Variable Selection Via Thompson Sampling

–Thompson sampling is a heuristic algorithm for the multi-armed bandit problem which has long tradition in machine learning. The Bayesian spirit sense that it selects arms based on posterior samples of reward probabilities each arm. By forging connection between combinatorial binary bandits and spike-and-slab variable selection, we propose stochastic optimization approach to subset selection called Thompson (TVS). TVS framework interpretable learning does not rely underlying model be linear. brings together reinforcement order extend reach nonparametric models large datasets with very many predictors and/or observations. Depending choice reward, can deployed offline as well online setups streaming data batches. Tailoring multiplay provide regret bounds without necessarily assuming arm mean rewards unrelated. We show strong empirical performance both simulated real data. Unlike deterministic methods nature makes less prone local convergence thereby more robust.