Simple Stochastic and Online Gradient Descent Algorithms for Pairwise Learning Article Swipe
Zhenhuan Yang
,
Yunwen Lei
,
Puyu Wang
,
Tianbao Yang
,
Yiming Ying
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2111.12050
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2111.12050
Pairwise learning refers to learning tasks where the loss function depends on a pair of instances. It instantiates many important machine learning tasks such as bipartite ranking and metric learning. A popular approach to handle streaming data in pairwise learning is an online gradient descent (OGD) algorithm, where one needs to pair the current instance with a buffering set of previous instances with a sufficiently large size and therefore suffers from a scalability issue. In this paper, we propose simple stochastic and online gradient descent methods for pairwise learning. A notable difference from the existing studies is that we only pair the current instance with the previous one in building a gradient direction, which is efficient in both the storage and computational complexity. We develop novel stability results, optimization, and generalization error bounds for both convex and nonconvex as well as both smooth and nonsmooth problems. We introduce novel techniques to decouple the dependency of models and the previous instance in both the optimization and generalization analysis. Our study resolves an open question on developing meaningful generalization bounds for OGD using a buffering set with a very small fixed size. We also extend our algorithms and stability analysis to develop differentially private SGD algorithms for pairwise learning which significantly improves the existing results.
Related Topics
Concepts
Pairwise comparison
Computer science
Stochastic gradient descent
Generalization
Stability (learning theory)
Online machine learning
Metric (unit)
Gradient descent
Scalability
Algorithm
Machine learning
Artificial intelligence
Simple (philosophy)
Set (abstract data type)
Mathematical optimization
Theoretical computer science
Mathematics
Artificial neural network
Epistemology
Mathematical analysis
Philosophy
Operations management
Programming language
Economics
Database
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2111.12050
- https://arxiv.org/pdf/2111.12050
- OA Status
- green
- Cited By
- 10
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3212345415
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3212345415Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2111.12050Digital Object Identifier
- Title
-
Simple Stochastic and Online Gradient Descent Algorithms for Pairwise LearningWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-11-23Full publication date if available
- Authors
-
Zhenhuan Yang, Yunwen Lei, Puyu Wang, Tianbao Yang, Yiming YingList of authors in order
- Landing page
-
https://arxiv.org/abs/2111.12050Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2111.12050Direct 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/2111.12050Direct OA link when available
- Concepts
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Pairwise comparison, Computer science, Stochastic gradient descent, Generalization, Stability (learning theory), Online machine learning, Metric (unit), Gradient descent, Scalability, Algorithm, Machine learning, Artificial intelligence, Simple (philosophy), Set (abstract data type), Mathematical optimization, Theoretical computer science, Mathematics, Artificial neural network, Epistemology, Mathematical analysis, Philosophy, Operations management, Programming language, Economics, DatabaseTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
10Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2024: 4, 2023: 4, 2022: 1Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.It | 16 |
| abstract_inverted_index.We | 123, 146, 190 |
| abstract_inverted_index.an | 41, 170 |
| abstract_inverted_index.as | 24, 138, 140 |
| abstract_inverted_index.in | 37, 108, 116, 160 |
| abstract_inverted_index.is | 40, 96, 114 |
| abstract_inverted_index.of | 14, 59, 154 |
| abstract_inverted_index.on | 11, 173 |
| abstract_inverted_index.to | 3, 33, 50, 150, 198 |
| abstract_inverted_index.we | 77, 98 |
| abstract_inverted_index.OGD | 179 |
| abstract_inverted_index.Our | 167 |
| abstract_inverted_index.SGD | 202 |
| abstract_inverted_index.and | 27, 67, 81, 120, 129, 136, 143, 156, 164, 195 |
| abstract_inverted_index.for | 86, 133, 178, 204 |
| abstract_inverted_index.one | 48, 107 |
| abstract_inverted_index.our | 193 |
| abstract_inverted_index.set | 58, 183 |
| abstract_inverted_index.the | 7, 52, 93, 101, 105, 118, 152, 157, 162, 210 |
