Anytime Safe PAC Efficient Reasoning
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.