arXiv Machine Learning

Tail Competition Explains Scaling in Best-of-N Sampling for Verifiable Problems

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
arXiv AI
Oct 9

How to post-train on a surrogate: Envelope sampling mitigates reward hacking

The paper addresses reward hacking that arises when large language models (LLMs) are post‑trained using cheap surrogate judges instead of expensive human feedback. It introduces envelope sampling, a theoretically grounded recalibration technique that uses a small set of ground‑truth annotated outputs to adjust the surrogate judge before further training. Experiments on clinical note generation and a sycophancy task demonstrate that envelope sampling reduces reward hacking compared to traditional base‑model recalibration methods.

By Sanjit Dandapanthula, Shuvom Sadhuka, Samir Khan, Michael Oberst, Aaditya Ramdas, Alexandra Chouldechova
arXiv Machine Learning
Aug 4

Tail-Aware Information-Theoretic Bounds for LLM Alignment under Heavy-Tailed Rewards

arXiv:2604. 10727v2 Announce Type: replace-cross Abstract: Classical information-theoretic learning bounds typically rely on KL mutual information and moment-generating-function (MGF) arguments, which are well matched to bounded or sub-Gaussian losses but can be ineffective when losses or rewards are heavy-tailed.

By Huiming Zhang, Binghan Li, Wan Tian, Qiang Sun
arXiv Machine Learning
Sep 14

Satisficing Regret Minimization in Bandits: Constant Rate and Light-Tailed Distribution

The paper introduces SELECT, an algorithmic framework for satisficing regret minimization in bandit problems, achieving constant expected satisficing regret when a satisficing arm exists. A variant, SELECT‑LITE, further ensures a light‑tailed satisficing regret distribution while maintaining constant expected regret in the realizable case and sub‑linear standard regret otherwise. Experiments on synthetic data and a real‑world dynamic pricing scenario demonstrate the practical effectiveness of both algorithms.

By Qing Feng, Tianyi Ma, Ruihao Zhu