Mitigate Overconservatism for Robust Optimization by Adapting to Opportunities

TL;DR

This paper introduces a new criterion for robust optimization that adaptively balances conservatism and opportunity, improving performance guarantees and competitive ratios, demonstrated through theoretical analysis and numerical experiments.

Contribution

A novel adaptive conservatism criterion is proposed, enabling continuous adjustment to opportunities while maintaining key robust optimization advantages.

Findings

Average reward improved by 4% to 17% in numerical tests.

Analytical solutions and competitive ratios derived for robust one-way trading.

Framework effectively balances conservatism and opportunity in robust optimization.

Abstract

Overconservatism has long been recognized as a major issue with robust optimization, despite its key advantages of tractability, performance guarantee, and limited information. To address this issue, a new criterion is proposed that can adapt its level of conservatism continuously to the opportunities out there, while maintaining all the key advantages just mentioned. With this criterion, a general framework of conservatism control based on optimal performance guarantee is developed and characterized, and a new approach to competitive ratio analysis is established. The criterion is then applied to the robust one-way trading problem, where analytical solution is obtained, and the competitive ratio is derived directly via the new approach. Numerical experiments are conducted to demonstrate the effectiveness of conservatism control based on the new criterion, with the average reward improvable by 4% - 17% over the other commonly used criteria.