How Far Are We from Optimal Reasoning Efficiency?

TL;DR

This paper introduces a new metric called REG to measure reasoning efficiency gaps in large reasoning models, proposes reinforcement learning algorithms to minimize this gap, and demonstrates significant efficiency improvements with minimal accuracy loss.

Contribution

It presents the reasoning efficiency frontiers, a unified metric REG, and the REO-RL algorithm to systematically improve reasoning efficiency in large models.

Findings

REG effectively captures accuracy-length trade-offs.

REO-RL reduces REG by over 50% across models.

Methods approach efficiency frontiers with minimal accuracy loss.

Abstract

Large Reasoning Models (LRMs) demonstrate remarkable problem-solving capabilities through extended Chain-of-Thought (CoT) reasoning but often produce excessively verbose and redundant reasoning traces. This inefficiency incurs high inference costs and limits practical deployment. While existing fine-tuning methods aim to improve reasoning efficiency, assessing their efficiency gains remains challenging due to inconsistent evaluations. In this work, we introduce the reasoning efficiency frontiers, empirical upper bounds derived from fine-tuning base LRMs across diverse approaches and training configurations. Based on these frontiers, we propose the Reasoning Efficiency Gap (REG), a unified metric quantifying deviations of any fine-tuned LRMs from these frontiers. Systematic evaluation on challenging mathematical benchmarks reveals significant gaps in current methods: they either sacrifice accuracy for short length or still remain inefficient under tight token budgets. To reduce the efficiency gap, we propose REO-RL, a class of Reinforcement Learning algorithms that minimizes REG by targeting a sparse set of token budgets. Leveraging numerical integration over strategically selected budgets, REO-RL approximates the full efficiency objective with low error using a small set of token budgets. Through systematic benchmarking, we demonstrate that our efficiency metric, REG, effectively captures the accuracy-length trade-off, with low-REG methods reducing length while maintaining accuracy. Our approach, REO-RL, consistently reduces REG by >=50 across all evaluated LRMs and matching Qwen3-4B/8B efficiency frontiers under a 16K token budget with minimal accuracy loss. Ablation studies confirm the effectiveness of our exponential token budget strategy. Finally, our findings highlight that fine-tuning LRMs to perfectly align with the efficiency frontiers remains an open challenge.