The Cost of Parallelizing Boosting
CoRR(2024)
摘要
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 AdaBoost algorithm produces an accurate
hypothesis by interacting with the weak learner for Õ(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 Õ(1/(t γ^2)) rounds, and only suffer a blow-up
of exp(d · 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.
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