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Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation
Xiaoyu Chen · Han Zhong · Zhuoran Yang · Zhaoran Wang · Liwei Wang

Tue Jul 19 03:30 PM -- 05:30 PM (PDT) @ Hall E #824
We study human-in-the-loop reinforcement learning (RL) with trajectory preferences, where instead of receiving a numeric reward at each step, the RL agent only receives preferences over trajectory pairs from a human overseer. The goal of the RL agent is to learn the optimal policy which is most preferred by the human overseer. Despite the empirical success in various real-world applications, 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. We prove that our algorithm achieves the regret bound 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.

Author Information

Xiaoyu Chen (Peking University)
Han Zhong (Peking University)
Zhuoran Yang (Yale University)
Zhaoran Wang (Northwestern University)
Liwei Wang (Peking University)

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