Sample-Efficient Reinforcement Learning for Linearly-Parameterized MDPs with a Generative Model

• URL: http://arxiv.org/abs/2105.14016v1
• Date: Fri, 28 May 2021 17:49:39 GMT
• Title: Sample-Efficient Reinforcement Learning for Linearly-Parameterized MDPs with a Generative Model
• Authors: Bingyan Wang, Yuling Yan, Jianqing Fan
• Abstract summary: This paper considers a Markov decision process (MDP) that admits a set of state-action features. We show that a model-based approach (resp.$$Q-learning) provably learns an $varepsilon$-optimal policy with high probability.
• Score: 3.749193647980305
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a nearly optimal policy with sampling access to a generative model, the minimax optimal sample complexity scales linearly with $|\mathcal{S}|\times|\mathcal{A}|$, which can be prohibitively large when $\mathcal{S}$ or $\mathcal{A}$ is large. This paper considers a Markov decision process (MDP) that admits a set of state-action features, which can linearly express (or approximate) its probability transition kernel. We show that a model-based approach (resp.$~$Q-learning) provably learns an $\varepsilon$-optimal policy (resp.$~$Q-function) with high probability as soon as the sample size exceeds the order of $\frac{K}{(1-\gamma)^{3}\varepsilon^{2}}$ (resp.$~$$\frac{K}{(1-\gamma)^{4}\varepsilon^{2}}$), up to some logarithmic factor. Here $K$ is the feature dimension and $\gamma\in(0,1)$ is the discount factor of the MDP. Both sample complexity bounds are provably tight, and our result for the model-based approach matches the minimax lower bound. Our results show that for arbitrarily large-scale MDP, both the model-based approach and Q-learning are sample-efficient when $K$ is relatively small, and hence the title of this paper.

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