In reinforcement studying from human suggestions, it is not uncommon to optimize in opposition to a reward mannequin educated to foretell human preferences. As a result of the reward mannequin is an imperfect proxy, optimizing its worth an excessive amount of can hinder floor reality efficiency, in accordance with Goodhart’s legislation. This impact has been ceaselessly noticed, however not fastidiously measured as a result of expense of amassing human choice knowledge. On this work, we use an artificial setup wherein a hard and fast “gold-standard” reward mannequin performs the function of people, offering labels used to coach a proxy reward mannequin. We examine how the gold reward mannequin rating modifications as we optimize in opposition to the proxy reward mannequin utilizing both reinforcement studying or best-of-n sampling. We discover that this relationship follows a unique useful kind relying on the strategy of optimization, and that in each circumstances its coefficients scale easily with the variety of reward mannequin parameters. We additionally examine the impact on this relationship of the dimensions of the reward mannequin dataset, the variety of reward mannequin and coverage parameters, and the coefficient of the KL penalty added to the reward within the reinforcement studying setup. We discover the implications of those empirical outcomes for theoretical issues in AI alignment.