Smoothed Online Classification can be Harder than Batch Classification

Vinod Raman, Unique Subedi, Ambuj Tewari

Keywords: Online Learning, Smoothed Analysis

TL;DR: We show that online classification under smoothed adversary is as easy as iid batch classification when the size of the label space is bounded, but can be harder than iid batch classification when the size of the label space is unbounded.

Abstract:

We study online classification under smoothed adversaries. In this setting, at each time point, the adversary draws an example from a distribution that has a bounded density with respect to a fixed base measure, which is known apriori to the learner. For binary classification and scalar-valued regression, previous works [Haghtalab et al., 2020, Block et al., 2022] have shown that smoothed online learning is as easy as learning in the iid batch setting under PAC model. However, we show that smoothed online classification can be harder than the iid batch classification when the label space is unbounded. In particular, we construct a hypothesis class that is learnable in the iid batch setting under the PAC model but is not learnable under the smoothed online model. Finally, we identify a condition that ensures that the PAC learnability of a hypothesis class is sufficient for its smoothed online learnability.

Primary Area: Online learning

Submission Number: 4697