Anytime Safe PAC Efficient Reasoning

TL;DR

This paper introduces B-PAC reasoning, a method for safe, efficient online reasoning with large models that adaptively balances performance and computational cost using statistical evidence, even with partial feedback.

Contribution

It proposes a novel B-PAC framework that guarantees safety and efficiency in online reasoning by dynamically adjusting thresholds based on statistical evidence.

Findings

Reduces thinking model usage by up to 81.01%.

Controls performance loss below user-specified levels.

Establishes theoretical guarantees for safety and efficiency.

Abstract

Large Reasoning Models (LRMs) have demonstrated remarkable performance on complex tasks but suffer from high computational costs and latency. While selective thinking strategies improve efficiency by routing easy queries to non-thinking models, existing approaches often incur uncontrollable errors, especially in online settings where the performance loss of a non-thinking model is only partially observed and data are non-stationary. To address this, we propose Betting Probably Approximately Correct (B-PAC) reasoning, a principled method that enables anytime safe and efficient online reasoning under partial feedback. Specifically, we utilize inverse propensity scoring estimators to construct test supermartingales for candidate thresholds, and then dynamically adjust the routing threshold based on the accumulated statistical evidence of safety. Theoretically, we establish the anytime-valid performance loss control and the efficiency of B-PAC reasoning. Extensive experiments demonstrate that B-PAC reasoning significantly reduces computational overhead, decreasing thinking model usage by up to 81.01\%, while controlling the performance loss below the user-specified level.