On general minimax theorems

By M. Sion. 1958

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Citations in the corpus

Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness (2017, background): “Since Λ is a compact and convex set, the minmax condition continues to hold [Sion, 1958]:”
Variational Bayesian Reinforcement Learning with Regret Bounds (2018, background): “P k i=1 exp K X i (1 = ) and ? / exp K X i (1 = ? ), which are unique. Since L isdifferentiable,convex-concave,and iscompact,itsatisesa strongmax-min or saddle-point property [17, Exercise 3.14][106, 95], i.e., max 2 L ( ? ; ) = L ( ? ; ? ) = min 0 L (; ? ): (8) This observation brings us to th”
A Reductions Approach to Fair Classification (2018, background): “Under standard non-degeneracy assumptions, such as the setH being closed under convex combinations [12], the optimization problem (3) is equivalent to the saddle-point problem”
Rényi Divergence and Kullback-Leibler Divergence (2012, methodology): “We will prove this identity using Sion’s minimax theorem [56], [57], which we state with its arguments exchanged to make them line up with the arguments of ψα: Theorem 35 (Sion’s Minimax Theorem).”
Loss-Sensitive Generative Adversarial Networks on Lipschitz Densities (2017, neutral): “Then, according to the Sion’s theorem [32], with Lθ and PG being optimized over Fκ, there exists a Nash equilibrium (θ∗, φ∗).”
How to Train Your DRAGAN (2017, methodology): “The minimax theorem has been significantly generalized since this original formulation, and the work of Sion [3] provides a broad class of scenarios in which inf sup{} = sup inf{}.”
A Shrinkage Approach to Model Uncertainty and Asset Allocation (2005, background): “With considerable doubts about both estimates, uncertainty-averse investors do not want to rely on either the estimate restricted by the CAPM or the unrestricted estimate.”
Games of incomplete information, ergodic theory, and the measurability of equilibria (2003, background): “The proof of the above follows Sion's Theorem [ 11 ], see also [9].”
Optimal Shape and Location of Sensors for Parabolic Equations with Random Initial Data (2014, methodology): “It follows from the Sion minimax theorem (see [59]) that”
Quantum Information Processing with Finite Resources - Mathematical Foundations (2015, methodology): “n sB2S(B D ts a B 0 C r E ABC : (5.56) At this points it only remains to show that the minimum over s B and the maximum over t C can be interchanged. This can be veriﬁed using Sion’s minimax theorem [146], noting that hrjs a0 B ta0 C jri ABC is convex in s B and concave in t C, and we are optimizing”
Importance Sampling, Large Deviations, and Differential Games (2004, methodology): “The interchange of the infimum and supremum is valid thanks to the min/max theorem [33], the convexity of C and {a : kak # M}; and the compactness of {a : kak # M}: We will use the definition LMðbÞ8 kak#M sup 1⁄2ka;bl2 HðaÞ :”
An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing (2010, unknown): “Theorem 4 (Sion's Minimax Theorem [88]).”
Intelligent Reflecting Surface Assisted Secrecy Communication: Is Artificial Noise Helpful or Not? (2019, unknown): “Therefore, following Sion’s minimax theorem [10], (P1.”
Convex Optimization in Signal Processing and Communications (2009, methodology): “In convexconcave problems we can replace the order of the minimization and the maximization [43], as incorporated in the following proposition.”