Exact Decomposition of Adversarial Dual-Objective Value Functions, with Applications to Optimal Drug Dosing

Area of Science:

• Control Theory
• Dynamic Systems
• Optimization

Background:

• Hamilton-Jacobi Reachability (HJR) is crucial for safe control.
• Scaling HJR to complex objectives is an active research area.
• Value function decomposition is key for HJR, but its validity with adversaries is uncertain.

Purpose of the Study:

• To theoretically certify the validity of specific HJR value function decompositions in the presence of an adversary.
• To extend the applicability of HJR to more complex, adversarial scenarios.
• To address challenges in applying HJR to optimal drug regimen design.

Main Methods:

• Development of theoretical approaches to analyze and certify value function decompositions.
• Mathematical analysis of composite value functions under adversarial conditions.
• Application of certified decompositions to a practical problem in drug regimen optimization.

Main Results:

• Theoretical certification that two key composite value function decompositions in HJR remain valid even with an adversary.
• Demonstration of how these certified decompositions resolve issues in adversarial HJR applications.
• Established a method to ensure the robustness of HJR frameworks in adversarial settings.

Conclusions:

• The study successfully validates critical HJR value function decompositions against adversarial perturbations.
• The findings enhance the robustness and applicability of HJR for complex control problems.
• The results provide a pathway for improved optimal drug regimen design using HJR.