A Unifying Lens on Reward Uncertainty in RLHF

Reinforcement learning from human feedback (RLHF) is bottlenecked by \emph{reward hacking}, where the policy exploits errors in a proxy reward model (RM) and produces high RM scores without genuine quality gains. A natural mitigation is \emph{pessimism}: penalizing rewards in regions where the RM is uncertain. However, standard scalar RMs provide no principled notion of uncertainty. We argue that the right object is a \emph{distributional} reward model $p(r\mid x,y)$. Under either a Bayesian inference or a KL-distributionally robust optimization (KL-DRO) lens, the KL-regularized RLHF objective admits a closed-form effective reward $\tilde r(x,y) = \pmβ\log\mathbb{E}_p[e^{\pm r/β}]$. The pessimistic branch unifies the prior heuristics for RM ensemble aggregation: mean aggregation, worst-case optimization (WCO), and uncertainty-weighted optimization (UWO) all emerge as limits or truncations of this single expression. This also clarifies the implicit assumptions of each existing rule.