Bayesian optimization (BO) has recently emerged as powerful method for the global optimization of expensive-to-evaluate black-box functions. However, these methods are usually limited to about 15 input parameters (levers). In the paper "A Framework for Bayesian Optimization in Embedded Subspaces" (to appear at ICML'19), Munteanu, Nayebi, and Poloczek propose a non-adaptive probabilistic subspace embedding that can be combined with many BO algorithms to enable them to higher dimensional problems.

This repository provides Python implementations of several algorithms that extend BO to problems with high input dimensions:

• The HeSBO algorithm proposed by Munteanu, Nayebi, and Poloczek (ICML '19) (see below for the citation) combined with

  • The Knowledge Gradient (KG) algorithm of Cornell-MOE (Wu & Frazier NIPS'16; Wu, Poloczek, Wilson, and Frazier NIPS'17)

  • The BLOSSOM algorithm of McLeod, Osborne, and Roberts (ICML '18)

  • Expected improvement, e.g., see Jones, Schonlau, and Welch (JGO '98)

• The REMBO method using

  • the K_Xand K_y kernels of Wang et al. (JMLR '18) and

  • the K kernel of Binois, Ginsbourger and Roustant (LION '15).

The codes are written in python 3.6, so it is recommended to use this version of python to run the scripts. To install the requirements one can simply use this line:

pip3 install -r requirements.txt

There are HeSBO and three different variants of REMBO implemented in this code. Three REMBO variants are called K_y, K_X, and K . These algorithms can be run as follows.

python experiments.py [algorithm] [first_job_id] [last_job_id] [test_function] [num_of_steps] [low_dim] [high_dim] [num_of_initial_sample] [noise_variance] [REMBO_variant]

To determine the algorithm, use REMBO or HeSBO input for the python script. If REMBO algorithm is selected to be run, the REMBO variant must be determined by X, Y, or psi as the last argument. If none of those variants is picked, all of those variants will be run. Here is an example of running HeSBO-EI on 100 dim noise-free Branin with 4 low dimensions:

python experiments.py HeSBO 1 1 Branin 80 4 100 10 0

To collect the output data, you must have a folder named "results". Here is a plot for running REMBO-K and HeSBO-EI on the Branin function.

@inproceedings{HeSBO19,
  author    = {Alex Munteanu and
               Amin Nayebi and
			   Matthias Poloczek},
  title     = {A Framework for Bayesian Optimization in Embedded Subspaces},
  booktitle = {Proceedings of the 36th International Conference on Machine Learning, {(ICML)}},
  year      = {2019},
  note={Accepted for publication. The code is available at https://github.com/aminnayebi/HesBO.}
}