📝 SummarXiv

Abstract

Overconservatism has long been recognized as a major issue of robust optimization, despite its major advantages of tractability, performance guarantee, and limited information. A new criterion based on adjustable regret is proposed to address this issue by adapting the level of conservatism to the environment, while maintaining all the aforementioned advantages. The level of conservatism can be fine-tuned by maximizing the reward guarantee for scenarios representative of opportunities provided by experts as most likely values, leading to a simple heuristic to best catch opportunities. This criterion also supports a new approach to competitive ratio analysis that is applicable even to multistage problems. The new criterion is then applied to the one-way trading problem with analytical solutions, from which the competitive ratio is easily derived by the new approach. Numerical experiments are conducted to demonstrate fine control of conservatism and the effectiveness of the heuristic, with the average reward improved in one case by 3 - 9% over other commonly used criteria.