Statistical Decision Functions Which Minimize the Maximum Risk

By A. Wald. 1945

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In Game & Decision Theory

Citations in the corpus

Adversarial Example Games (2020, background): “It implies that, while optimized, the model f c converges to a robust classiﬁer against any attack generated by the generator g [51, 67], and leads to increasingly transferable attacks as the adversarial game progresses.”
Towards Deep Learning Models Resistant to Adversarial Attacks (2017, background): “This gives rise to the following saddle point problem, which is our central object of study: (2.1) Formulations of this type (and their ﬁnite-sample counterparts) have a long history in robust optimization, going back to Wald [26, 27, 28].”
Adversarial Vulnerability of Neural Networks Increases With Input Dimension (2018, background): “iption length). More generally, the gradient regularized objective (4) is essentially the ﬁrst-order approximation of the robust training objective max kkL(x+;c) which has a long history in math (Wald, 1945), machine learning (Xu et al., 2009) and now adversarial vulnerability (Sinha et al., 2018). ”
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”
A system of systems approach to energy sustainability assessment: Are all renewables really green? (2015, methodology): “Maximin Wald (1945) Selects the alternative with the maximumlowest performanceunder all criteria”
Image Synthesis with a Single (Robust) Classifier (2019, methodology): “Adversarially robust classiﬁers are trained using the robust optimization objective [Wal45; Mad+18], where instead of minimizing the expected loss L over the data we minimize the worst case loss over a speciﬁc perturbation set ∆ E ( x,y ) ∼D max δ ∈ ∆ L ( x + δ, y ) .”
Do Adversarially Robust ImageNet Models Transfer Better? (2020, methodology): “In robust optimization (dating back to the work of Wald [Wal45]), we replace this standard ERM objective with a robust risk minimization objective: where d is a ﬁxed but arbitrary norm.”
Intriguing properties of adversarial training (2019, methodology): “We note this min-max type optimization can be dated as early as Wald (1945).”
Learning Models with Uniform Performance via Distributionally Robust Optimization (2018, background): “An alternative to our f -divergence based sets {Q : Df (Q||P0) ≤ ρ} are Wasserstein balls [99, 72, 100, 81, 18, 17, 41, 38, 87, 65].”
Maximin effects in inhomogeneous large-scale data (2014, methodology): “If we are looking for effects that guarantee a good performance throughout all possible parameter values, in analogy to decision theoretic consideration [Wald (1945)], two possible definitions of effects are”
Adapt or Perish: A Review of Planning Approaches for Adaptation under Deep Uncertainty (2013, unknown): “Other ways of operationalizing robustness include Wald’s minimax criterion, which chooses the decision alternative that minimizes the maximum risk [93]; minimax regret [94], which results in choosing the solution with the least maximum”
Minimax regret treatment choice with covariates or with limited validity of experiments (2012, methodology): “An important technique to establish this kind of finite sample result is game theoretic analysis (Wald (1945)).”
Computer Vision with a Single (Robust) Classifier (2019, methodology): “Adversarially robust classiﬁers are trained using the robust optimization objective [Wal45; Mad+18], where instead of minimizing the expected loss L over the data (1) we minimize the worst case loss over a speciﬁc perturbation set ∆ Typically, the set ∆ captures imperceptible changes (e.g., small…”
Regular Quantal Response Equilibrium (2005, background): “This concept was introduced by von Neumann and Morgenstern (1944), and is closely related to simultaneous developments of the notion of a statistical decision function in theoretical statistics (Wald, 1945).”
The Art and Science of Modeling Decision-Making Under Severe Uncertainty (2007, background): “This principle is far more radical (Wald 1945, 1950).”