Robust Satisficing

63 Pages Posted: 12 Nov 2019 Last revised: 20 Jul 2021

See all articles by Daniel Zhuoyu Long

Daniel Zhuoyu Long

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management

Melvyn Sim

National University of Singapore (NUS) - NUS Business School

Minglong Zhou

National University of Singapore (NUS) - NUS Business School

Date Written: March 10, 2021

Abstract

We present a general framework for data-driven optimization called robustness optimization that favors solutions for which a risk-aware objective function would best attain an acceptable target even when the actual probability distribution deviates from the empirical distribution. Unlike robust optimization approaches, the decision maker does not have to size the ambiguity set, but specifies an acceptable target, or loss of optimality compared to the empirical optimization model, as a trade off for the model’s ability to withstand greater uncertainty. We axiomatize the decision criterion associated with robustness optimization, termed as the fragility measure and present its representation theorem. Focusing on Wasserstein distance measure with l1-norm, we present tractable robustness optimization models for risk-based linear optimization, combinatorial optimization, and linear optimization problems with recourse. Serendipitously, the insights to the approximation also provide a recipe for approximating solutions for hard stochastic optimization prob- lems without relatively complete recourse. We illustrate in a portfolio optimization problem and a network lot-sizing problem on how we can set targets in the robustness optimization model, which can be more intuitive and effective than specifying the hyper-parameter used in a robust optimization model. The numerical studies show that the solutions to the robustness optimization models are more effective in alleviating the Optimizer’s Curse (Smith and Winkler 2006) by improving the out-of-sample performance evaluated on a variety of metrics.

Keywords: robust optimization, robustness optimization, data-driven optimization, fragility measure

Suggested Citation

Long, Daniel Zhuoyu and Sim, Melvyn and Zhou, Minglong, Robust Satisficing (March 10, 2021). Available at SSRN: https://ssrn.com/abstract=3478930 or http://dx.doi.org/10.2139/ssrn.3478930

Daniel Zhuoyu Long

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management ( email )

Hong Kong
China

Melvyn Sim

National University of Singapore (NUS) - NUS Business School ( email )

1 Business Link
Singapore, 117592
Singapore

Minglong Zhou (Contact Author)

National University of Singapore (NUS) - NUS Business School ( email )

1 Business Link
Singapore, 117592
Singapore

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