FOUNDATIONS OF BARE-SIMULATION OPTIMIZATION OF DISTANCES
Broniatowski M, Stummer W (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 36
Pages Range: 2237-2291
Journal Issue: 3
DOI: 10.1214/25-AAP2278
Abstract
The constrained minimization—respectively maximization—of dissimilarity-modeling divergences (i.e., generally nonsymmetric, directed distances) and of related generalized entropies is a fundamental task in many areas of quantitative sciences. On ℕ^K of arbitrary dimension K, we derive a method which tackles such kind of constrained optimization problems—and beyond—by limits of sequences of appropriately constructed, dimension-free, typically comfortably simulable random vectors; almost no assumptions (like convexity) on the set of constraints are needed. This very largely extends our recent results on f-divergences which can be connected to light-tailed probability distributions in a certain manner (cf. IEEE Trans. Inform. Theory (2023) 69 3062–3120). For instance, in the current paper we cover constrained optimizations of arbitrary f-divergences, Bregman distances, scaled Bregman distances and weighted ℓ_r-distances.
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France (FR)How to cite
APA:
Broniatowski, M., & Stummer, W. (2026). FOUNDATIONS OF BARE-SIMULATION OPTIMIZATION OF DISTANCES. Annals of Applied Probability, 36(3), 2237-2291. https://doi.org/10.1214/25-AAP2278
MLA:
Broniatowski, Michel, and Wolfgang Stummer. "FOUNDATIONS OF BARE-SIMULATION OPTIMIZATION OF DISTANCES." Annals of Applied Probability 36.3 (2026): 2237-2291.
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