# Scalable Distributional Robustness in a Class of Non Convex Optimization with Guarantees

arXiv: https://arxiv.org/abs/2205.15624 · HTML: https://mlsanity.com/paper/2205.15624/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 11 of 11)

- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [An Online Method for A Class of Distributionally Robust Optimization with Non-Convex Objectives](https://mlsanity.com/paper/2006.10138/) (2020)
- [Distributionally Robust Submodular Maximization](https://mlsanity.com/paper/1802.05249/) (2018)
- [Optimistic bounds for multi-output prediction](https://mlsanity.com/paper/2002.09769/) (2020)
- [Submodularity and Local Search Approaches for Maximum Capture Problems under Generalized Extreme Value Models](https://mlsanity.com/paper/2102.05754/) (2021)
- [The Mysteries of Security Games: Equilibrium Computation Becomes Combinatorial Algorithm Design](https://mlsanity.com/paper/1603.02377/) (2016)
- [Stochastic Optimization for Non-convex Inf-Projection Problems](https://mlsanity.com/paper/1908.09941/) (2019)

## Built on by (most cited first, 2 of 2)

- [Initializing Services in Interactive ML Systems for Diverse Users](https://mlsanity.com/paper/2312.11846/) (2023)
- [Temporal Robustness in Discrete Time Linear Dynamical Systems](https://mlsanity.com/paper/2505.02347/) (2025)

## Abstract (arXiv)

Distributionally robust optimization (DRO) has shown lot of promise in providing robustness in learning as well as sample based optimization problems. We endeavor to provide DRO solutions for a class of sum of fractionals, non-convex optimization which is used for decision making in prominent areas such as facility location and security games. In contrast to previous work, we find it more tractable to optimize the equivalent variance regularized form of DRO rather than the minimax form. We transform the variance regularized form to a mixed-integer second order cone program (MISOCP), which, while guaranteeing near global optimality, does not scale enough to solve problems with real world data-sets. We further propose two abstraction approaches based on clustering and stratified sampling to increase scalability, which we then use for real world data-sets. Importantly, we provide near global optimality guarantees for our approach and show experimentally that our solution quality is better than the locally optimal ones achieved by state-of-the-art gradient-based methods. We experimentally compare our different approaches and baselines, and reveal nuanced properties of a DRO solution.