arXiv AI
Oct 1

Revisiting scaling laws for reward optimization

The paper presents a new scaling law for reward optimization in AI alignment, showing that performance scales as Θ(√min{log(M), K}), where M is the number of preference comparisons used to train a proxy reward model and K is the KL‑divergence budget relative to a reference policy. The authors derive this law using an information‑theoretic model, prove its tightness, and validate it with extensive experiments involving a 70B gold reward model and smaller proxy models (0.6B–4B). The empirical results demonstrate a strong fit (R² 97–99 %) across different model sizes, noise levels, and optimization methods, suggesting that reward optimization behaves like a simple selection task over IID Gaussian variables with noisy feedback.

By Ali Aouad, Aymane El Gadarri, Vivek F. Farias