# Distributionally Robust Learning with Weakly Convex Losses: Convergence Rates and Finite-Sample Guarantees

arXiv: https://arxiv.org/abs/2301.06619 · HTML: https://mlsanity.com/paper/2301.06619/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2023.

## Built on by (most cited first, 4 of 4)

- [Not All Semantics are Created Equal: Contrastive Self-supervised Learning with Automatic Temperature Individualization](https://mlsanity.com/paper/2305.11965/) (2023)
- [Asynchronous Multi-Model Dynamic Federated Learning over Wireless Networks: Theory, Modeling, and Optimization](https://mlsanity.com/paper/2305.13503/) (2023)
- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)
- [Stochastic Nested Compositional Bi-level Optimization for Robust Feature Learning](https://mlsanity.com/paper/2307.05384/) (2023)

## Abstract (arXiv)

We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single time-scale algorithm, involving two versions of the inner function value tracking: linearized tracking of a continuously differentiable loss function, and SPIDER tracking of a weakly convex loss function. We adopt the norm of the gradient of the Moreau envelope as our measure of stationarity and show that the sample complexity of O(varepsilon-3) is possible in both cases, with only the constant larger in the second case. Finally, we demonstrate the performance of our algorithm with a robust learning example and a weakly convex, non-smooth regression example.