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Researchers often face data fusion problems, where multiple data sources areavailable, each capturing a distinct subset of variables. While problemformulations typically take the data as given, in practice, data acquisitioncan be an ongoing process. In this paper, we aim to estimate any functional ofa probabilistic model (e.g., a causal effect) as efficiently as possible, bydeciding, at each time, which data source to query. We propose online momentselection (OMS), a framework in which structural assumptions are encoded asmoment conditions. The optimal action at each step depends, in part, on thevery moments that identify the functional of interest. Our algorithms balanceexploration with choosing the best action as suggested by current estimates ofthe moments. We propose two selection strategies: (1) explore-then-commit(OMS-ETC) and (2) explore-then-greedy (OMS-ETG), proving that both achieve zeroasymptotic regret as assessed by MSE. We instantiate our setup for averagetreatment effect estimation, where structural assumptions are given by a causalgraph and data sources may include subsets of mediators, confounders, andinstrumental variables.

Efficient Online Estimation of Causal Effects by Deciding What to Observe