| abstract_inverted_index.also | 191 |
| abstract_inverted_index.both | 117, 134, 141, 161 |
| abstract_inverted_index.data | 36 |
| abstract_inverted_index.from | 70, 92 |
| abstract_inverted_index.loss | 8 |
| abstract_inverted_index.many | 18 |
| abstract_inverted_index.only | 99 |
| abstract_inverted_index.open | 171 |
| abstract_inverted_index.pair | 13, 51, 100 |
| abstract_inverted_index.size | 66 |
| abstract_inverted_index.such | 23 |
| abstract_inverted_index.that | 97 |
| abstract_inverted_index.this | 75 |
| abstract_inverted_index.very | 186 |
| abstract_inverted_index.well | 139 |
| abstract_inverted_index.with | 55, 62, 104, 184 |
| abstract_inverted_index.(OGD) | 45 |
| abstract_inverted_index.error | 131 |
| abstract_inverted_index.fixed | 188 |
| abstract_inverted_index.large | 65 |
| abstract_inverted_index.needs | 49 |
| abstract_inverted_index.novel | 125, 148 |
| abstract_inverted_index.size. | 189 |
| abstract_inverted_index.small | 187 |
| abstract_inverted_index.study | 168 |
| abstract_inverted_index.tasks | 5, 22 |
| abstract_inverted_index.using | 180 |
| abstract_inverted_index.where | 6, 47 |
| abstract_inverted_index.which | 113, 207 |
| abstract_inverted_index.bounds | 132, 177 |
| abstract_inverted_index.convex | 135 |
| abstract_inverted_index.extend | 192 |
| abstract_inverted_index.handle | 34 |
| abstract_inverted_index.issue. | 73 |
| abstract_inverted_index.metric | 28 |
| abstract_inverted_index.models | 155 |
| abstract_inverted_index.online | 42, 82 |
| abstract_inverted_index.paper, | 76 |
| abstract_inverted_index.refers | 2 |
| abstract_inverted_index.simple | 79 |
| abstract_inverted_index.smooth | 142 |
| abstract_inverted_index.current | 53, 102 |
| abstract_inverted_index.depends | 10 |
| abstract_inverted_index.descent | 44, 84 |
| abstract_inverted_index.develop | 124, 199 |
| abstract_inverted_index.machine | 20 |
| abstract_inverted_index.methods | 85 |
| abstract_inverted_index.notable | 90 |
| abstract_inverted_index.popular | 31 |
| abstract_inverted_index.private | 201 |
| abstract_inverted_index.propose | 78 |
| abstract_inverted_index.ranking | 26 |
| abstract_inverted_index.storage | 119 |
| abstract_inverted_index.studies | 95 |
| abstract_inverted_index.suffers | 69 |
| abstract_inverted_index.Pairwise | 0 |
| abstract_inverted_index.analysis | 197 |
| abstract_inverted_index.approach | 32 |
| abstract_inverted_index.building | 109 |
| abstract_inverted_index.decouple | 151 |
| abstract_inverted_index.existing | 94, 211 |
| abstract_inverted_index.function | 9 |
| abstract_inverted_index.gradient | 43, 83, 111 |
| abstract_inverted_index.improves | 209 |
| abstract_inverted_index.instance | 54, 103, 159 |
| abstract_inverted_index.learning | 1, 4, 21, 39, 206 |
| abstract_inverted_index.pairwise | 38, 87, 205 |
| abstract_inverted_index.previous | 60, 106, 158 |
| abstract_inverted_index.question | 172 |
| abstract_inverted_index.resolves | 169 |
| abstract_inverted_index.results, | 127 |
| abstract_inverted_index.results. | 212 |
| abstract_inverted_index.analysis. | 166 |
| abstract_inverted_index.bipartite | 25 |
| abstract_inverted_index.buffering | 57, 182 |
| abstract_inverted_index.efficient | 115 |
| abstract_inverted_index.important | 19 |
| abstract_inverted_index.instances | 61 |
| abstract_inverted_index.introduce | 147 |
| abstract_inverted_index.learning. | 29, 88 |
| abstract_inverted_index.nonconvex | 137 |
| abstract_inverted_index.nonsmooth | 144 |
| abstract_inverted_index.problems. | 145 |
| abstract_inverted_index.stability | 126, 196 |
| abstract_inverted_index.streaming | 35 |
| abstract_inverted_index.therefore | 68 |
| abstract_inverted_index.algorithm, | 46 |
| abstract_inverted_index.algorithms | 194, 203 |
| abstract_inverted_index.dependency | 153 |
| abstract_inverted_index.developing | 174 |
| abstract_inverted_index.difference | 91 |
| abstract_inverted_index.direction, | 112 |
| abstract_inverted_index.instances. | 15 |
| abstract_inverted_index.meaningful | 175 |
| abstract_inverted_index.stochastic | 80 |
| abstract_inverted_index.techniques | 149 |
| abstract_inverted_index.complexity. | 122 |
| abstract_inverted_index.scalability | 72 |
| abstract_inverted_index.instantiates | 17 |
| abstract_inverted_index.optimization | 163 |
| abstract_inverted_index.sufficiently | 64 |
| abstract_inverted_index.computational | 121 |
| abstract_inverted_index.optimization, | 128 |
| abstract_inverted_index.significantly | 208 |
| abstract_inverted_index.differentially | 200 |
| abstract_inverted_index.generalization | 130, 165, 176 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile |