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High-Dimensional Discrete Bayesian Optimization with Intrinsic Dimension

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PRICAI 2022: Trends in Artificial Intelligence (PRICAI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13629))

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Abstract

Bayesian optimization (BO) has achieved remarkable success in optimizing low-dimensional continuous problems. Recently, BO in high-dimensional discrete solution space is in demand. However, satisfying BO algorithms tailored to this issue still lack. Fortunately, it is observed that high-dimensional discrete optimization problems may exist low-dimensional intrinsic subspace. Inspired by this observation, this paper proposes a Locality Sensitive Hashing based Bayesian Optimization (LSH-BO) method for high-dimensional discrete functions with intrinsic dimension. Via randomly embedding solutions from intrinsic subspace to original space and discretization, LSH-BO turns high-dimensional discrete optimization problems into low-dimensional continuous ones. Theoretically we prove that, with probability 1, there exists a corresponding optimal solution in the intrinsic subspace. The empirically results on both synthetic functions and binary quadratic programming task verify that LSH-BO surpasses the compared methods and possesses the versatility across low-dimensional and high-dimensional kernels.

This work is supported by National Natural Science Foundation of China (No. 62106076), Natural Science Foundation of Shanghai (No. 21ZR1420300), “Chenguang Program” sponsored by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (No. 21CGA32), and National Key Laboratory for Novel Software Technology at Nanjing University (No. KFKT2021B14). Hong Qian is the corresponding author of this paper.

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Authors and Affiliations

  1. School of Computer Science and Technology, East China Normal University, Shanghai, 200062, China

    Shu-Jun Li, Mingjia Li & Hong Qian

  2. National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 210023, China

    Hong Qian

Authors
  1. Shu-Jun Li
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  2. Mingjia Li
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  3. Hong Qian
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Correspondence to Hong Qian .

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Editors and Affiliations

  1. CSIRO Australian e-Health Research Centre, Brisbane, QLD, Australia

    Sankalp Khanna

  2. Shanghai Jiao Tong University, Shanghai, China

    Jian Cao

  3. University of Tasmania, Hobart, TAS, Australia

    Quan Bai

  4. University of Technology Sydney, Sydney, NSW, Australia

    Guandong Xu

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Li, SJ., Li, M., Qian, H. (2022). High-Dimensional Discrete Bayesian Optimization with Intrinsic Dimension. In: Khanna, S., Cao, J., Bai, Q., Xu, G. (eds) PRICAI 2022: Trends in Artificial Intelligence. PRICAI 2022. Lecture Notes in Computer Science, vol 13629. Springer, Cham. https://doi.org/10.1007/978-3-031-20862-1_39

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  • DOI: https://doi.org/10.1007/978-3-031-20862-1_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-20861-4

  • Online ISBN: 978-3-031-20862-1

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