# Risk-sensitive control, single controller games and linear programming

arXiv: https://arxiv.org/abs/2310.17277 · HTML: https://mlsanity.com/paper/2310.17277/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2023.

## Built on by (most cited first, 1 of 1)

- [Tractable Equilibrium Computation in Markov Games through Risk Aversion](https://mlsanity.com/paper/2406.14156/) (2024)

## Abstract (arXiv)

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.