Kullback-Leibler divergence constrained distributionally robust optimization

By Zhaolin Hu, J. Hong. 2012

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FOSTER: Feature Boosting and Compression for Class-Incremental Learning (2022, background): “KLD is more suitable for classification tasks, and there are some works [2,6] that point out that the KLD has many advantages in many aspects, including faster optimization and better feature representation.”
Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations (2015, methodology): “Moreover, closed-form counterparts of distributionally robust expectation constraints with Kullback–Leibler ambiguity sets have been derived in [25].”
Data-Driven Optimal Transport Cost Selection For Distributionally Robust Optimization (2017, methodology): “Other discrepancy notions between probability models have been considered, typically using the Kullback-Leibler divergence and other divergence based notions Hu and Hong (2013).”
Distributionally Robust Convex Optimization (2014, background): “We remark that our framework does not cover ambiguity sets that impose infinitely many moment restrictions, as would be required to describe symmetry, independence or unimodality characteristics of the distributions contained in P [36, 50].”
Data-driven chance constrained stochastic program (2015, background): “To address these drawbacks, stochastic programs with distributionally robust (or ambiguous) chance constraints (DCCs) are proposed (see, e.g., [2,8,15,16,32,44,48,49], and [19] 1 ).”
Distributionally Robust Logistic Regression (2015, background): “However, ambiguity sets can also be constructed via distance measures in the spa c of probability distributions such as the Prohorov metric [21] or the Kullback-Leibler divergenc [22].”
Outlier detection using distributionally robust optimization under the Wasserstein metric (2017, methodology): “. The other is to dene Pas a ball of distributions using some probability distance functions such as the ˚-divergences [Bayraksan and Love, 2015], which include the Kullback-Leibler (KL) divergence [Hu and Hong, 2013, Jiang and Guan, 2015] as a special case, the Prokhorov metric [Erdogan and Iyengar”
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, unknown): “[120].”
Distributionally Robust Optimization: A Review (2019, background): “Hu and Hong [156] study a variety of distributionally robust optimization problems, where the ambiguity is in either the objective function or constraints.”