Risk-sensitive control, single controller games and linear programming

Vivek Shripad Borkar

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arXiv · 2310.17277

Risk-sensitive control, single controller games and linear programming

Vivek Shripad Borkar

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Abstract

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.

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Vivek Shripad Borkar. 2023-10-26. Risk-sensitive control, single controller games and linear programming. https://arxiv.org/abs/2310.17277

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