When Does Learning to Stop Help? A Cost-Aware Study of Early Exits in Reasoning Models

Reasoning models spend test-time compute unevenly across instances, and a growing family of early-exit rules -- confidence thresholds, entropy monitors, answer-stability checks, and learned stoppers -- promises to reclaim the waste. These rules, however, are evaluated under heterogeneous protocols that leave the deployment question unanswered: at a fixed tolerance for losing correct answers, which policy saves more compute, and does the saving survive probe overhead? We answer this question with a controlled study across 18 task-model settings spanning GSM8K, MATH-500, MMLU-Pro, AIME-90, and GPQA on Qwen3 and DeepSeek-R1-distilled models, using LearnStop, a hidden-state-free logistic stopper over prefix-observable features, as the learned policy instrument. Under matched lost-correct risk at α = 0.15, with the scalar competitor selected on calibration data from confidence, entropy, confidence-leap, and run-stability exits, the answer forms three regimes. Learned stopping wins on all four primary Qwen3 free-form math settings (+3.2 to +21.2 pp additional total-token saving); calibrated scalar exits win on multiple-choice MMLU-Pro; and small hard benchmarks (AIME-90, GPQA) admit no certifiable aggressive policy at all. A trajectory decomposition predicts the regime: learning pays where answers oscillate and correctness evidence is spread across complementary signals, while a single confidence threshold suffices where most instances are already solved at the first checkpoint. Cost accounting sharpens the picture further -- the same policy that saves 32% of tokens under KV-cache forking costs 121% extra under black-box repeated prefilling. Together, these results replace the single-method race with a decision procedure for choosing a stopping rule from the trajectory structure and serving regime of the target workload.