# Robust learning with anytime-guaranteed feedback

arXiv: https://arxiv.org/abs/2105.11135 · HTML: https://mlsanity.com/paper/2105.11135/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 24 May 2021.

## Builds on (most cited first, 10 of 10)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping](https://mlsanity.com/paper/2005.10785/) (2020)
- [SGD and Hogwild! Convergence Without the Bounded Gradients Assumption](https://mlsanity.com/paper/1802.03801/) (2018)
- [Robust Estimation via Robust Gradient Estimation](https://mlsanity.com/paper/1802.06485/) (2018)
- [Geometric Median in Nearly Linear Time](https://mlsanity.com/paper/1606.05225/) (2016)
- [Empirical risk minimization for heavy-tailed losses](https://mlsanity.com/paper/1406.2462/) (2014)
- [Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method](https://mlsanity.com/paper/1907.02707/) (2019)
- [From low probability to high confidence in stochastic convex optimization](https://mlsanity.com/paper/1907.13307/) (2019)

## Abstract (arXiv)

Under data distributions which may be heavy-tailed, many stochastic gradient-based learning algorithms are driven by feedback queried at points with almost no performance guarantees on their own. Here we explore a modified "anytime online-to-batch" mechanism which for smooth objectives admits high-probability error bounds while requiring only lower-order moment bounds on the stochastic gradients. Using this conversion, we can derive a wide variety of "anytime robust" procedures, for which the task of performance analysis can be effectively reduced to regret control, meaning that existing regret bounds (for the bounded gradient case) can be robustified and leveraged in a straightforward manner. As a direct takeaway, we obtain an easily implemented stochastic gradient-based algorithm for which all queried points formally enjoy sub-Gaussian error bounds, and in practice show noteworthy gains on real-world data applications.