Batched Gaussian Process Bandit Optimization via Determinantal Point\n Processes

Abstract

Gaussian Process bandit optimization has emerged as a powerful tool for\noptimizing noisy black box functions. One example in machine learning is\nhyper-parameter optimization where each evaluation of the target function\nrequires training a model which may involve days or even weeks of computation.\nMost methods for this so-called "Bayesian optimization" only allow sequential\nexploration of the parameter space. However, it is often desirable to propose\nbatches or sets of parameter values to explore simultaneously, especially when\nthere are large parallel processing facilities at our disposal. Batch methods\nrequire modeling the interaction between the different evaluations in the\nbatch, which can be expensive in complex scenarios. In this paper, we propose a\nnew approach for parallelizing Bayesian optimization by modeling the diversity\nof a batch via Determinantal point processes (DPPs) whose kernels are learned\nautomatically. This allows us to generalize a previous result as well as prove\nbetter regret bounds based on DPP sampling. Our experiments on a variety of\nsynthetic and real-world robotics and hyper-parameter optimization tasks\nindicate that our DPP-based methods, especially those based on DPP sampling,\noutperform state-of-the-art methods.\n