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.

Reinforcement learning (RL) heavily depends on well-designed reward functions, which are often biased and difficult to design for complex behaviors. Preference-based RL (PbRL) addresses this by learning reward models from human feedback, but its practicality is constrained by a critical dilemma: while existing methods reduce human effort through query optimization, they neglect the preference buffer's restricted coverage -- a factor that fundamentally determines the reliability of reward model. We systematically demonstrate this limitation creates distributional mismatch: reward models trained on static buffers reliably assess in-distribution trajectories but falter with out-of-distribution (OOD) trajectories from policy exploration.

Wefirstshowthataunique optimal policymaynot exist if preferences over trajectories are deterministic for PbRL.

We first show that a unique optimal policy may not exist if preferences over trajectories are deterministic for PbRL.

Our technical contribution is mainly two-fold.

Preference-based Reinforcement Learning (PbRL) replaces reward values in traditional reinforcement learning by preferences to better elicit human opinion on the target objective, especially when numerical reward values are hard to design or interpret. Despite promising results in applications, the theoretical understanding of PbRL is still in its infancy. In this paper, we present the first finite-time analysis for general PbRL problems. We first show that a unique optimal policy may not exist if preferences over trajectories are deterministic for PbRL. If preferences are stochastic, and the preference probability relates to the hidden reward values, we present algorithms for PbRL, both with and without a simulator, that are able to identify the best policy up to accuracy $\varepsilon$ with high probability. Our method explores the state space by navigating to under-explored states, and solves PbRL using a combination of dueling bandits and policy search. Experiments show the efficacy of our method when it is applied to real-world problems.

Preference-based reinforcement learning (PbRL) enables agents to learn control policies without requiring manually designed reward functions, making it well-suited for tasks where objectives are difficult to formalize or inherently subjective. Acrobatic flight poses a particularly challenging problem due to its complex dynamics, rapid movements, and the importance of precise execution. In this work, we explore the use of PbRL for agile drone control, focusing on the execution of dynamic maneuvers such as powerloops. Building on Preference-based Proximal Policy Optimization (Preference PPO), we propose Reward Ensemble under Confidence (REC), an extension to the reward learning objective that improves preference modeling and learning stability. Our method achieves 88.4% of the shaped reward performance, compared to 55.2% with standard Preference PPO. We train policies in simulation and successfully transfer them to real-world drones, demonstrating multiple acrobatic maneuvers where human preferences emphasize stylistic qualities of motion. Furthermore, we demonstrate the applicability of our probabilistic reward model in a representative MuJoCo environment for continuous control. Finally, we highlight the limitations of manually designed rewards, observing only 60.7% agreement with human preferences. These results underscore the effectiveness of PbRL in capturing complex, human-centered objectives across both physical and simulated domains.

We first show that a unique optimal policy may not exist if preferences over trajectories are deterministic for PbRL.