Preference Optimization as Probabilistic Inference

The use of preference annotated data for training machine learning models has a long history going back to early algorithms for recommender systems and market research (Bonilla et al., 2010; Boutilier, 2002; Guo and Sanner, 2010). These days preference optimization algorithms are receiving renewed attention since they are a natural candidate for shaping the outputs of deep learning systems, such as large language models (Ouyang et al., 2022; Team et al., 2024) or control policies, via human feedback (Azar et al., 2023; Christiano et al., 2017; Rafailov et al., 2023). Arguably, preference optimization algorithms can also be a natural choice even when direct human feedback is not available but one instead aims to optimize a machine learning model based on feedback from a hand-coded or learned critic function (judging desirability of solutions). Here preference optimization methods are useful since they let us optimize the model to achieve desired outcomes based on relative rankings between outcomes alone (rather than requiring absolute labels or carefully crafted reward functions). Among preference optimization approaches, those based on directly using preference data - as opposed to casting preference optimization as reinforcement learning from (human) feedback - such as DPO (Rafailov et al., 2023), have emerged as particularly successful since they only require access to an offline dataset of paired preference data, and are fairly robust to application domain and hyperparameter settings. However, algorithms within this class make specific assumptions tailored to their application domain. They were designed to optimize LLMs from human feedback in the form of comparisons of generated sentences and thus, by design, require paired preference data (since they directly model a specific choice of preference distribution). We are interested in finding algorithms that are more flexible, and applicable in settings where the assumptions underlying DPO do not apply.