To ensure that large language model (LLM) responses are helpful and non-toxic, we usually fine-tune a reward model on human preference data. We then select policy responses with high rewards (best-of-n sampling) or further optimize the policy to produce responses with high rewards (reinforcement learning from human feedback). However, this process is vulnerable to reward overoptimization or hacking, in which the responses selected have high rewards due to errors in the reward model rather than a genuine preference. This is especially problematic as the prompt or response diverges from the training data. It should be possible to mitigate these issues by training a Bayesian reward model, which signals higher uncertainty further from the training data distribution. Therefore, we trained Bayesian reward models using Laplace-LoRA (Yang et al., 2024) and found that the resulting uncertainty estimates can successfully mitigate reward overoptimization in best-of-n sampling.