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Principal component regression (PCR) is a popular technique for fixed-designerror-in-variables regression, a generalization of the linear regressionsetting in which the observed covariates are corrupted with random noise. Weprovide the first time-uniform finite sample guarantees for online(regularized) PCR whenever data is collected adaptively. Since the prooftechniques for analyzing PCR in the fixed design setting do not readily extendto the online setting, our results rely on adapting tools from modernmartingale concentration to the error-in-variables setting. As an applicationof our bounds, we provide a framework for experiment design in panel datasettings when interventions are assigned adaptively. Our framework may bethought of as a generalization of the synthetic control and syntheticinterventions frameworks, where data is collected via an adaptive interventionassignment policy.

Adaptive Principal Component Regression with Applications to Panel Data