Exact Decomposition of Adversarial Dual-Objective Value Functions, with Applications to Optimal Drug Dosing
arXiv:2607.14023
The paper proves that certain decompositions of dual‑objective value functions remain valid when an adversary is present, and demonstrates how this can be used to design optimal drug dosing regimens safely.
Abstract
Hamilton-Jacobi Reachability (HJR) is a central framework in safe control theory. While HJR has traditionally focused on a few fundamental tasks, there is increasing interest in scaling to more complex objectives. Recent works have studied the exact decomposition of the value functions for two fundamental dual-objective tasks in the adversary-free setting. However, not all value function decompositions in HJR remain valid with an adversary. In this work, we develop theoretical approaches to certify that for these two composite value functions, the proposed decompositions still hold with an adversary. Finally, we show how these results can solve issues that arise when applying HJR to optimal drug regimen design.
D.H. and W.S. contributed equally to this work. 8 pages, 2 figures. Accepted to 2026 Conference on Decision and Control (CDC)