Anytime Safe PAC Efficient Reasoning

2026-01-30

AI Summary

This work addresses the high computational cost and latency of large reasoning models, as well as the challenge of controlling performance loss in existing selective inference methods under online non-stationary environments. To this end, the authors propose B-PAC, a novel selective inference framework that introduces Probably Approximately Correct (PAC) safety guarantees valid at any time. By constructing a test supermartingale based on inverse propensity score estimators, B-PAC dynamically adjusts routing thresholds using accumulated statistical evidence, enabling safe and efficient online inference under partial feedback and non-stationary data distributions. Experimental results demonstrate that the method reduces model invocations by up to 81.01% while consistently ensuring that performance loss remains below a user-specified threshold.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Natural Language Processing: Safety and Robustness
• Machine Learning: Online Learning & Bandits

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements

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.

Problem

• Large Reasoning Models
• Selective Thinking
• Online Reasoning
• Partial Feedback
• Non-stationary Data

Innovation

• B-PAC reasoning
• anytime safety
• inverse propensity scoring
• test supermartingales
• selective reasoning