Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation

• URL: http://arxiv.org/abs/2205.11140v2
• Date: Tue, 24 May 2022 02:42:19 GMT
• Title: Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation
• Authors: Xiaoyu Chen, Han Zhong, Zhuoran Yang, Zhaoran Wang, Liwei Wang
• Abstract summary: We study human-in-the-loop reinforcement learning (RL) with trajectory preferences. Instead of receiving a numeric reward at each step, the agent only receives preferences over trajectory pairs from a human overseer. We propose the first optimistic model-based algorithm for PbRL with general function approximation.
• Score: 107.54516740713969
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study human-in-the-loop reinforcement learning (RL) with trajectory preferences, where instead of receiving a numeric reward at each step, the agent only receives preferences over trajectory pairs from a human overseer. The goal of the agent is to learn the optimal policy which is most preferred by the human overseer. Despite the empirical successes, the theoretical understanding of preference-based RL (PbRL) is only limited to the tabular case. In this paper, we propose the first optimistic model-based algorithm for PbRL with general function approximation, which estimates the model using value-targeted regression and calculates the exploratory policies by solving an optimistic planning problem. Our algorithm achieves the regret of $\tilde{O} (\operatorname{poly}(d H) \sqrt{K} )$, where $d$ is the complexity measure of the transition and preference model depending on the Eluder dimension and log-covering numbers, $H$ is the planning horizon, $K$ is the number of episodes, and $\tilde O(\cdot)$ omits logarithmic terms. Our lower bound indicates that our algorithm is near-optimal when specialized to the linear setting. Furthermore, we extend the PbRL problem by formulating a novel problem called RL with $n$-wise comparisons, and provide the first sample-efficient algorithm for this new setting. To the best of our knowledge, this is the first theoretical result for PbRL with (general) function approximation.

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