Conformal mirror descent with logarithmic divergences

Abstract The logarithmic divergence is an extension of the Bregman motivated by optimal transport and a generalized convex duality, satisfies many remarkable properties. Using geometry induced divergence, we introduce generalization continuous time mirror descent that term conformal descent. We derive its dynamics under map, show it change corresponding Hessian gradient flow. also prove convergence results in time. apply to online estimation exponential family, construct family flows on unit simplex via Dirichlet problem.