Seminar

Department of Systems Engineering and Engineering Management
                    The Chinese University of Hong Kong

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Title: Calibration of robust empirical optimization problems

Speaker: Prof. Andrew Lim

                 Department of Analytics and Operations and the Department of Finance

                 National University of Singapore

Abstract: In this talk, I will discuss recent results on the out-of-sample properties of robust empirical optimization and develop a theory for data-driven calibration of the “robustness parameter” for worst-case maximization problems with concave reward functions. Building on the intuition that robust optimization reduces the sensitivity to model misspecification by controlling the spread of the reward distribution, I show that the first-order benefit of “little bit of robustness” is a significant reduction in the variance of the out-of-sample reward while the corresponding impact on the mean is almost an order of magnitude smaller. One implication is that a substantial reduction in the variance of the out-of-sample reward (i.e., sensitivity of the expected reward to model misspecification) is possible at little cost if the robustness parameter is properly calibrated. To this end, I introduce the notion of a robust mean-variance frontier to select the robustness parameter and show that it can be approximated using resampling methods like the bootstrap. Examples show that robust solutions resulting from “open loop” calibration methods (e.g., selecting a 90% confidence level regardless of the data and objective function) can be very conservative out-of-sample, while selecting an ambiguity parameter that optimizes an estimate of the out-of-sample expected reward (e.g., via the bootstrap) with no regard for the variance is often insufficiently robust. I also explain why the out-of-sample expected reward generated by the solution of a worst-case problem can sometimes exceed that of a sample-average optimizer. (Joint work with Junya Gotoh (Chuo University) and Michael Kim (University of British Columbia)).