α-GAN: Convergence and Estimation Guarantees

Gowtham R. Kurri; Monica Welfert; Tyler Sypherd; Lalitha Sankar

doi:10.1109/ISIT50566.2022.9834890

α-GAN: Convergence and Estimation Guarantees

Gowtham R. Kurri, Monica Welfert, Tyler Sypherd, Lalitha Sankar

Engineering, Ira A. Fulton Schools of (IAFSE)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Scopus citations

Abstract

We prove a two-way correspondence between the min-max optimization of general CPE loss function GANs and the minimization of associated f-divergences. We then focus on α-GAN, defined via the α-loss, which interpolates several GANs (Hellinger, vanilla, Total Variation) and corresponds to the minimization of the Arimoto divergence. We show that the Arimoto divergences induced by α-GAN equivalently converge, for all α∈ℝ>0∪{∞}. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a function of α. Finally, we present empirical results on a toy dataset that highlight the practical utility of tuning the α hyperparameter.

Original language	English (US)
Title of host publication	2022 IEEE International Symposium on Information Theory, ISIT 2022
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	276-281
Number of pages	6
ISBN (Electronic)	9781665421591
DOIs	https://doi.org/10.1109/ISIT50566.2022.9834890
State	Published - 2022
Event	2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland Duration: Jun 26 2022 → Jul 1 2022

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2022-June
ISSN (Print)	2157-8095

Conference

Conference	2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/Territory	Finland
City	Espoo
Period	6/26/22 → 7/1/22

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT50566.2022.9834890

Cite this

Kurri, G. R., Welfert, M., Sypherd, T., & Sankar, L. (2022). α-GAN: Convergence and Estimation Guarantees. In 2022 IEEE International Symposium on Information Theory, ISIT 2022 (pp. 276-281). (IEEE International Symposium on Information Theory - Proceedings; Vol. 2022-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT50566.2022.9834890

α-GAN: Convergence and Estimation Guarantees. / Kurri, Gowtham R.; Welfert, Monica; Sypherd, Tyler et al.
2022 IEEE International Symposium on Information Theory, ISIT 2022. Institute of Electrical and Electronics Engineers Inc., 2022. p. 276-281 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2022-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kurri, GR, Welfert, M, Sypherd, T & Sankar, L 2022, α-GAN: Convergence and Estimation Guarantees. in 2022 IEEE International Symposium on Information Theory, ISIT 2022. IEEE International Symposium on Information Theory - Proceedings, vol. 2022-June, Institute of Electrical and Electronics Engineers Inc., pp. 276-281, 2022 IEEE International Symposium on Information Theory, ISIT 2022, Espoo, Finland, 6/26/22. https://doi.org/10.1109/ISIT50566.2022.9834890

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abstract = "We prove a two-way correspondence between the min-max optimization of general CPE loss function GANs and the minimization of associated f-divergences. We then focus on α-GAN, defined via the α-loss, which interpolates several GANs (Hellinger, vanilla, Total Variation) and corresponds to the minimization of the Arimoto divergence. We show that the Arimoto divergences induced by α-GAN equivalently converge, for all α∈ℝ>0∪{∞}. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a function of α. Finally, we present empirical results on a toy dataset that highlight the practical utility of tuning the α hyperparameter.",

author = "Kurri, {Gowtham R.} and Monica Welfert and Tyler Sypherd and Lalitha Sankar",

note = "Funding Information: This work is supported in part by NSF grants CIF-1901243, CIF-1815361, CIF-2007688, CIF-2134256, CIF-2031799, and CIF-1934766. Publisher Copyright: {\textcopyright} 2022 IEEE.; 2022 IEEE International Symposium on Information Theory, ISIT 2022 ; Conference date: 26-06-2022 Through 01-07-2022",

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α-GAN: Convergence and Estimation Guarantees

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