The success of Reinforcement Learning from Human Feedback (RLHF) critically depends on the quality of the reward model. While this quality is primarily evaluated through accuracy, it remains unclear whether accuracy fully captures what makes a reward model an effective teacher. We address this question from an optimization perspective. First, we prove that regardless of how accurate a reward model is, if it induces low reward variance, then the RLHF objective suffers from a flat landscape. Consequently, even a perfectly accurate reward model can lead to extremely slow optimization, underperforming less accurate models that induce higher reward variance. We additionally show that a reward model that works well for one language model can induce low reward variance, and thus a flat objective landscape, for another. These results establish a fundamental limitation of evaluating reward models solely based on accuracy or independently of the language model they guide. Experiments using models of up to 8B parameters corroborate our theory, demonstrating the interplay between reward variance, accuracy, and reward maximization rate. Overall, our findings highlight that beyond accuracy, a reward model needs to induce sufficient variance for efficient optimization.

Machine unlearning algorithms are increasingly important as legal concerns arise around the provenance of training data, but verifying the success of unlearning is often difficult. Provable guarantees for unlearning are often limited to supervised learning settings. In this paper, we provide the first theoretical guarantees for unlearning in the pre-training and fine-tuning paradigm by studying topic models, simple bag-of-words language models that can be adapted to solve downstream tasks like retrieval and classification. First, we design a provably effective unlearning algorithm for topic models that incurs a computational overhead independent of the size of the original dataset. Our analysis additionally quantifies the deletion capacity of the model -- i.e., the number of examples that can be unlearned without incurring a significant cost in model performance. Finally, we formally extend our analyses to account for adaptation to a given downstream task. In particular, we design an efficient algorithm to perform unlearning after fine-tuning the topic model via a linear head. Notably, we show that it is easier to unlearn pre-training data from models that have been fine-tuned to a particular task, and one can unlearn this data without modifying the base model.