# Adaptive Stochastic Mirror Descent for Constrained Optimization

## TL;DR

This paper introduces an adaptive stochastic mirror descent method for constrained convex optimization, demonstrating faster convergence rates than fixed stepsize approaches and achieving optimality in theoretical bounds.

## Contribution

It proposes an adaptive stepsize scheme for stochastic mirror descent, improving convergence speed and optimality guarantees over traditional fixed stepsize methods.

## Key findings

- Faster convergence with adaptive stepsizes
- Optimal convergence rates in theory
- Enhanced performance on constrained problems

## Abstract

Mirror Descent (MD) is a well-known method of solving non-smooth convex optimization problems. This paper analyzes the stochastic variant of MD with adaptive stepsizes. Its convergence on average is shown to be faster than with the fixed stepsizes and optimal in terms of lower bounds.