## On the Sample Complexity of Learning Infinite-horizon Discounted Linear Kernel MDPs

### Yuanzhou Chen · Jiafan He · Quanquan Gu

##### Hall E #807

Keywords: [ RL: Online ] [ RL: Function Approximation ] [ RL: Discounted Cost/Reward ]

[ Abstract ]
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Wed 20 Jul 3:30 p.m. PDT — 5:30 p.m. PDT

Spotlight presentation: Reinforcement Learning
Wed 20 Jul 10:15 a.m. PDT — 11:45 a.m. PDT

Abstract: We study reinforcement learning for infinite-horizon discounted linear kernel MDPs, where the transition probability function is linear in a predefined feature mapping. Existing UCLK \citep{zhou2020provably} algorithm for this setting only has a regret guarantee, which cannot lead to a tight sample complexity bound. In this paper, we extend the uniform-PAC sample complexity from episodic setting to the infinite-horizon discounted setting, and propose a novel algorithm dubbed UPAC-UCLK that achieves an $\Tilde{O}\big(d^2/((1-\gamma)^4\epsilon^2)+1/((1-\gamma)^6\epsilon^2)\big)$ uniform-PAC sample complexity, where $d$ is the dimension of the feature mapping, $\gamma \in(0,1)$ is the discount factor of the MDP and $\epsilon$ is the accuracy parameter. To the best of our knowledge, this is the first $\tilde{O}(1/\epsilon^2)$ sample complexity bound for learning infinite-horizon discounted MDPs with linear function approximation (without access to the generative model).

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