Two Polyak-Type Step Sizes for Mirror Descent

TL;DR

This paper introduces two new Polyak-type step sizes for mirror descent algorithms that do not require knowledge of the optimal function value, and proves their convergence for convex locally Lipschitz functions.

Contribution

The paper presents novel Polyak-type step sizes for mirror descent that eliminate the need for the optimal value, expanding the applicability of these methods.

Findings

Both step sizes converge for convex locally Lipschitz functions.

The proposed step sizes do not require the optimal objective value.

Convergence proofs are provided for the new step sizes.

Abstract

We propose two Polyak-type step sizes for mirror descent and prove their convergences for minimizing convex locally Lipschitz functions. Both step sizes, unlike the original Polyak step size, do not need the optimal value of the objective function.