Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size

no code implementations • 8 Apr 2024 • Huafu Liao, Alpár R. Mészáros, Chenchen Mou, Chao Zhou

Using these uniform regularity results, we show the convergence of the minima of objective functionals and optimal parameters of the neural SDEs as the sample size N tends to infinity.

Mean Field Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity

no code implementations • 29 Jan 2021 • Wilfrid Gangbo, Alpár R. Mészáros, Chenchen Mou, Jianfeng Zhang

In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games master equations.

Analysis of PDEs Optimization and Control Probability 35R15, 49N80, 49Q22, 60H30, 91A16, 93E20