Preference Optimization by Estimating the Ratio of the Data Distribution

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.