Ensemble Bayesian Optimization
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Bayesian Optimization (BO) has been shown to be a very effective paradigm for tackling hard black-box and non-convex optimization problems encountered in Machine Learning. Despite these successes, the computational complexity of the underlying function approximation has restricted the use of BO to problems that can be handled with less than a few thousand function evaluations. Harder problems like those involving functions operating in very high dimensional spaces may require hundreds of thousands or millions of evaluations or more and become computationally intractable to handle using standard Bayesian Optimization methods. In this paper, we propose Ensemble Bayesian Optimization (EBO) to overcome this problem. Unlike conventional BO methods that operate on a single posterior GP model, EBO works with an ensemble of posterior GP models. Further, we represent each GP model using tile coding random features and an additive function structure. Our approach generates speedups by parallelizing the time consuming hyper-parameter posterior inference and functional evaluations on hundreds of cores and aggregating the models in every iteration of BO. Our extensive experimental evaluation shows that EBO can speed up the posterior inference between 2-3 orders of magnitude (400 times in one experiment) compared to the state-of-the-art by putting data into Mondrian bins without sacrificing the sample quality. We demonstrate the ability of EBO to handle sample-intensive hard optimization problems by applying it to a rover navigation problem with tens of thousands of observations.
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