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arXiv · 2503.12998

An entropy penalized approach for stochastic optimization with marginal law constraints. Complete version

Thibaut Bourdais·Nadia Oudjane·Francesco Russo
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Abstract

This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of problems by splitting the optimization variable and adding an entropic penalization term. We prove that this penalized version constitutes a good approximation of the original control problem and we provide an alternating procedure which converges, under a so called ''Stability Condition'', to an approximate solution of the original problem. We extend the approach introduced in a previous paperof the same authors including a jump dynamics, non-convex costs and constraints on the marginal laws of the controlled process. The interest of our approach is illustrated by numerical simulations related to demand-side management problems arising in power systems.

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Thibaut Bourdais, Nadia Oudjane, Francesco Russo. 2025-03-17. An entropy penalized approach for stochastic optimization with marginal law constraints. Complete version. https://arxiv.org/abs/2503.12998

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