2023/10/26 by Vivek S. Borkar, Borkar, Vivek Shripad · 1 citation
Biochemistry, Genetics and Molecular Biology · #93E20 #Eicosanoids and Hypertension Pharmacology #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2310.17277
openalex publication_date 2023/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article recalls the recent work on a linear programming formulation of infinite horizon risk-sensitive control via its equivalence with a single controller game, using a classic work of Vrieze. This is then applied to a constrained risk-sensitive control problem with a risk-sensitive cost and risk-sensitive constraint. This facilitates a Lagrange multiplier based resolution thereof. In the process, this leads to an unconstrained linear program and its dual, parametrized by a parameter that is a surrogate for Lagrange multiplier. This also opens up the possibility of a primal - dual type numerical scheme wherein the linear program is a subroutine within the subgradient ascent based update rule for the Lagrange multiplier. This equivalent unconstrained risk-sensitive control formulation does not seem obvious without the linear programming equivalents as intermediaries. We also discuss briefly other related algorithmic possibilities for future research.