Optimizing Anytime Reasoning via Budget Relative Policy Optimization

TL;DR

This paper introduces AnytimeReasoner, a framework that improves large language models' reasoning efficiency and flexibility by optimizing token usage and reasoning under variable budgets through a novel RL approach with verifiable rewards.

Contribution

The paper proposes a new RL-based framework, AnytimeReasoner, with a novel variance reduction technique, BRPO, to optimize reasoning performance across varying token budgets.

Findings

Outperforms GRPO across all thinking budgets.

Enhances token and training efficiency.

Demonstrates effectiveness in mathematical reasoning tasks.

Abstract

Scaling test-time compute is crucial for enhancing the reasoning capabilities of large language models (LLMs). Existing approaches typically employ reinforcement learning (RL) to maximize a verifiable reward obtained at the end of reasoning traces. However, such methods optimize only the final performance under a large and fixed token budget, which hinders efficiency in both training and deployment. In this work, we present a novel framework, AnytimeReasoner, to optimize anytime reasoning performance, which aims to improve token efficiency and the flexibility of reasoning under varying token budget constraints. To achieve this, we truncate the complete thinking process to fit within sampled token budgets from a prior distribution, compelling the model to summarize the optimal answer for each truncated thinking for verification. This introduces verifiable dense rewards into the reasoning process, facilitating more effective credit assignment in RL optimization. We then optimize the thinking and summary policies in a decoupled manner to maximize the cumulative reward. Additionally, we introduce a novel variance reduction technique, Budget Relative Policy Optimization (BRPO), to enhance the robustness and efficiency of the learning process when reinforcing the thinking policy. Empirical results in mathematical reasoning tasks demonstrate that our method consistently outperforms GRPO across all thinking budgets under various prior distributions, enhancing both training and token efficiency.