On the convergence of loss and uncertainty-based active learning algorithms
arxiv(2023)
摘要
We consider the convergence rates of loss and uncertainty-based active
learning algorithms under various assumptions. Firstly, we establish a set of
conditions that ensure convergence rates when applied to linear classifiers and
linearly separable datasets. This includes demonstrating convergence rate
guarantees for loss-based sampling with various loss functions. Secondly, we
introduce a framework that allows us to derive convergence rate bounds for
loss-based sampling by leveraging known convergence rate bounds for stochastic
gradient descent algorithms. Lastly, we propose a new algorithm that combines
point sampling and stochastic Polyak's step size. We establish a condition on
the sampling process, ensuring a convergence rate guarantee for this algorithm,
particularly in the case of smooth convex loss functions. Our numerical results
showcase the efficiency of the proposed algorithm.
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