Compute When Worth It: Risk Control for Reasoning on a Compute Budget

Reasoning Large Language Models (LLMs) enable test-time scaling, with dataset-level accuracy improving as the token budget increases, motivating adaptive reasoning---spending tokens when they improve reliability and stopping early when additional computation is unlikely to help. However, setting the token budget, as well as the threshold for adaptive reasoning, is a practical challenge that entails a fundamental risk-accuracy trade-off. We re-frame the budget setting problem as risk control, limiting the error rate while minimizing compute. Our framework introduces an \emph{upper} threshold that stops reasoning when the model is confident (risking incorrect output) and a novel parametric lower threshold that preemptively stops unsolvable instances (risking premature stoppage). Given a target risk and a validation set, we use distribution-free risk control to optimally specify these stopping mechanisms. For scenarios with multiple budget controlling criteria, we incorporate an efficiency loss to select the most computationally efficient exiting mechanism. Empirical results across diverse reasoning tasks and models demonstrate the effectiveness of our risk control approach, demonstrating computational efficiency gains from the lower threshold and ensemble stopping mechanisms while adhering to the user-specified risk target.