Bayesian Optimization with Discrete Variables

  • Phuc LuongEmail author
  • Sunil Gupta
  • Dang Nguyen
  • Santu Rana
  • Svetha Venkatesh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11919)


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.


Bayesian optimization Gaussian process Discrete variables Hyper-parameter tuning 



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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Phuc Luong
    • 1
    Email author
  • Sunil Gupta
    • 1
  • Dang Nguyen
    • 1
  • Santu Rana
    • 1
  • Svetha Venkatesh
    • 1
  1. 1.Applied Artificial Intelligence InstituteDeakin UniversityGeelongAustralia

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