the shortest path (SSP) problem in reinforcement learning with linear function approximation, where the transition kernel is represented as a linear mixture of unknown models. We propose a novel algorithm for learning the linear mixture SSP, which can attain a $tilde O(d B_star1.5sqrtK/c_min)$ regret.
• Score: 74.08819218747341
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the stochastic shortest path (SSP) problem in reinforcement learning with linear function approximation, where the transition kernel is represented as a linear mixture of unknown models. We call this class of SSP problems the linear mixture SSP. We propose a novel algorithm for learning the linear mixture SSP, which can attain a $\tilde O(d B_{\star}^{1.5}\sqrt{K/c_{\min}})$ regret. Here $K$ is the number of episodes, $d$ is the dimension of the feature mapping in the mixture model, $B_{\star}$ bounds the expected cumulative cost of the optimal policy, and $c_{\min}>0$ is the lower bound of the cost function. Our algorithm also applies to the case when $c_{\min} = 0$, where a $\tilde O(K^{2/3})$ regret is guaranteed. To the best of our knowledge, this is the first algorithm with a sublinear regret guarantee for learning linear mixture SSP. In complement to the regret upper bounds, we also prove a lower bound of $\Omega(d B_{\star} \sqrt{K})$, which nearly matches our upper bound.

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