Nice Fold or Hero Call: Learning Budget-Efficient Thinking under Policy-Dependent Solvability
TL;DR
Adaptive reasoning is formulated as a computational investment under uncertainty, where budget follows the expected return of reasoning rather than perceived difficulty, and Budget-Efficient Thinking (BET) is proposed, a two-stage framework that combines behavioral cold-start with GRPO under an investment-cost-aware reward.
Abstract
Large reasoning models (LRMs) improve problem solving through extended reasoning, but often misallocate test-time compute. Existing efficiency methods reduce cost by compressing reasoning traces or conditioning budget on perceived difficulty, yet read the resulting pass rate as a difficulty score, leaving the zero-return regime unmodeled. As a result, they overspend on queries beyond the model's capability while compressing hard-but-solvable ones that need deeper reasoning. In this work, we formulate adaptive reasoning as a computational investment under uncertainty, where budget follows the expected return of reasoning rather than perceived difficulty. To instantiate this principle, we propose Budget-Efficient Thinking (BET), a two-stage framework that combines behavioral cold-start with GRPO under an investment-cost-aware reward. By aligning solve-or-fold decisions with rollout-derived solvability, BET learns three behaviors: (1) short solve, answering easy queries concisely; (2) nice fold, abstaining early when continued reasoning has near-zero expected return; and (3) hero call, preserving sufficient compute for hard-but-solvable queries. Across seven benchmarks and three base models, BET reduces reasoning tokens by 54% while improving up to 3.2% accuracy, and transfers zero-shot to scientific QA and logical reasoning with comparable efficiency gains. Code is available at https://github.com/houqiii/BET
