How can we make use of information parallelism in online decision making problems while efficiently balancing the exploration-exploitation trade-off? In this paper, we introduce a batch Thompson Sampling framework for two canonical online decision making problems, namely, stochastic multi-arm bandit and linear contextual bandit with finitely many arms. Over a time horizon $T$, our textit{batch} Thompson Sampling policy achieves the same (asymptotic) regret bound of a fully sequential one while carrying out only $O(log T)$ batch queries. To achieve this exponential reduction, i.e., reducing the number of interactions from $T$ to $O(log T)$, our batch policy dynamically determines the duration of each batch in order to balance the exploration-exploitation trade-off. We also demonstrate experimentally that dynamic batch allocation dramatically outperforms natural baselines such as static batch allocations.
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