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Online machine learning systems need to adapt to domain shifts. Meanwhile,acquiring label at every timestep is expensive. We propose a surprisinglysimple algorithm that adaptively balances its regret and its number of labelqueries in settings where the data streams are from a mixture of hiddendomains. For online linear regression with oblivious adversaries, we provide atight tradeoff that depends on the durations and dimensionalities of the hiddendomains. Our algorithm can adaptively deal with interleaving spans of inputsfrom different domains. We also generalize our results to non-linear regressionfor hypothesis classes with bounded eluder dimension and adaptive adversaries.Experiments on synthetic and realistic datasets demonstrate that our algorithmachieves lower regret than uniform queries and greedy queries with equallabeling budget.

Active Online Learning with Hidden Shifting Domains