Élise Devey - A Frank–Wolfe-Type Algorithm for High-Dimensional Stochastic Control Problems with Non-Exchangeable Agents

vendredi 6 nov. 2026, 16:00 → 17:00 Europe/Paris

Salle Maurice Fréchet (IHP - Bâtiment Borel)

Abstract : This paper presents a Frank--Wolfe type algorithm for computing approximately optimal distributed stochastic controls in a large population of $N$ agents cooperating to minimize a convex cost functional. The cost includes a heterogeneous pairwise interaction term between the agents' controls, which rules out a direct treatment by the classical Mean Field Control framework. Working directly at finite $N$ rather than through a mean-field limit, we prove that the distributed controls returned by our algorithm are $N^{-1/2}$-optimal for the original problem, with an explicit rate in the number of iterations $K$ and in a measure of interaction heterogeneity, $\Delta_{\mathrm{spread}}$, that we introduce. The algorithm avoids the curse of dimensionality: at each iteration, the coupled $N$-agent problem is linearized and decomposed into $N$ independent, low-dimensional subproblems. We illustrate the approach on a linear-quadratic benchmark, for which we derive a closed-form Riccati-type characterization of the optimal control, and validate the predicted convergence rate numerically. Interaction structures of this heterogeneous, pairwise-penalized type arise naturally in applications such as electricity grid flexibility management, where local storage units are coupled through shared transmission-line capacity constraints.