Robust Data-Driven Accelerated Mirror Descent

TL;DR

This paper introduces a momentum-augmented accelerated mirror descent algorithm that leverages data-driven neural network parameterization to achieve faster convergence and enhanced robustness in optimization tasks.

Contribution

It extends the learning-to-optimize framework by integrating momentum into neural network-based mirror descent, combining acceleration with stability.

Findings

Achieves faster convergence in optimization problems.

Demonstrates increased robustness to parameter variations.

Effective in denoising and deconvolution tasks.

Abstract

Learning-to-optimize is an emerging framework that leverages training data to speed up the solution of certain optimization problems. One such approach is based on the classical mirror descent algorithm, where the mirror map is modelled using input-convex neural networks. In this work, we extend this functional parameterization approach by introducing momentum into the iterations, based on the classical accelerated mirror descent. Our approach combines short-time accelerated convergence with stable long-time behavior. We empirically demonstrate additional robustness with respect to multiple parameters on denoising and deconvolution experiments.