Raghav Tripathi (UW)
Monday, February 13, 2023 - 2:30pm
MGH-085
Optimization on graphons naturally arise in many different contexts. In particular, such problems can be seen as limits of optimization problems over large dense graphs with unlabelled vertices. We show that discrete noisy stochastic optimization algorithms over finite graphs have a well-defined analytical scaling limit as the size of the network grows to infinity. The limiting curves are curves of graphons and can be are given by a novel notion of McKean-Vlasov equation on graphons. In the asymptotically zero-noise case, the limit can be interpreted as a gradient flow on the metric space of graphons. This mirrors the Wasserstein gradient flows on probability measures which arise as a continuum limit of particle systems in mean field interaction with a gradient type potential.