Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem
Abstract
We investigate exploratory randomization for an extended linear-exponential-quadratic-Gaussian (LEQG) control problem in discrete time. This extended control problem is related to the structure of risk-sensitive investment management applications. We introduce exploration through a randomization of the control. Next, we apply the duality between free energy and relative entropy to reduce the LEQG problem to an equivalent risk-neutral LQG control problem with an entropy regularization term, see, e.g. Dai Pra et al. (1996), for which we present a solution approach based on Dynamic Programming. Our approach, based on the energy-entropy duality may also be considered as leading to a justification for the use, in the literature, of an entropy regularization when applying a randomized control.
Keywords
Cite
@article{arxiv.2501.06275,
title = {Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem},
author = {Sebastien Lleo and Wolfgang Runggaldier},
journal= {arXiv preprint arXiv:2501.06275},
year = {2025}
}