# High Probability Convergence for Accelerated Stochastic Mirror Descent

arXiv: https://arxiv.org/abs/2210.00679 · HTML: https://mlsanity.com/paper/2210.00679/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 7 references that are in the map.
- First posted on arXiv 3 Oct 2022.

## Builds on (most cited first, 1 of 1)

- [Tight Analyses for Non-Smooth Stochastic Gradient Descent](https://mlsanity.com/paper/1812.05217/) (2018)

## Built on by (most cited first, 1 of 1)

- [Is Stochastic Mirror Descent Vulnerable to Adversarial Delay Attacks? A Traffic Assignment Resilience Study](https://mlsanity.com/paper/2304.01161/) (2023)

## Abstract (arXiv)

In this work, we describe a generic approach to show convergence with high probability for stochastic convex optimization. In previous works, either the convergence is only in expectation or the bound depends on the diameter of the domain. Instead, we show high probability convergence with bounds depending on the initial distance to the optimal solution as opposed to the domain diameter. The algorithms use step sizes analogous to the standard settings and are universal to Lipschitz functions, smooth functions, and their linear combinations.