Predicting and improving test-time scaling laws via reward tail-guided search

TL;DR

This paper introduces a novel tail-guided search method for test-time scaling of large language models, enabling more efficient compute allocation and improved performance without exhaustive evaluation.

Contribution

It proposes a new tail distribution estimation technique and a scaling-law guided search algorithm with theoretical guarantees, optimizing test-time scaling for LLMs.

Findings

Tail-guided search outperforms Best-of-N under same compute budgets

Theoretical proof of vanishing regret for the proposed method

Empirical validation across multiple LLMs and reward models

Abstract

Test-time scaling has emerged as a critical avenue for enhancing the reasoning capabilities of Large Language Models (LLMs). Though the straight-forward ''best-of-$N$'' (BoN) strategy has already demonstrated significant improvements in performance, it lacks principled guidance on the choice of $N$, budget allocation, and multi-stage decision-making, thereby leaving substantial room for optimization. While many works have explored such optimization, rigorous theoretical guarantees remain limited. In this work, we propose new methodologies to predict and improve scaling properties via tail-guided search. By estimating the tail distribution of rewards, our method predicts the scaling law of LLMs without the need for exhaustive evaluations. Leveraging this prediction tool, we introduce Scaling-Law Guided (SLG) Search, a new test-time algorithm that dynamically allocates compute to identify and exploit intermediate states with the highest predicted potential. We theoretically prove that SLG achieves vanishing regret compared to perfect-information oracles, and achieves expected rewards that would otherwise require a polynomially larger compute budget required when using BoN. Empirically, we validate our framework across different LLMs and reward models, confirming that tail-guided allocation consistently achieves higher reward yields than Best-of-$N$ under identical compute budgets. Our code is available at https://github.com/PotatoJnny/Scaling-Law-Guided-search.