  In this work, we introduce the Personalized Online Super Learner (POSL) -- an
online ensembling algorithm for streaming data whose optimization procedure
accommodates varying degrees of personalization. Namely, POSL optimizes
predictions with respect to baseline covariates, so personalization can vary
from completely individualized (i.e., optimization with respect to baseline
covariate subject ID) to many individuals (i.e., optimization with respect to
common baseline covariates). As an online algorithm, POSL learns in real-time.
POSL can leverage a diversity of candidate algorithms, including online
algorithms with different training and update times, fixed algorithms that are
never updated during the procedure, pooled algorithms that learn from many
individuals' time-series, and individualized algorithms that learn from within
a single time-series. POSL's ensembling of this hybrid of base learning
strategies depends on the amount of data collected, the stationarity of the
time-series, and the mutual characteristics of a group of time-series. In
essence, POSL decides whether to learn across samples, through time, or both,
based on the underlying (unknown) structure in the data. For a wide range of
simulations that reflect realistic forecasting scenarios, and in a medical data
application, we examine the performance of POSL relative to other current
ensembling and online learning methods. We show that POSL is able to provide
reliable predictions for time-series data and adjust to changing
data-generating environments. We further cultivate POSL's practicality by
extending it to settings where time-series enter/exit dynamically over
chronological time.
