Budget-Aware Anytime Reasoning with LLM-Synthesized Preference Data

TL;DR

This paper introduces an anytime reasoning framework for large language models that optimizes solution quality within fixed computational budgets, using synthesized preference data for self-improvement.

Contribution

It proposes a novel anytime reasoning method with the Anytime Index metric and a self-improvement technique leveraging LLM-synthesized preferences, enhancing efficiency and quality.

Findings

Consistent performance improvements across multiple datasets and models.

Effective solution quality enhancement within limited reasoning tokens.

Demonstrated benefits of self-improvement using synthesized preference data.

Abstract

We study the reasoning behavior of large language models (LLMs) under limited computation budgets. In such settings, producing useful partial solutions quickly is often more practical than exhaustive reasoning, which incurs high inference costs. Many real-world tasks, such as trip planning, require models to deliver the best possible output within a fixed reasoning budget. We introduce an anytime reasoning framework and the Anytime Index, a metric that quantifies how effectively solution quality improves as reasoning tokens increase. To further enhance efficiency, we propose an inference-time self-improvement method using LLM-synthesized preference data, where models learn from their own reasoning comparisons to produce better intermediate solutions. Experiments on NaturalPlan (Trip), AIME, and GPQA datasets show consistent gains across Grok-3, GPT-oss, GPT-4.1/4o, and LLaMA models, improving both reasoning quality and efficiency under budget constraints.