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arXiv · 2211.15652

Stochastic Optimal Control via Local Occupation Measures

Flemming Holtorf·Alan Edelman·Christopher Rackauckas
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Abstract

Viewing stochastic processes through the lens of occupation measures has proved to be a powerful angle of attack for the theoretical and computational analysis of stochastic optimal control problems. We present a simple modification of the traditional occupation measure framework derived from resolving the occupation measures locally on a partition of the control problem's space-time domain. This notion of local occupation measures provides fine-grained control over the construction of structured semidefinite programming relaxations for a rich class of stochastic optimal control problems with embedded diffusion and jump processes via the moment-sum-of-squares hierarchy. As such, it bridges the gap between discretization-based approximations to the Hamilton-Jacobi-Bellmann equations and occupation measure relaxations. We demonstrate with examples that this approach enables the computation of high quality bounds for the optimal value of a large class of stochastic optimal control problems with significant performance gains relative to the traditional occupation measure framework.

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Flemming Holtorf, Alan Edelman, Christopher Rackauckas. 2025-01-17. Stochastic Optimal Control via Local Occupation Measures. https://arxiv.org/abs/2211.15652

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