Jun-ya Gotoh, Michael Jong Kim, Andrew E. B. Lim
arXiv 26 May 2021 · Mathematics — Optimization · publishedOperations Research (2023) · 8 citations (OpenAlex)
arXiv:2105.12342 · PDF · DOI · OpenAlex · Extracted main text
While solutions of Distributionally Robust Optimization (DRO) problems can sometimes have a higher out-of-sample expected reward than the Sample Average Approximation (SAA), there is no guarantee. In this paper, we introduce a class of Distributionally Optimistic Optimization (DOO) models, and show that it is always possible to “beat" SAA out-of-sample if we consider not just worst-case (DRO) models but also best-case (DOO) ones. We also show, however, that this comes at a cost: Optimistic solutions are more sensitive to model error than either worst-case or SAA optimizers, and hence are less robust and calibrating the worst- or best-case model to outperform SAA may be difficult when data is limited.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Gotoh, J., Kim, M.J., Lim, A.E.B (2020) Calibration of robust empirical optimization models self | 1.000 | 6 | 4 | 100% |
| 2 | Lam, H (2021) On the Impossibility of Statistically Improving Empirical Optimization: A Second-Order Stochastic Dominance Perspective | 0.874 | 9 | 2 | 100% |
| 3 | Anderson, E.J., Philpott, A (2020) Improving sample average approximation using distributional robustness | 0.874 | 5 | 2 | 100% |
| 4 | Gotoh, J., Kim, M.J., Lim, A.E.B (2018) Robust empirical optimization is almost the same as mean-variance optimization self | 0.830 | 7 | 6 | 57% |
| 5 | van der Vaart, A.W (2000) Asymptotic Statistics | 0.644 | 3 | 2 | 67% |
| 6 | Nguyen, V.A., Shafieezadeh-Abadeh, S., Yue, M.C., Kuhn, D., Wieseman… (2019) Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation | 0.644 | 2 | 2 | 100% |
| 7 | Gotoh, J., Kim, M.J., Lim, A.E.B (2020) Worst-case sensitivity self | 0.585 | 3 | 1 | 100% |
| 8 | Kundhi, G., Rilstone, P (2008) The third order bias of nonlinear estimators | 0.511 | 2 | 2 | 50% |
| 9 | Chen, L.L., Royset, J.O (2022) Rockafellian Relaxation in Optimization under Uncertainty: Asymptotically Exact Formulations (https://arxiv.org/abs/2204.04762) | 0.511 | 2 | 1 | 100% |
| 10 | Duchi, J.C., Glynn, P.W., Namkoong, H (2016) Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 28 scored citations.