Generative Value Classifier

Q-learning is premised on learning a function to predict the value of a state-action pair, with the goal of using such a function to guide policy improvement. Most approaches learn this function from scratch using scalar or distributional return targets. This discriminative approach leaves another source of supervision for learning representations unused: the actions themselves. Rather than directly predict a return distribution $p(z\mid s,a)$, we ask how likely the state-action pair is under each possible return, $p(s,a\mid z)$. This perspective yields a critic based on Bayes' rule whose generative component is a return-conditioned policy, which can share the actor's architecture. Training this policy supervises the critic with every action rather than with returns alone, and a squared-error loss anchors the critic's Q-value to the bootstrapped target. We evaluate our approach on both offline and online RL tasks and show gains over leading discriminative methods, including distributional RL methods.