The Cost of Parallelizing Boosting
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910341786501120 |
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| author | Lyu, Xin Wu, Hongxun Yang, Junzhao |
| author_facet | Lyu, Xin Wu, Hongxun Yang, Junzhao |
| contents | We study the cost of parallelizing weak-to-strong boosting algorithms for learning, following the recent work of Karbasi and Larsen. Our main results are two-fold:
- First, we prove a tight lower bound, showing that even "slight" parallelization of boosting requires an exponential blow-up in the complexity of training.
Specifically, let $γ$ be the weak learner's advantage over random guessing. The famous \textsc{AdaBoost} algorithm produces an accurate hypothesis by interacting with the weak learner for $\tilde{O}(1 / γ^2)$ rounds where each round runs in polynomial time.
Karbasi and Larsen showed that "significant" parallelization must incur exponential blow-up: Any boosting algorithm either interacts with the weak learner for $Ω(1 / γ)$ rounds or incurs an $\exp(d / γ)$ blow-up in the complexity of training, where $d$ is the VC dimension of the hypothesis class. We close the gap by showing that any boosting algorithm either has $Ω(1 / γ^2)$ rounds of interaction or incurs a smaller exponential blow-up of $\exp(d)$.
-Complementing our lower bound, we show that there exists a boosting algorithm using $\tilde{O}(1/(t γ^2))$ rounds, and only suffer a blow-up of $\exp(d \cdot t^2)$.
Plugging in $t = ω(1)$, this shows that the smaller blow-up in our lower bound is tight. More interestingly, this provides the first trade-off between the parallelism and the total work required for boosting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Cost of Parallelizing Boosting Lyu, Xin Wu, Hongxun Yang, Junzhao Machine Learning Data Structures and Algorithms We study the cost of parallelizing weak-to-strong boosting algorithms for learning, following the recent work of Karbasi and Larsen. Our main results are two-fold: - First, we prove a tight lower bound, showing that even "slight" parallelization of boosting requires an exponential blow-up in the complexity of training. Specifically, let $γ$ be the weak learner's advantage over random guessing. The famous \textsc{AdaBoost} algorithm produces an accurate hypothesis by interacting with the weak learner for $\tilde{O}(1 / γ^2)$ rounds where each round runs in polynomial time. Karbasi and Larsen showed that "significant" parallelization must incur exponential blow-up: Any boosting algorithm either interacts with the weak learner for $Ω(1 / γ)$ rounds or incurs an $\exp(d / γ)$ blow-up in the complexity of training, where $d$ is the VC dimension of the hypothesis class. We close the gap by showing that any boosting algorithm either has $Ω(1 / γ^2)$ rounds of interaction or incurs a smaller exponential blow-up of $\exp(d)$. -Complementing our lower bound, we show that there exists a boosting algorithm using $\tilde{O}(1/(t γ^2))$ rounds, and only suffer a blow-up of $\exp(d \cdot t^2)$. Plugging in $t = ω(1)$, this shows that the smaller blow-up in our lower bound is tight. More interestingly, this provides the first trade-off between the parallelism and the total work required for boosting. |
| title | The Cost of Parallelizing Boosting |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2402.15145 |