对抗性双目标值函数的精确分解及其在最优给药中的应用
Exact Decomposition of Adversarial Dual-Objective Value Functions, with Applications to Optimal Drug Dosing
浏览论文内容
中文总结 AI 辅助
研究HJR框架下对抗性双目标值函数的精确分解，开发理论方法证明特定复合值函数分解在有对抗时仍成立，并展示其可解决HJR用于最优药物方案设计时出现的问题。
中文摘要 AI 辅助
哈密顿-雅可比可达性（HJR）是安全控制理论的核心框架。传统上HJR专注于一些基本任务，如今对扩展到更复杂目标的兴趣日增。近期工作研究了无对抗环境下两个基本双目标任务值函数的精确分解。但HJR中并非所有值函数分解在有对抗时仍有效。本文开发理论方法证明这两个复合值函数的分解在有对抗时依然成立。最后展示这些结果如何解决将HJR应用于最优药物方案设计时出现的问题。
英文摘要
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.
