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arXiv · 2501.06275

Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem

Sebastien Lleo·Wolfgang Runggaldier
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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.

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Sebastien Lleo, Wolfgang Runggaldier. 2025-01-10. Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem. https://arxiv.org/abs/2501.06275

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