On Robust Optimization

By Elisabeth Köbis. 2015

2,680 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability, Optimization & Training

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Citations in the corpus

Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates (2019, background): “These problems encompass both convex minimization and saddle point problems arising in robust supervised learning [8, 84] and learning with non-separable losses or regularizers [4, 34].”
Towards Deep Learning Models Resistant to Adversarial Attacks (2017, background): “We refer the reader to (Ben-Tal et al., 2009) for an overview of this field.”
On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima (2016, methodology): “A natural way of avoiding sharp minima is through Robust Optimization techniques [1].”
A Rotation and a Translation Suffice: Fooling CNNs with Simple Transformations (2017, background): “Robust optimization has a rich history (Ben-Tal et al., 2009) and has recently been applied successfully in the context of defending neural networks against adversarial examples (Madry et al.”
Provable defenses against adversarial examples via the convex outer adversarial polytope (2017, background): “Our work also fundamentally relates to the field of robust optimization (Ben-Tal et al., 2009), the task of solving an optimization problem where some of the problem data is unknown, but belong to a bounded set.”
Certifying Some Distributional Robustness with Principled Adversarial Training (2017, background): “Unfortunately, this approach is intractable except for specially structured losses, such as the composition of a linear and simple convex function (Ben-Tal et al., 2009; Xu et al., 2009; 2012).”
Invariant Risk Minimization (2019, background): “Second, we could minimize R(f) = maxe∈Etr R (f) − re, a robust learning objective where the constants re serve as environment baselines [2, 6, 15, 46].”
Variance-based Regularization with Convex Objectives (2016, methodology): “, 2014; Lam and Zhou, 2015), where the goal (as in robust optimization more broadly (Ben-Tal et al., 2009)) is to protect against all deviations from a nominal data model.”
Robustness May Be at Odds with Accuracy (2018, background): “Speciﬁcally, adversarial training corresponds to a natural robust optimization approach to solving this problem (Ben-Tal et al., 2009).”
Adversarially Robust Generalization Requires More Data (2018, background): “the standard robust optimization approach [6, 36, 54] – also known as adversarial training [21, 51] – and (approximately) solve the saddle point problem”
Stochastic Variance Reduction Methods for Saddle-Point Problems (2016, neutral): “The framework of robust optimization [16] aims at optimizing an objective function with uncertain data.”
A Survey on Metric Learning for Feature Vectors and Structured Data (2013, methodology): “The approach is based on robust optimization (Ben-Tal et al., 2009): assuming that a proportion 1 − η of the m training constraints (say triplets) are incorrect, it minimizes some loss function ℓ for any η fraction of the triplets: min M∈Sd + ,t t + λ 2 ‖M‖F s.t. t ≥ m ∑ i=1 qiℓ ( d2M (xi,x ′′ i )−…”
Cyberbullying Detection With Fairness Constraints (2020, background): “Essentially, such worst-case oriented reformulation of the fairness constraints can be considered as a robust optimization problem [57].”
Wasserstein Distributional Robustness and Regularization in Statistical Learning (2017, positive): “In addition, DRSO reduces to robust optimization (Bertsimas and Sim 2004, Ben-Tal et al. 2009) if the set is speciﬁed only by the support of the distributions.”
Stochastic Gradient Methods for Distributionally Robust Optimization with f-divergences (2016, neutral): “For k 2 [2,1), any p 2 P ⇢,n, , Algorithm 1 with ↵ p = n k p ⇢ k (1)/ (4C(3)”
Quantifying Distributional Model Risk via Optimal Transport (2016, neutral): “…(2016) for Wasserstein distance based neighborhoods, Erdoğan and Iyengar (2006) for neighborhoods based on Prokhorov metric, Bandi et al. (2015); Bandi and Bertsimas (2014) for uncertainty sets based on statistical tests and Ben-Tal et al. (2009); Bertsimas and Sim (2004) for a general overview.”
Robust Dynamic Operating Envelopes for DER Integration in Unbalanced Distribution Networks (2022, methodology): “Note that while the notion of RDOEs discussed in this article provides for DOE solutions hedged against uncertainty, as done more generally in the discipline of robust mathematical optimisation (RO) [37], [38], the speciﬁc approaches used to compute RDOEsarenotnecessarilyROmethods.”
Adaptive Robust Optimization With Dynamic Uncertainty Sets for Multi-Period Economic Dispatch Under Significant Wind (2014, methodology): “For the uncertainty set to be computationally tractable, f should be semi-definite representable [2].”
Adversarial Risk and Robustness: General Definitions and Implications for the Uniform Distribution (2018, positive): “A more recent framework was developed in [MMS + 18, SST + 18] for modeling risk and robustness that is inspired by robust optimization [BTGN09] (with an underlying metric space) and model adversaries that corrupt the the original instance in (exponentially more) ways.”