Numerical approximation of McKean-Vlasov SDEs via Stochastic Gradient Descent


We propose a novel approach of numerically approximate McKean-Vlasov SDEs that avoids the usual interacting particle approximation and Propagation of Chaos results altogether. After (possibly) leveraging the projection of SDEs coefficients on the Fourier basis [1], we use the stochastic gradient descent algorithm to approximate its measure-dependent components — our technique approximates the functional of the measure instead of the measure itself. This technique avoids particle approximation. We present several numerical experiments in support of the algorithm. 
This talk is based on join work [2] with A. Agarwal (U. of Glasgow) and S. Pagliarani (U. of Bologna).

[1] Belomestny, D., and Schoenmakers, J. Projected particle methods for solving McKean-Vlasov stochastic differential equations. SIAM Journal on Numerical Analysis 56, 6, 3169–3195, 2018
[2] Agarwal, A., Pagliarani, S., and dos Reis, G. Approximating McKean-Vlasov SDEs via SGD. Forthcoming, 2022

Brief Biography

Gonçalo dos Reis is an associate professor at the University of Edinburgh, School of Mathematics. His research topics include Stochastic analysis, Numerical analysis, Finance, economics and game theory.

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