Preference Optimization by Estimating the Ratio of the Data Distribution

TL;DR

This paper introduces Bregman preference optimization (BPO), a generalized framework for preference alignment in large language models that improves performance and theoretical guarantees over existing methods like DPO and $f$-DPO.

Contribution

The paper proposes BPO, a novel ratio matching framework that generalizes DPO, providing theoretical guarantees, simplicity, and improved empirical performance in preference optimization.

Findings

BPO improves win rate and entropy over DPO.

BPO achieves state-of-the-art results on Llama-3-8B with AlpacaEval2.

BPO offers a family of objective functions with theoretical guarantees.

Abstract

Direct preference optimization (DPO) is widely used as a simple and stable method for aligning large language models (LLMs) with human preferences. This paper investigates a generalized DPO loss that enables a policy model to match the target policy from a likelihood ratio estimation perspective. The ratio of the target policy provides a unique identification of the policy distribution without relying on reward models or partition functions. This allows the generalized loss to retain both simplicity and theoretical guarantees, which prior work such as $f$-PO fails to achieve simultaneously. We propose Bregman preference optimization (BPO), a generalized framework for ratio matching that provides a family of objective functions achieving target policy optimality. BPO subsumes DPO as a special case and offers tractable forms for all instances, allowing implementation with a few lines of code. We further develop scaled Basu's power divergence (SBA), a gradient scaling method that can be used for BPO instances. The BPO framework complements other DPO variants and is applicable to target policies defined by these variants. In experiments, unlike other probabilistic loss extensions such as $f$-DPO or $f$-PO, which exhibit a trade-off between generation fidelity and diversity, instances of BPO improve both win rate and entropy compared with DPO. When applied to Llama-3-8B-Instruct, BPO achieves state-of-the-art performance among Llama-3-8B backbones, with a 55.9\% length-controlled win rate on AlpacaEval2. Project page: https://github.com/aailab-kaist/BPO.