  We present a data-driven algorithm that advertisers can use to automate their
digital ad-campaigns at online publishers. The algorithm enables the advertiser
to search across available target audiences and ad-media to find the best
possible combination for its campaign via online experimentation. The problem
of finding the best audience-ad combination is complicated by a number of
distinctive challenges, including (a) a need for active exploration to resolve
prior uncertainty and to speed the search for profitable combinations, (b) many
combinations to choose from, giving rise to high-dimensional search
formulations, and (c) very low success probabilities, typically just a fraction
of one percent. Our algorithm (designated LRDL, an acronym for Logistic
Regression with Debiased Lasso) addresses these challenges by combining four
elements: a multiarmed bandit framework for active exploration; a Lasso penalty
function to handle high dimensionality; an inbuilt debiasing kernel that
handles the regularization bias induced by the Lasso; and a semi-parametric
regression model for outcomes that promotes cross-learning across arms. The
algorithm is implemented as a Thompson Sampler, and to the best of our
knowledge, it is the first that can practically address all of the challenges
above. Simulations with real and synthetic data show the method is effective
and document its superior performance against several benchmarks from the
recent high-dimensional bandit literature.
