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Parallelizing Exploration-Exploitation Tradeoffs in Gaussian Process Bandit Optimization

机译:高斯过程土匪优化中的并行勘探与开发权衡

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摘要

How can we take advantage of opportunities for experimental parallelization in exploration-exploitation tradeoffs? In many experimental scenarios, it is often desirable to execute experiments simultaneously or in batches, rather than only performing one at a time. Additionally, observations may be both noisy and expensive. We introduce Gaussian Process Batch Upper Confidence Bound (GP-BUCB), an upper confidence bound-based algorithm, which models the reward function as a sample from a Gaussian process and which can select batches of experiments to run in parallel. We prove a general regret bound for GP-BUCB, as well as the surprising result that for some common kernels, the asymptotic average regret can be made independent of the batch size. The GP-BUCB algorithm is also applicable in the related case of a delay between initiation of an experiment and observation of its results, for which the same regret bounds hold. We also introduce Gaussian Process Adaptive Upper Confidence Bound (GP-AUCB), a variant of GP-BUCB which can exploit parallelism in an adaptive manner. We evaluate GP-BUCB and GP-AUCB on several simulated and real data sets. These experiments show that GP-BUCB and GP-AUCB are competitive with state-of-the-art heuristics.
机译:我们如何在勘探与开发权衡中利用实验并行化的机会?在许多实验场景中,通常希望同时或分批执行实验,而不是一次仅执行一次。另外,观察结果可能既嘈杂又昂贵。我们引入了基于高可信度边界的高斯过程批量上置信界(GP-BUCB)算法,该算法将奖励函数建模为高斯过程的样本,并且可以选择要并行运行的实验批次。我们证明了GP-BUCB的普遍遗憾,以及令人惊讶的结果,对于某些常见内核,可以使渐进平均遗憾独立于批处理大小。 GP-BUCB算法也适用于从实验开始到观察结果之间存在延迟的相关情况,对此,同样的遗憾也适用。我们还介绍了高斯过程自适应上置信界(GP-AUCB),它是GP-BUCB的一种变体,可以以自适应方式利用并行性。我们在几个模拟和真实数据集上评估GP-BUCB和GP-AUCB。这些实验表明,GP-BUCB和GP-AUCB与最新的启发式技术具有竞争力。

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