Deterministic particle flows for constraining SDEs

Dimitra Maoutsa; Manfred Opper

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arXiv · 2110.13020

Deterministic particle flows for constraining SDEs

Dimitra Maoutsa·Manfred Opper

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Abstract

Devising optimal interventions for diffusive systems often requires the solution of the Hamilton-Jacobi-Bellman (HJB) equation, a nonlinear backward partial differential equation (PDE), that is, in general, nontrivial to solve. Existing control methods either tackle the HJB directly with grid-based PDE solvers, or resort to iterative stochastic path sampling to obtain the necessary controls. Here, we present a framework that interpolates between these two approaches. By reformulating the optimal interventions in terms of logarithmic gradients ( scores ) of two forward probability flows, and by employing deterministic particle methods for solving Fokker-Planck equations, we introduce a novel fully deterministic framework that computes the required optimal interventions in one shot.

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BibTeX RIS

Dimitra Maoutsa, Manfred Opper. 2021-10-25. Deterministic particle flows for constraining SDEs. https://arxiv.org/abs/2110.13020

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