Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918143923847168 |
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| author | Lleo, Sebastien Runggaldier, Wolfgang |
| author_facet | Lleo, Sebastien Runggaldier, Wolfgang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem Lleo, Sebastien Runggaldier, Wolfgang Optimization and Control Portfolio Management 93E20, 93E35, 91G80, 68T05 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. |
| title | Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem |
| topic | Optimization and Control Portfolio Management 93E20, 93E35, 91G80, 68T05 |
| url | https://arxiv.org/abs/2501.06275 |