Artificial Replay: A Meta-Algorithm for Harnessing Historical Data in Bandits

How best to incorporate historical data to "warm start" bandit algorithms is an open question: naively initializing reward estimates using all historical samples can suffer from spurious data and imbalanced data coverage, leading to computational and storage issues $\unicode{x2014}$ particularly salient in continuous action spaces. We propose Artificial Replay, a meta-algorithm for incorporating historical data into any arbitrary base bandit algorithm. Artificial Replay uses only a fraction of the historical data compared to a full warm-start approach, while still achieving identical regret for base algorithms that satisfy independence of irrelevant data (IIData), a novel and broadly applicable property that we introduce. We complement these theoretical results with experiments on $K$-armed and continuous combinatorial bandit algorithms, including a green security domain using real poaching data. We show the practical benefits of Artificial Replay, including for base algorithms that do not satisfy IIData.