Differentially Private SGDA for Minimax Problems Article Swipe
Zhenhuan Yang
,
Shu Hu
,
Yunwen Lei
,
Kush R. Varshney
,
Siwei Lyu
,
Yiming Ying
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2201.09046
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2201.09046
Stochastic gradient descent ascent (SGDA) and its variants have been the workhorse for solving minimax problems. However, in contrast to the well-studied stochastic gradient descent (SGD) with differential privacy (DP) constraints, there is little work on understanding the generalization (utility) of SGDA with DP constraints. In this paper, we use the algorithmic stability approach to establish the generalization (utility) of DP-SGDA in different settings. In particular, for the convex-concave setting, we prove that the DP-SGDA can achieve an optimal utility rate in terms of the weak primal-dual population risk in both smooth and non-smooth cases. To our best knowledge, this is the first-ever-known result for DP-SGDA in the non-smooth case. We further provide its utility analysis in the nonconvex-strongly-concave setting which is the first-ever-known result in terms of the primal population risk. The convergence and generalization results for this nonconvex setting are new even in the non-private setting. Finally, numerical experiments are conducted to demonstrate the effectiveness of DP-SGDA for both convex and nonconvex cases.
Related Topics
Concepts
Generalization
Minimax
Stochastic gradient descent
Mathematical optimization
Population
Mathematics
Convergence (economics)
Regular polygon
Stability (learning theory)
Gradient descent
Dual (grammatical number)
Applied mathematics
Computer science
Artificial intelligence
Economics
Machine learning
Artificial neural network
Mathematical analysis
Geometry
Art
Literature
Sociology
Demography
Economic growth
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2201.09046
- https://arxiv.org/pdf/2201.09046
- OA Status
- green
- Cited By
- 2
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4226143575
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4226143575Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2201.09046Digital Object Identifier
- Title
-
Differentially Private SGDA for Minimax ProblemsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-01-22Full publication date if available
- Authors
-
Zhenhuan Yang, Shu Hu, Yunwen Lei, Kush R. Varshney, Siwei Lyu, Yiming YingList of authors in order
- Landing page
-
https://arxiv.org/abs/2201.09046Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2201.09046Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2201.09046Direct OA link when available
- Concepts
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Generalization, Minimax, Stochastic gradient descent, Mathematical optimization, Population, Mathematics, Convergence (economics), Regular polygon, Stability (learning theory), Gradient descent, Dual (grammatical number), Applied mathematics, Computer science, Artificial intelligence, Economics, Machine learning, Artificial neural network, Mathematical analysis, Geometry, Art, Literature, Sociology, Demography, Economic growthTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
- Citations by year (recent)
-
2023: 2Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.our | 96 |
| abstract_inverted_index.the | 10, 20, 37, 50, 56, 67, 73, 84, 101, 107, 117, 122, 128, 145, 155 |
| abstract_inverted_index.use | 49 |
| abstract_inverted_index.(DP) | 29 |
| abstract_inverted_index.SGDA | 41 |
| abstract_inverted_index.been | 9 |
| abstract_inverted_index.best | 97 |
| abstract_inverted_index.both | 90, 160 |
| abstract_inverted_index.even | 143 |
| abstract_inverted_index.have | 8 |
| abstract_inverted_index.rate | 80 |
| abstract_inverted_index.risk | 88 |
| abstract_inverted_index.that | 72 |
| abstract_inverted_index.this | 46, 99, 138 |
| abstract_inverted_index.weak | 85 |
| abstract_inverted_index.with | 26, 42 |
| abstract_inverted_index.work | 34 |
| abstract_inverted_index.(SGD) | 25 |
| abstract_inverted_index.case. | 109 |
| abstract_inverted_index.prove | 71 |
| abstract_inverted_index.risk. | 131 |
| abstract_inverted_index.terms | 82, 126 |
| abstract_inverted_index.there | 31 |
| abstract_inverted_index.which | 120 |
| abstract_inverted_index.(SGDA) | 4 |
| abstract_inverted_index.ascent | 3 |
| abstract_inverted_index.cases. | 94, 164 |
| abstract_inverted_index.convex | 161 |
| abstract_inverted_index.little | 33 |
| abstract_inverted_index.paper, | 47 |
| abstract_inverted_index.primal | 129 |
| abstract_inverted_index.result | 103, 124 |
| abstract_inverted_index.smooth | 91 |
| abstract_inverted_index.DP-SGDA | 60, 74, 105, 158 |
| abstract_inverted_index.achieve | 76 |
| abstract_inverted_index.descent | 2, 24 |
| abstract_inverted_index.further | 111 |
| abstract_inverted_index.minimax | 14 |
| abstract_inverted_index.optimal | 78 |
| abstract_inverted_index.privacy | 28 |
| abstract_inverted_index.provide | 112 |
| abstract_inverted_index.results | 136 |
| abstract_inverted_index.setting | 119, 140 |
| abstract_inverted_index.solving | 13 |
| abstract_inverted_index.utility | 79, 114 |
| abstract_inverted_index.Finally, | 148 |
| abstract_inverted_index.However, | 16 |
| abstract_inverted_index.analysis | 115 |
| abstract_inverted_index.approach | 53 |
| abstract_inverted_index.contrast | 18 |
| abstract_inverted_index.gradient | 1, 23 |
| abstract_inverted_index.setting, | 69 |
| abstract_inverted_index.setting. | 147 |
| abstract_inverted_index.variants | 7 |
| abstract_inverted_index.(utility) | 39, 58 |
| abstract_inverted_index.conducted | 152 |
| abstract_inverted_index.different | 62 |
| abstract_inverted_index.establish | 55 |
| abstract_inverted_index.nonconvex | 139, 163 |
| abstract_inverted_index.numerical | 149 |
| abstract_inverted_index.problems. | 15 |
| abstract_inverted_index.settings. | 63 |
| abstract_inverted_index.stability | 52 |
| abstract_inverted_index.workhorse | 11 |
| abstract_inverted_index.Stochastic | 0 |
| abstract_inverted_index.knowledge, | 98 |
| abstract_inverted_index.non-smooth | 93, 108 |
| abstract_inverted_index.population | 87, 130 |
| abstract_inverted_index.stochastic | 22 |
| abstract_inverted_index.algorithmic | 51 |
| abstract_inverted_index.convergence | 133 |
| abstract_inverted_index.demonstrate | 154 |
| abstract_inverted_index.experiments | 150 |
| abstract_inverted_index.non-private | 146 |
| abstract_inverted_index.particular, | 65 |
| abstract_inverted_index.primal-dual | 86 |
| abstract_inverted_index.constraints, | 30 |
| abstract_inverted_index.constraints. | 44 |
| abstract_inverted_index.differential | 27 |
| abstract_inverted_index.well-studied | 21 |
| abstract_inverted_index.effectiveness | 156 |
| abstract_inverted_index.understanding | 36 |
| abstract_inverted_index.convex-concave | 68 |
| abstract_inverted_index.generalization | 38, 57, 135 |
| abstract_inverted_index.first-ever-known | 102, 123 |
| abstract_inverted_index.nonconvex-strongly-concave | 118 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 6 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/16 |
| sustainable_development_goals[0].score | 0.5899999737739563 |
| sustainable_development_goals[0].display_name | Peace, Justice and strong institutions |
| citation_normalized_percentile |