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

arXiv: https://arxiv.org/abs/2501.06275 · HTML: https://mlsanity.com/paper/2501.06275/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2025.

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

- [Exploratory Randomization for Discrete-Time Risk-Sensitive Benchmarked Investment Management with Reinforcement Learning](https://mlsanity.com/paper/2603.00738/) (2026)

## Abstract (arXiv)

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.