Title: Active Learning for Accurate Estimation of Linear Models,
Abstract: We explore the sequential decision making problem where the goal is to
estimate uniformly well a number of linear models, given a shared budget of
random contexts independently sampled from a known distribution. The decision
maker must query one of the linear models for each incoming context, and
receives an observation corrupted by noise levels that are unknown, and depend
on the model instance. We present Trace-UCB, an adaptive allocation algorithm
that learns the noise levels while balancing contexts accordingly across the
different linear functions, and derive guarantees for simple regret in both
expectation and high-probability. Finally, we extend the algorithm and its
guarantees to high dimensional settings, where the number of linear models
times the dimension of the contextual space is higher than the total budget of
samples. Simulations with real data suggest that Trace-UCB is remarkably
robust, outperforming a number of baselines even when its assumptions are
violated.