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Standard approaches to decision-making under uncertainty focus on sequential exploration of the space of decisions. However, textit{simultaneously} proposing a batch of decisions, which leverages available resources for parallel experimentation, has the potential to rapidly accelerate exploration. We present a family of (parallel) contextual linear bandit algorithms, whose regret is nearly identical to their perfectly sequential counterparts -- given access to the same total number of oracle queries -- up to a lower-order burn-in term that is dependent on the context-set geometry. We provide matching information-theoretic lower bounds on parallel regret performance to establish our algorithms are asymptotically optimal in the time horizon. Finally, we also present an empirical evaluation of these parallel algorithms in several domains, including materials discovery and biological sequence design problems, to demonstrate the utility of parallelized bandits in practical settings.
Stochastic linear contextual bandit algorithms have substantial applications in practice, such as recommender systems, online advertising, clinical trials, etc. Recent works show that optimal bandit algorithms are vulnerable to adversarial attacks an
The contextual combinatorial semi-bandit problem with linear payoff functions is a decision-making problem in which a learner chooses a set of arms with the feature vectors in each round under given constraints so as to maximize the sum of rewards of
The contextual bandit literature has traditionally focused on algorithms that address the exploration-exploitation tradeoff. In particular, greedy algorithms that exploit current estimates without any exploration may be sub-optimal in general. Howeve
We study the problem of dynamic batch learning in high-dimensional sparse linear contextual bandits, where a decision maker can only adapt decisions at a batch level. In particular, the decision maker, only observing rewards at the end of each batch,
Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $Omega(n^{2/3})$ dimension-free minimax regret lower bound for s