Abstract
Bayesian Optimization (BO) is an efficient method to optimize an expensive black-box function with continuous variables. However, in many cases, the function has only discrete variables as inputs, which cannot be optimized by traditional BO methods. A typical approach to optimize such functions assumes the objective function is on a continuous domain, then applies a normal BO method with a rounding of suggested continuous points to nearest discrete points at the end. This may cause BO to get stuck and repeat pre-existing observations. To overcome this problem, we propose a method (named Discrete-BO) that manipulates the exploration of an acquisition function and the length scale of a covariance function, which are two key components of a BO method, to prevent sampling a pre-existing observation. Our experiments on both synthetic and real-world applications show that the proposed method outperforms state-of-the-art baselines in terms of convergence rate. More importantly, we also show some theoretical analyses to prove the correctness of our method.
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Acknowledgements
This research was partially funded by the Australian Government through the Australian Research Council (ARC). Prof Venkatesh is the recipient of an ARC Australian Laureate Fellowship (FL170100006).
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Luong, P., Gupta, S., Nguyen, D., Rana, S., Venkatesh, S. (2019). Bayesian Optimization with Discrete Variables. In: Liu, J., Bailey, J. (eds) AI 2019: Advances in Artificial Intelligence. AI 2019. Lecture Notes in Computer Science(), vol 11919. Springer, Cham. https://doi.org/10.1007/978-3-030-35288-2_38
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