Conformal Arbitrage: Risk-Controlled Balancing of Competing Objectives in Language Models

Modern language-model deployments must often balance competing objectives-for example, helpfulness versus harmlessness, cost versus accuracy, and reward versus safety. We introduce Conformal Arbitrage, a post-hoc framework that learns a data-driven threshold to mediate between a Primary model optimized for a primary objective and a more conservative Guardian-which could be another model or a human domain expert-aligned with a guardrail objective. The threshold is calibrated with conformal risk control, yielding finite-sample, distribution-free guarantees that the long-run frequency of undesirable events (such as factual errors or safety violations) does not exceed a user-specified quota. Because Conformal Arbitrage operates wholly at the API level-without requiring access to model logits or updating model weights-it complements weight-based alignment techniques and integrates seamlessly with existing cost-aware cascades. Empirically, Conformal Arbitrage traces an efficient frontier, allowing users to define an acceptable performance level for one objective while maximizing utility in another. We observe that our method outperforms (in terms of accuracy on multiple-choice style questions) cost-matched random routing between models. These properties make Conformal Arbitrage a practical, theoretically grounded tool for trustworthy and economical deployment of large language models across a broad range of potentially competing objectives.