Preference-based Reinforcement Learning beyond Pairwise Comparisons: Benefits of Multiple Options

• URL: http://arxiv.org/abs/2510.18713v1
• Date: Tue, 21 Oct 2025 15:11:01 GMT
• Title: Preference-based Reinforcement Learning beyond Pairwise Comparisons: Benefits of Multiple Options
• Abstract summary: We study online preference-based reinforcement learning (PbRL) with the goal of improving sample efficiency.<n>We propose M-AUPO, an algorithm that selects multiple actions by maximizing the average uncertainty within the offered subset.<n>We prove that M-AUPO achieves a suboptimality gap of $tildemathcalOleft( fracdT sqrt sum_t=1T frac1|S_t| right)$, where $T$ is the total number of rounds, $d$
• Score: 35.41703011973504
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study online preference-based reinforcement learning (PbRL) with the goal of improving sample efficiency. While a growing body of theoretical work has emerged-motivated by PbRL's recent empirical success, particularly in aligning large language models (LLMs)-most existing studies focus only on pairwise comparisons. A few recent works (Zhu et al., 2023, Mukherjee et al., 2024, Thekumparampil et al., 2024) have explored using multiple comparisons and ranking feedback, but their performance guarantees fail to improve-and can even deteriorate-as the feedback length increases, despite the richer information available. To address this gap, we adopt the Plackett-Luce (PL) model for ranking feedback over action subsets and propose M-AUPO, an algorithm that selects multiple actions by maximizing the average uncertainty within the offered subset. We prove that M-AUPO achieves a suboptimality gap of $\tilde{\mathcal{O}}\left( \frac{d}{T} \sqrt{ \sum_{t=1}^T \frac{1}{|S_t|}} \right)$, where $T$ is the total number of rounds, $d$ is the feature dimension, and $|S_t|$ is the size of the subset at round $t$. This result shows that larger subsets directly lead to improved performance and, notably, the bound avoids the exponential dependence on the unknown parameter's norm, which was a fundamental limitation in most previous works. Moreover, we establish a near-matching lower bound of $\Omega \left( \frac{d}{K \sqrt{T}} \right)$, where $K$ is the maximum subset size. To the best of our knowledge, this is the first theoretical result in PbRL with ranking feedback that explicitly shows improved sample efficiency as a function of the subset size.

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