Learning Thresholds with Latent Values and Censored Feedback Article Swipe
Jiahao Zhang
,
T. Lin
,
Weiqiang Zheng
,
Zhe Feng
,
Yifeng Teng
,
Xiaotie Deng
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2312.04653
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2312.04653
In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward $g(γ, v)$ depends on the proposed threshold $γ$ and latent value $v$ and it can be $only$ achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most $ε$ smaller than the optimum and prove that the number of queries needed can be infinitely large even when $g(γ, v)$ is monotone with respect to both $γ$ and $v$. On the positive side, we provide a tight query complexity $\tildeΘ(1/ε^3)$ when $g$ is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight $\tildeΘ(1/ε^3)$ query complexity can be achieved as long as $g$ satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight $Θ(T^{2/3})$ regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2312.04653
- https://arxiv.org/pdf/2312.04653
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4389599111
All OpenAlex metadata
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https://openalex.org/W4389599111Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2312.04653Digital Object Identifier
- Title
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Learning Thresholds with Latent Values and Censored FeedbackWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-12-07Full publication date if available
- Authors
-
Jiahao Zhang, T. Lin, Weiqiang Zheng, Zhe Feng, Yifeng Teng, Xiaotie DengList of authors in order
- Landing page
-
https://arxiv.org/abs/2312.04653Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2312.04653Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2312.04653Direct OA link when available
- Concepts
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Monotone polygon, Regret, Mathematics, Lipschitz continuity, Value (mathematics), Upper and lower bounds, Space (punctuation), Common value auction, Combinatorics, Online learning, Discrete mathematics, Computer science, Statistics, Pure mathematics, Mathematical analysis, World Wide Web, Geometry, Operating systemTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.reward | 17, 88 |
| abstract_inverted_index.space, | 13 |
| abstract_inverted_index.value. | 48 |
| abstract_inverted_index.depends | 20 |
| abstract_inverted_index.hiring, | 73 |
| abstract_inverted_index.optimum | 95 |
| abstract_inverted_index.problem | 6, 50 |
| abstract_inverted_index.provide | 126 |
| abstract_inverted_index.queries | 102 |
| abstract_inverted_index.reserve | 58 |
| abstract_inverted_index.respect | 115 |
| abstract_inverted_index.setting | 69, 179 |
| abstract_inverted_index.smaller | 92 |
| abstract_inverted_index.unknown | 16, 46 |
| abstract_inverted_index.Finally, | 170 |
| abstract_inverted_index.achieved | 35, 154 |
| abstract_inverted_index.actively | 8 |
| abstract_inverted_index.complete | 165 |
| abstract_inverted_index.expected | 87 |
| abstract_inverted_index.learning | 9, 82, 178 |
| abstract_inverted_index.monotone | 113, 135 |
| abstract_inverted_index.positive | 123 |
| abstract_inverted_index.problem. | 169 |
| abstract_inverted_index.proposed | 23 |
| abstract_inverted_index.provides | 163 |
| abstract_inverted_index.results. | 196 |
| abstract_inverted_index.Moreover, | 144 |
| abstract_inverted_index.auctions, | 63 |
| abstract_inverted_index.one-sided | 160 |
| abstract_inverted_index.practical | 55 |
| abstract_inverted_index.satisfies | 159 |
| abstract_inverted_index.threshold | 10, 24, 38, 84 |
| abstract_inverted_index.Lipschitz. | 143 |
| abstract_inverted_index.complexity | 80, 130, 151, 195 |
| abstract_inverted_index.infinitely | 106 |
| abstract_inverted_index.recruiting | 70 |
| abstract_inverted_index.scenarios, | 56 |
| abstract_inverted_index.techniques | 190 |
| abstract_inverted_index.assignments | 66 |
| abstract_inverted_index.demonstrate | 181 |
| abstract_inverted_index.investigate | 4 |
| abstract_inverted_index.applications | 53 |
| abstract_inverted_index.characterize | 77 |
| abstract_inverted_index.distribution | 141 |
| abstract_inverted_index.optimization | 60 |
| abstract_inverted_index.$Θ(T^{2/3})$ | 184 |
| abstract_inverted_index.Lipschitzness, | 161 |
| abstract_inverted_index.aforementioned | 193 |
| abstract_inverted_index.continuous-arm | 188 |
| abstract_inverted_index.crowdsourcing, | 68 |
| abstract_inverted_index.characterization | 166 |
| abstract_inverted_index.$\tildeΘ(1/ε^3)$ | 131, 149 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 6 |
| citation_normalized_percentile |