Replicable Learning of Large-Margin Halfspaces
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917009519804416 |
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| author | Kalavasis, Alkis Karbasi, Amin Larsen, Kasper Green Velegkas, Grigoris Zhou, Felix |
| author_facet | Kalavasis, Alkis Karbasi, Amin Larsen, Kasper Green Velegkas, Grigoris Zhou, Felix |
| contents | We provide efficient replicable algorithms for the problem of learning large-margin halfspaces. Our results improve upon the algorithms provided by Impagliazzo, Lei, Pitassi, and Sorrell [STOC, 2022]. We design the first dimension-independent replicable algorithms for this task which runs in polynomial time, is proper, and has strictly improved sample complexity compared to the one achieved by Impagliazzo et al. [2022] with respect to all the relevant parameters. Moreover, our first algorithm has sample complexity that is optimal with respect to the accuracy parameter $ε$. We also design an SGD-based replicable algorithm that, in some parameters' regimes, achieves better sample and time complexity than our first algorithm. Departing from the requirement of polynomial time algorithms, using the DP-to-Replicability reduction of Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sorrell, and Sivakumar [STOC, 2023], we show how to obtain a replicable algorithm for large-margin halfspaces with improved sample complexity with respect to the margin parameter $τ$, but running time doubly exponential in $1/τ^2$ and worse sample complexity dependence on $ε$ than one of our previous algorithms. We then design an improved algorithm with better sample complexity than all three of our previous algorithms and running time exponential in $1/τ^{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Replicable Learning of Large-Margin Halfspaces Kalavasis, Alkis Karbasi, Amin Larsen, Kasper Green Velegkas, Grigoris Zhou, Felix Machine Learning Data Structures and Algorithms We provide efficient replicable algorithms for the problem of learning large-margin halfspaces. Our results improve upon the algorithms provided by Impagliazzo, Lei, Pitassi, and Sorrell [STOC, 2022]. We design the first dimension-independent replicable algorithms for this task which runs in polynomial time, is proper, and has strictly improved sample complexity compared to the one achieved by Impagliazzo et al. [2022] with respect to all the relevant parameters. Moreover, our first algorithm has sample complexity that is optimal with respect to the accuracy parameter $ε$. We also design an SGD-based replicable algorithm that, in some parameters' regimes, achieves better sample and time complexity than our first algorithm. Departing from the requirement of polynomial time algorithms, using the DP-to-Replicability reduction of Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sorrell, and Sivakumar [STOC, 2023], we show how to obtain a replicable algorithm for large-margin halfspaces with improved sample complexity with respect to the margin parameter $τ$, but running time doubly exponential in $1/τ^2$ and worse sample complexity dependence on $ε$ than one of our previous algorithms. We then design an improved algorithm with better sample complexity than all three of our previous algorithms and running time exponential in $1/τ^{2}$. |
| title | Replicable Learning of Large-Margin Halfspaces |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2402.13857 |