From $r$ to $Q^*$: Your Language Model is Secretly a Q-Function
Rafael Rafailov Joey Hejna Ryan Park Chelsea Finn
Reinforcement Learning From Human Feedback (RLHF) has been a critical to the
success of the latest generation of generative AI models. In response to the
complex nature of the classical RLHF pipeline, direct alignment algorithms such
as Direct Preference Optimization (DPO) have emerged as an alternative
approach. Although DPO solves the same objective as the standard RLHF setup,
there is a mismatch between the two approaches. Standard RLHF deploys
reinforcement learning in a specific token-level MDP, while DPO is derived as a
bandit problem in which the whole response of the model is treated as a single
arm. In this work we rectify this difference, first we theoretically show that
we can derive DPO in the token-level MDP as a general inverse Q-learning
algorithm, which satisfies the Bellman equation. Using our theoretical results,
we provide three concrete empirical insights. First, we show that because of
its token level interpretation, DPO is able to perform some type of credit
assignment. Next, we prove that under the token level formulation, classical
search-based algorithms, such as MCTS, which have recently been applied to the
language generation space, are equivalent to likelihood-based search on a DPO
policy. Empirically we show that a simple beam search yields meaningful
improvement over the base DPO policy. Finally, we show how the choice of
reference policy causes implicit rewards to decline during training. We
conclude by discussing applications of our work, including information
elicitation in multi-tun dialogue, reasoning, agentic applications and
end-to-end training of multi-model systems.