MultiRisk: Multiple Risk Control via Iterative Score Thresholding

Abstract: As generative AI systems are increasingly deployed in real-world applications, regulating multiple dimensions of model behavior has become essential. We focus on test-time filtering: a lightweight mechanism for behavior control that compares performance scores to estimated thresholds, and modifies outputs when these bounds are violated. We formalize the problem of enforcing multiple risk constraints with user-defined priorities, and introduce two efficient dynamic programming algorithms that leverage this sequential structure. The first, MULTIRISK-BASE, provides a direct finite-sample procedure for selecting thresholds, while the second, MULTIRISK, leverages data exchangeability to guarantee simultaneous control of the risks. Under mild assumptions, we show that MULTIRISK achieves nearly tight control of all constraint risks. The analysis requires an intricate iterative argument, upper bounding the risks by introducing several forms of intermediate symmetrized risk functions, and carefully lower bounding the risks by recursively counting jumps in symmetrized risk functions between appropriate risk levels. We evaluate our framework on a three-constraint LLM alignment task using the PKU-SafeRLHF dataset, where the goal is to maximize helpfulness subject to multiple safety constraints, and where scores are generated by a LLM judge and a perplexity filter. Our experimental results show that our algorithm can control each individual risk at close to the target level.