BRiTE: Bootstrapping Reinforced Thinking Process to Enhance Language Model Reasoning

TL;DR

BRiTE introduces a probabilistic framework and reinforcement learning algorithm to improve reasoning in large language models, achieving better performance without human-annotated data.

Contribution

The paper proposes BRiTE, a novel reinforcement learning method that enhances LLM reasoning by bootstrapping rationales within a probabilistic graphical model.

Findings

Consistently improves performance on math and coding benchmarks.

Matches or exceeds supervised fine-tuning results.

Converges at a rate of 1/T with iterative reinforcement learning.

Abstract

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, yet generating reliable reasoning processes remains a significant challenge. We present a unified probabilistic framework that formalizes LLM reasoning through a novel graphical model incorporating latent thinking processes and evaluation signals. Within this framework, we introduce the Bootstrapping Reinforced Thinking Process (BRiTE) algorithm, which works in two steps. First, it generates high-quality rationales by approximating the optimal thinking process through reinforcement learning, using a novel reward shaping mechanism. Second, it enhances the base LLM by maximizing the joint probability of rationale generation with respect to the model's parameters. Theoretically, we demonstrate BRiTE's convergence at a rate of $1/T$ with $T$ representing the number of iterations. Empirical evaluations on math and coding benchmarks demonstrate that our approach consistently improves performance across different base models without requiring human-annotated thinking processes. In addition, BRiTE demonstrates superior performance compared to existing algorithms that bootstrap thinking processes use alternative methods such as rejection sampling, and can even match or exceed the results achieved through supervised fine-tuning with human-annotated data.