# Optimistic Robust Optimization With Applications To Machine Learning

arXiv: https://arxiv.org/abs/1711.07511 · HTML: https://mlsanity.com/paper/1711.07511/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2017.

## Built on by (most cited first, 3 of 3)

- [A data-driven approach to beating SAA out-of-sample](https://mlsanity.com/paper/2105.12342/) (2021)
- [Rockafellian Relaxation and Stochastic Optimization under Perturbations](https://mlsanity.com/paper/2204.04762/) (2022)
- [On Tractability, Complexity, and Mixed-Integer Convex Programming Representability of Distributionally Favorable Optimization](https://mlsanity.com/paper/2401.17899/) (2024)

## Abstract (arXiv)

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this paper, we explore an optimistic, or best-case view of uncertainty and show that it can be a fruitful approach. We show that these techniques can be used to address a wide variety of problems. First, we apply our methods in the context of robust linear programming, providing a method for reducing conservatism in intuitive ways that encode economically realistic modeling assumptions. Second, we look at problems in machine learning and find that this approach is strongly connected to the existing literature. Specifically, we provide a new interpretation for popular sparsity inducing non-convex regularization schemes. Additionally, we show that successful approaches for dealing with outliers and noise can be interpreted as optimistic robust optimization problems. Although many of the problems resulting from our approach are non-convex, we find that DCA or DCA-like optimization approaches can be intuitive and efficient.