Minimax-Optimal Reward-Agnostic Exploration in Reinforcement Learning
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913358713716736 |
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| author | Li, Gen Yan, Yuling Chen, Yuxin Fan, Jianqing |
| author_facet | Li, Gen Yan, Yuling Chen, Yuxin Fan, Jianqing |
| contents | This paper studies reward-agnostic exploration in reinforcement learning (RL) -- a scenario where the learner is unware of the reward functions during the exploration stage -- and designs an algorithm that improves over the state of the art. More precisely, consider a finite-horizon inhomogeneous Markov decision process with $S$ states, $A$ actions, and horizon length $H$, and suppose that there are no more than a polynomial number of given reward functions of interest. By collecting an order of \begin{align*}
\frac{SAH^3}{\varepsilon^2} \text{ sample episodes (up to log factor)} \end{align*} without guidance of the reward information, our algorithm is able to find $\varepsilon$-optimal policies for all these reward functions, provided that $\varepsilon$ is sufficiently small. This forms the first reward-agnostic exploration scheme in this context that achieves provable minimax optimality. Furthermore, once the sample size exceeds $\frac{S^2AH^3}{\varepsilon^2}$ episodes (up to log factor), our algorithm is able to yield $\varepsilon$ accuracy for arbitrarily many reward functions (even when they are adversarially designed), a task commonly dubbed as ``reward-free exploration.'' The novelty of our algorithm design draws on insights from offline RL: the exploration scheme attempts to maximize a critical reward-agnostic quantity that dictates the performance of offline RL, while the policy learning paradigm leverages ideas from sample-optimal offline RL paradigms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07278 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimax-Optimal Reward-Agnostic Exploration in Reinforcement Learning Li, Gen Yan, Yuling Chen, Yuxin Fan, Jianqing Machine Learning Information Theory Systems and Control Statistics Theory This paper studies reward-agnostic exploration in reinforcement learning (RL) -- a scenario where the learner is unware of the reward functions during the exploration stage -- and designs an algorithm that improves over the state of the art. More precisely, consider a finite-horizon inhomogeneous Markov decision process with $S$ states, $A$ actions, and horizon length $H$, and suppose that there are no more than a polynomial number of given reward functions of interest. By collecting an order of \begin{align*} \frac{SAH^3}{\varepsilon^2} \text{ sample episodes (up to log factor)} \end{align*} without guidance of the reward information, our algorithm is able to find $\varepsilon$-optimal policies for all these reward functions, provided that $\varepsilon$ is sufficiently small. This forms the first reward-agnostic exploration scheme in this context that achieves provable minimax optimality. Furthermore, once the sample size exceeds $\frac{S^2AH^3}{\varepsilon^2}$ episodes (up to log factor), our algorithm is able to yield $\varepsilon$ accuracy for arbitrarily many reward functions (even when they are adversarially designed), a task commonly dubbed as ``reward-free exploration.'' The novelty of our algorithm design draws on insights from offline RL: the exploration scheme attempts to maximize a critical reward-agnostic quantity that dictates the performance of offline RL, while the policy learning paradigm leverages ideas from sample-optimal offline RL paradigms. |
| title | Minimax-Optimal Reward-Agnostic Exploration in Reinforcement Learning |
| topic | Machine Learning Information Theory Systems and Control Statistics Theory |
| url | https://arxiv.org/abs/2304.07278 |