A Robust Robust Optimization Result

TL;DR

This paper investigates the impact of optimizing an inaccurate objective instead of the true one, demonstrating that the average loss in objective value remains small across any compact feasible region.

Contribution

It provides a theoretical analysis showing that the expected loss from objective inaccuracies is minimal, offering robustness insights for optimization problems.

Findings

Average loss in objective value is very small with inaccurate objectives.

The result holds for any arbitrary compact feasible region.

Provides theoretical bounds on objective loss due to inaccuracies.

Abstract

We study the loss in objective value when an inaccurate objective is optimized instead of the true one, and show that "on average" this loss is very small, for an arbitrary compact feasible region.