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

Dylan Hirsch, William Sharpless, Sylvia Herbert

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Article in ArXiv, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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0 citing papers in PubMed.

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5 · Who and what money

Authors and funding

3 authors.

Dylan HirschDepartment of Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive MC 0411, La Jolla, CA 92093.

William SharplessDepartment of Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive MC 0411, La Jolla, CA 92093.

Sylvia HerbertDepartment of Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive MC 0411, La Jolla, CA 92093.

Funding

Training in Multi-Scale Analysis of Biological Structure and FunctionT32EB009380 · NIBIB · UNIVERSITY OF CALIFORNIA, SAN DIEGO · PI Andrew D. McCulloch, Padmini Rangamani · 2009 to 2026

$4.8M

NIBIB NIH HHS T32 EB009380

6 · The paper itself

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.

Identifiers

PMID42523535

PMCPMC13405416

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.