The Power Descent, defined for allα = 1, is one such algorithm and we establish in our work the full proof ofits convergence towards the optimal mixture weights whenα < 1.

Bayesian Inference involves being able to compute or sample from the posterior density.

This paper focuses on applying entropic mirror descent to solve linear systems, where the main challenge for the convergence analysis stems from the unboundedness of the domain. To overcome this without imposing restrictive assumptions, we introduce a variant of Polyak-type stepsizes. Along the way, we strengthen the bound for $\ell_1$-norm implicit bias, obtain sublinear and linear convergence results, and generalize the convergence result to arbitrary convex $L$-smooth functions. We also propose an alternative method that avoids exponentiation, resembling the original Hadamard descent, but with provable convergence.