LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning

TL;DR

LLaMA-Berry introduces a novel framework combining Monte Carlo Tree Search, Self-Refine, and pairwise reward modeling to significantly improve mathematical reasoning in Large Language Models, especially for complex Olympiad problems.

Contribution

The paper presents a new optimization framework that integrates pairwise reward models with MCTS and Self-Refine, enhancing reasoning efficiency and accuracy in LLMs for advanced mathematical tasks.

Findings

Outperforms existing methods like ToT and rStar on Olympiad benchmarks.

Achieves higher problem-solving accuracy and search efficiency.

Effective in complex and diverse mathematical reasoning tasks.

Abstract

This paper presents an advanced mathematical problem-solving framework, LLaMA-Berry, for enhancing the mathematical reasoning ability of Large Language Models (LLMs). The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path and utilizes a pairwise reward model to evaluate different paths globally. By leveraging the self-critic and rewriting capabilities of LLMs, Self-Refine applied to MCTS (SR-MCTS) overcomes the inefficiencies and limitations of conventional step-wise and greedy search algorithms by fostering a more efficient exploration of solution spaces. Pairwise Preference Reward Model~(PPRM), inspired by Reinforcement Learning from Human Feedback (RLHF), is then used to model pairwise preferences between solutions, utilizing an Enhanced Borda Count (EBC) method to synthesize these preferences into a global ranking score to find better answers. This approach addresses the challenges of scoring variability and non-independent distributions in mathematical reasoning tasks. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability compared to existing methods like ToT and rStar, particularly in complex Olympiad-level benchmarks, including GPQA, AIME24 and AMC23.