Bradley-Terry Policy Optimization for Generative Preference Modeling

Abstract

Reinforcement learning (RL) has recently proven effective at scaling chain-of-thought (CoT) reasoning in large language models for tasks with verifiable answers. However, extending RL-based thought training to more general non-verifiable tasks-where supervision is provided only through pairwise human preferences-remains challenging. Existing approaches typically apply RL objectives designed for verifiable rewards to preference-based settings in a heuristic manner. In this work, we show that introducing CoT reasoning into preference modeling fundamentally changes the structure of the Bradley-Terry (BT) likelihood, as the reasoning process must be treated as a latent variable. This results in a preference likelihood expressed as a ratio of expectations over stochastic generation trajectories, which cannot be optimized using Jensen-style bounds or standard RL objectives. To address this challenge, we derive a consistent Monte Carlo estimator for the gradient of the resulting likelihood, leading to Bradley-Terry Policy Optimization (BTPO). Empirically, BTPO enables stable and effective training of generative preference models with CoT reasoning, consistently outperforming prior heuristic approaches across multiple benchmarks and model scales.

Reproductions