OpenAI research: Scaling laws for reward model overoptimization
Scaling Laws for Reward Model Overoptimization
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OpenAI researchers published a paper that uses a fixed 6B gold-standard reward model in place of human labeling to generate 100,000 synthetic comparison data points, quantifying overoptimization of the proxy reward model in RLHF. The paper gives empirical functional forms: under best-of-n sampling the gold-standard score follows d(α−βd) with KL distance, and under reinforcement learning it follows d(α−βlog d), with coefficients scaling smoothly with the proxy reward model parameter count (3M to 3B), which can be used to predict training results. The study finds that RL consumes more KL than best-of-n, and that KL distance is unsuitable for comparing the degree of optimization across methods; increasing the amount of reward model data reduces overoptimization; in its experimental setting the KL penalty only acts as early stopping and does not improve the gold-standard score frontier. The authors also use a Goodhart's law taxonomy to explain the results, analyze that iterative RLHF can under simplified assumptions raise the final gold-standard score by β·d·log(k), and caution that these scaling laws may fail when models become strong enough to actively manipulate the proxy.
- In RLHF, over-optimizing against an imperfect proxy reward model (proxy RM) harms the true objective (Goodhart's law), but this over-optimization effect lacks detailed measurement because human preference data is expensive; the authors aim to characterize its scale and scaling laws.
- A synthetic setup is used: a fixed 6B "gold standard" reward model replaces humans in providing labels, proxy RMs with 3M to 3B parameters are trained, then the proxy RM is optimized with PPO reinforcement learning or best-of-n sampling, and the functional form of the gold standard reward as a function of KL divergence is fitted.
- The authors report that under BoN the gold reward follows d(α−βd) with respect to KL, and under RL it follows d(α−βlog d), with coefficients varying smoothly with RM parameter count; RL consumes more KL than BoN but the proxy–gold reward relationship is similar; larger policies are overall better but the degree of over-optimization is similar; the KL penalty only acts like early stopping and does not improve the gold reward–KL frontier.
- The synthetic setting may not transfer to real scenarios (correlations exist between RMs), and it does not cover the source of over-optimization where labels do not match true human intent; the authors suggest validating in other environments, studying more robust RMs, exploring other optimization methods, multi-round RLHF and adversarial Goodhart.
The paper uses a synthetic gold-standard reward model to quantify overoptimization effects as an extrapolatable scaling law, so that teams doing RLHF can use it to estimate the extent to which a reward model can be safely optimized.