CURVE: Dynamic Cost-Accuracy Control for LLM Reasoning via Online Constrained Optimization

Recent reasoning frameworks for large language models (LLMs) improve accuracy by generating multiple candidates and applying verification, but typically rely on fixed reasoning budgets, offering limited control over the cost-accuracy trade-off. We propose Constrained Update for Risk-aware Verification Ensemble (CURVE), an online, label-free decision-making framework that enables explicit test-time control of this trade-off. CURVE formulates answer acceptance as an online constrained optimization problem, adaptively allocating verification effort by updating acceptance thresholds from proxy risk estimates and reweighting verifiers via inter-verifier consensus. Across diverse reasoning benchmarks, CURVE consistently achieves a more favorable cost-accuracy trade-off than fixed-budget baselines under comparable computational budgets. We provide an empirical analysis suggesting a regime where verification signals become weakly informative, clarifying when additional test-time verification is likely to help.