Robust empirical optimization is almost the same as mean-variance optimization

By Jun-ya Gotoh, Michael Jong Kim, Andrew E. B. Lim. 2018

115 citations recorded by the source corpus.

Abstract We formulate a distributionally robust optimization problem where the deviation of the alternative distribution is controlled by a ϕ -divergence penalty in the objective, and show that a large class of these problems are essentially equivalent to a mean–variance problem. We also show that while a “small amount of robustness” always reduces the in-sample expected reward, the reduction in the variance, which is a measure of sensitivity to model misspecification, is an order of magnitude larger.

Subfields: Electrical and Electronic Engineering, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Variance-based Regularization with Convex Objectives (2016, background): “[16] also provide a number of asymptotic results showing relationships between the robust risk Rn(θ;Pn) and variance regularization, but they do not leverage these results for guarantees on the solutions θ̂n.”
Learning Models with Uniform Performance via Distributionally Robust Optimization (2018, result): “Although it is hard to draw conclusions from this experiment due to improved overall performance when increasing ρ, we conjecture that is due to the regularization effect for relatively small values of ρ described by many previous authors [45, 60, 35, 62, 69].”
Wasserstein Distributional Robustness and Regularization in Statistical Learning (2017, background): “For example, Gotoh et al. (2015) and Lam (2016) have pointed out that DRSO with φ -divergence is ﬁrst-order equivalent to variance regularization.”
Fairness risk measures (2019, background): “The idea of moving beyond expectations to a general aggregation of the per-instance losses has precedent in learning theory [Chapelle et al., 2001, Maurer and Pontil, 2009] and robust optimisation [Duchi et al., 2016, Gotoh et al., 2018].”