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Inversion-based Latent Bayesian Optimization

Jaewon Chu, Jinyoung Park, Seunghun Lee, Hyunwoo J. Kim

TL;DR

Inversion-based Latent Bayesian Optimization (InvBO), a plug-and-play module for LBO that considers the potential capability of the trust region for better local optimization, is proposed.

Abstract

Latent Bayesian optimization (LBO) approaches have successfully adopted Bayesian optimization over a continuous latent space by employing an encoder-decoder architecture to address the challenge of optimization in a high dimensional or discrete input space. LBO learns a surrogate model to approximate the black-box objective function in the latent space. However, we observed that most LBO methods suffer from the `misalignment problem`, which is induced by the reconstruction error of the encoder-decoder architecture. It hinders learning an accurate surrogate model and generating high-quality solutions. In addition, several trust region-based LBO methods select the anchor, the center of the trust region, based solely on the objective function value without considering the trust region`s potential to enhance the optimization process. To address these issues, we propose Inversion-based Latent Bayesian Optimization (InvBO), a plug-and-play module for LBO. InvBO consists of two components: an inversion method and a potential-aware trust region anchor selection. The inversion method searches the latent code that completely reconstructs the given target data. The potential-aware trust region anchor selection considers the potential capability of the trust region for better local optimization. Experimental results demonstrate the effectiveness of InvBO on nine real-world benchmarks, such as molecule design and arithmetic expression fitting tasks. Code is available at https://github.com/mlvlab/InvBO.

Inversion-based Latent Bayesian Optimization

TL;DR

Inversion-based Latent Bayesian Optimization (InvBO), a plug-and-play module for LBO that considers the potential capability of the trust region for better local optimization, is proposed.

Abstract

Latent Bayesian optimization (LBO) approaches have successfully adopted Bayesian optimization over a continuous latent space by employing an encoder-decoder architecture to address the challenge of optimization in a high dimensional or discrete input space. LBO learns a surrogate model to approximate the black-box objective function in the latent space. However, we observed that most LBO methods suffer from the `misalignment problem`, which is induced by the reconstruction error of the encoder-decoder architecture. It hinders learning an accurate surrogate model and generating high-quality solutions. In addition, several trust region-based LBO methods select the anchor, the center of the trust region, based solely on the objective function value without considering the trust region`s potential to enhance the optimization process. To address these issues, we propose Inversion-based Latent Bayesian Optimization (InvBO), a plug-and-play module for LBO. InvBO consists of two components: an inversion method and a potential-aware trust region anchor selection. The inversion method searches the latent code that completely reconstructs the given target data. The potential-aware trust region anchor selection considers the potential capability of the trust region for better local optimization. Experimental results demonstrate the effectiveness of InvBO on nine real-world benchmarks, such as molecule design and arithmetic expression fitting tasks. Code is available at https://github.com/mlvlab/InvBO.

Paper Structure

This paper contains 36 sections, 2 theorems, 13 equations, 17 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Latent Bayesian Optimization
  4. Inversion in Generative Models
  5. Preliminaries
  6. Method
  7. Misalignment in Latent Bayesian Optimization
  8. Inversion-based Latent Bayesian Optimization
  9. Potential-aware Trust Region Anchor Selection
  10. Experiments
  11. Tasks
  12. Baselines
  13. Implementation Details
  14. Experimental Results
  15. Analysis
  16. ...and 21 more sections

Key Result

Proposition 1

Let $f$ be a black-box objective function and $m$ be a posterior mean of Gaussian process, $p_\theta$ be a decoder of the variational autoencoder, $c$ be an arbitrarily small constant, $d_{\mathcal{X}}$ and $d_\mathcal{Z}$ be the distance function on input $\mathcal{X}$ and latent $\mathcal{Z}$ spac Then the difference between the posterior mean of the arbitrary point $\mathbf{z}'$ in the trust re

Figures (17)

  • Figure 1: Comparison of solutions to the misalignment problem. (a) Some works maus2022locallee2023advancing solve the misalignment problem by the recentering technique that generates the aligned triplet $\left(\mathbf{x}', \mathbf{z}, y' \right)$. However, it requests additional oracle calls as $y' = f(\mathbf{x}')$ is unevaluated, and does not fully use the evaluated function value $y = f(\mathbf{x})$. (b) The inversion method (ours) aims to find $\mathbf{z}_{\text{inv}}$ that generates the evaluated data $\mathbf{x}$ to get the aligned triplet $\left(\mathbf{x}, \mathbf{z}_{\text{inv}}, y\right)$ without any additional oracle calls.
  • Figure 2: (Left) The number of oracle calls to evaluate the queries selected by the acquisition function (blue) and during the recentering (Red). (Right) The number of objective function evaluation that updates the best score.
  • Figure 3: Optimization results on Guacamol benchmark tasks. The lines and ranges indicate the average and standard error of ten runs under the same settings. A higher score is a better score.
  • Figure 4: Optimization results on various tasks and settings. Note that: (a) A lower score is a better score. (b) A higher score is a better score.
  • Figure 5: Optimization results of component ablation on zale, med2, osmb, and valt.
  • ...and 12 more figures

Theorems & Definitions (3)

  • Proposition 1
  • Proposition 1
  • proof