# Robust Optimization for Non-Convex Objectives

**Authors:** Robert Chen, Brendan Lucier, Yaron Singer, Vasilis Syrgkanis  
**arXiv:** [1707.01047](https://arxiv.org/abs/1707.01047)  
**Date:** 2017-07-04  
**Summary page:** https://www.summarizepaper.com/en/paper/1707.01047v1/

## Key points

- The paper addresses the problem of robust optimization
- The authors propose a reduction from robust improper optimization to Bayesian optimization
- They utilize an oracle that provides $\alpha$-approximate solutions for distributions over objectives
- Using this oracle, they compute a distribution over solutions that is also $\alpha$-approximate in the worst case
- De-randomizing this solution is generally NP-hard, but achievable for a wide range of statistical learning tasks
- The authors apply their approach to robust neural network training and submodular optimization as specific problems
- Experimental tests are conducted on corrupted character classification and robust influence maximization in networks
- The experiments provide empirical evidence of the effectiveness and applicability of their approach
- This paper presents a novel approach to robust optimization by leveraging Bayesian optimization techniques with implications for various domains such as machine learning and network analysis.

## Summary

The paper titled "Robust Optimization for Non-Convex Objectives" addresses the problem of robust optimization, where the objective is to optimize in the worst-case scenario over a class of objective functions. The authors propose a reduction from robust improper optimization to Bayesian optimization. They achieve this by utilizing an oracle that provides $\alpha$-approximate solutions for distributions over objectives. Using this oracle, they compute a distribution over solutions that is also $\alpha$-approximate in the worst case. The authors demonstrate that de-randomizing this solution is generally NP-hard. However, they show that it can be achieved for a wide range of statistical learning tasks. To validate their approach, they apply their results to two specific problems: robust neural network training and submodular optimization. In order to evaluate their proposed method experimentally, the authors conduct tests on corrupted character classification and robust influence maximization in networks. These experiments provide empirical evidence of the effectiveness and applicability of their approach. Overall, this paper presents a novel approach to robust optimization by leveraging Bayesian optimization techniques with implications for various domains such as machine learning and network analysis.