When Errors Can Be Beneficial: A Categorization of Imperfect Rewards for Policy Gradient

Reinforcement Learning from Human Feedback (RLHF) or Verifiable Rewards (RLVR) are two key steps in the post-training of modern Language Models (LMs). A common problem is reward hacking, where the policy may exploit inaccuracies of the reward and learn an unintended behavior. Most previous works address this by limiting the policy update with a Kullback-Leibler (KL) penalty towards a reference model. We propose a different framing: Train the LM in a way that biases policy updates towards regions in which the reward is more accurate. First, we derive a theoretical connection between the accuracy of a reward model and the flatness of an optimum at convergence. Gradient regularization (GR) can then be used to bias training to flatter regions and thereby maintain reward model accuracy. We confirm these results by showing that the gradient norm and reward accuracy are empirically correlated in RLHF. We then empirically show that Reference Resets of the KL penalty find flatter regions with a higher reward accuracy. We further improve on this by proposing to use explicit GR with an efficient finite-difference estimate. Empirically, GR performs better than a KL penalty across a diverse set of RL experiments with LMs. GR achieves a higher GPT-judged win-rate in RLHF, avoids overly focusing on the format in rule-based math rewards, and prevents hacking the judge in LLM-as-a-Judge math tasks.

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for improving reasoning in language models, yet models trained with RLVR often suffer from diversity collapse: while single-sample accuracy improves, multi-sample coverage degrades, sometimes falling below the base model. We provide a structural account of this phenomenon grounded in the properties of binary rewards. Binary rewards create a fundamental degeneracy for policy gradient methods: the set of distributions maximizing expected reward is infinite, with no distinguished element. KL-control resolves this degeneracy by selecting, in the limit $β\to 0$, the filtered model $p_*:=a(\cdot\mid\mathcal{Y}_1)$ -- the base model conditioned on validity -- which is the unique fully valid distribution closest to the base model in KL divergence. This selection operates through a nontrivial asymmetry: the tilted distribution $p_{[β]}\propto a(y)\,e^{v(y)/β}$ converges to $p_*$ in forward KL as $β\to 0$, yet $p_*$ cannot serve as a direct optimization target because $\mathrm{KL}(q\,\|\,p_*)$ is infinite for any full-support policy $q$. We develop explicit formulas relating the hyperparameter $β$ to the more interpretable target validity rate $μ$. Under model misspecification -- the typical practical regime -- the pressure to decrease $β$ drives the optimizer toward highly concentrated distributions over a small number of valid outputs, collapsing toward ever fewer as $β$ decreases, rather than toward the filtered model. We illustrate this mechanism on a toy autoregressive experiment and discuss how alternative divergences that target $p_*$ directly -- as pursued empirically by \citet{kruszewski_whatever_2026} -- avoid this failure mode by rewarding coverage of $p_*$'s support rather than concentration on high-validity outputs.

Reward models are essential for aligning language model outputs with human preferences, yet existing approaches often lack both controllability and interpretability. These models are typically optimized for narrow objectives, limiting their generalizability to broader downstream tasks. Moreover, their scalar outputs are difficult to interpret without contextual reasoning. To address these limitations, we introduce R3, a novel reward modeling framework that is rubric-agnostic, generalizable across evaluation dimensions, and provides interpretable, reasoned score assignments. R3 enables more transparent and flexible evaluation of language models, supporting robust alignment with diverse human values and use cases. Our models, data, and code are available as open source at https://github.com/rubricreward/r3.