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We introduce two algorithms for nonconvex regularized finite summinimization, where typical Lipschitz differentiability assumptions are relaxedto the notion of relative smoothness. The first one is a Bregman extension ofFinito/MISO, studied for fully nonconvex problems when the sampling israndomized, or under convexity of the nonsmooth term when it is essentiallycyclic. The second algorithm is a low-memory variant, in the spirit of SVRG andSARAH, that also allows for fully nonconvex formulations. Our analysis is maderemarkably simple by employing a Bregman Moreau envelope as Lyapunov function.In the randomized case, linear convergence is established when the costfunction is strongly convex, yet with no convexity requirements on theindividual functions in the sum. For the essentially cyclic and low-memoryvariants, global and linear convergence results are established when the costfunction satisfies the Kurdyka-\L ojasiewicz property.

Bregman Finito/MISO for nonconvex regularized finite sum minimization without Lipschitz gradient continuity