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Multi-Task Surrogate-Assisted Search with Bayesian Competitive Knowledge Transfer for Expensive Optimization

Yi Lu, Xiaoming Xue, Kai Zhang, Liming Zhang, Guodong Chen, Chenming Cao, Piyang Liu, Kay Chen Tan

TL;DR

This paper tackles the cold-start problem in expensive optimization by introducing Bayesian Competitive Knowledge Transfer (BCKT) to MSAS. By modeling transferability as a latent variable and updating it with both prior beliefs and empirical data, MSAS-BCKT enables a competitive selection between source and target solutions for real evaluation, yielding adaptive, nonnegative improvements across multiple EOPs. The authors prove asymptotic unbiasedness and efficiency of the transferability estimation, analyze computational complexity, and demonstrate broad empirical gains across MTOPs and MaTOPs, including a petroleum well-placement case. The work showcases strong portability, scalability, and adaptability of BCKT and provides code for replication, highlighting practical impact for resource-constrained optimization in diverse domains.

Abstract

Expensive optimization problems (EOPs) present significant challenges for traditional evolutionary optimization due to their limited evaluation calls. Although surrogate-assisted search (SAS) has become a popular paradigm for addressing EOPs, it still suffers from the cold-start issue. In response to this challenge, knowledge transfer has been gaining popularity for its ability to leverage search experience from potentially related instances, ultimately facilitating head-start optimization for more efficient decision-making. However, the curse of negative transfer persists when applying knowledge transfer to EOPs, primarily due to the inherent limitations of existing methods in assessing knowledge transferability. On the one hand, a priori transferability assessment criteria are intrinsically inaccurate due to their imprecise understandings. On the other hand, a posteriori methods often necessitate sufficient observations to make correct inferences, rendering them inefficient when applied to EOPs. Considering the above, this paper introduces a Bayesian competitive knowledge transfer (BCKT) method developed to improve multi-task SAS (MSAS) when addressing multiple EOPs simultaneously. Specifically, the transferability of knowledge is estimated from a Bayesian perspective that accommodates both prior beliefs and empirical evidence, enabling accurate competition between inner-task and inter-task solutions, ultimately leading to the adaptive use of promising solutions while effectively suppressing inferior ones. The effectiveness of our method in boosting various SAS algorithms for both multi-task and many-task problems is empirically validated, complemented by comparative studies that demonstrate its superiority over peer algorithms and its applicability to real-world scenarios. The source code of our method is available at https://github.com/XmingHsueh/MSAS-BCKT.

Multi-Task Surrogate-Assisted Search with Bayesian Competitive Knowledge Transfer for Expensive Optimization

TL;DR

This paper tackles the cold-start problem in expensive optimization by introducing Bayesian Competitive Knowledge Transfer (BCKT) to MSAS. By modeling transferability as a latent variable and updating it with both prior beliefs and empirical data, MSAS-BCKT enables a competitive selection between source and target solutions for real evaluation, yielding adaptive, nonnegative improvements across multiple EOPs. The authors prove asymptotic unbiasedness and efficiency of the transferability estimation, analyze computational complexity, and demonstrate broad empirical gains across MTOPs and MaTOPs, including a petroleum well-placement case. The work showcases strong portability, scalability, and adaptability of BCKT and provides code for replication, highlighting practical impact for resource-constrained optimization in diverse domains.

Abstract

Expensive optimization problems (EOPs) present significant challenges for traditional evolutionary optimization due to their limited evaluation calls. Although surrogate-assisted search (SAS) has become a popular paradigm for addressing EOPs, it still suffers from the cold-start issue. In response to this challenge, knowledge transfer has been gaining popularity for its ability to leverage search experience from potentially related instances, ultimately facilitating head-start optimization for more efficient decision-making. However, the curse of negative transfer persists when applying knowledge transfer to EOPs, primarily due to the inherent limitations of existing methods in assessing knowledge transferability. On the one hand, a priori transferability assessment criteria are intrinsically inaccurate due to their imprecise understandings. On the other hand, a posteriori methods often necessitate sufficient observations to make correct inferences, rendering them inefficient when applied to EOPs. Considering the above, this paper introduces a Bayesian competitive knowledge transfer (BCKT) method developed to improve multi-task SAS (MSAS) when addressing multiple EOPs simultaneously. Specifically, the transferability of knowledge is estimated from a Bayesian perspective that accommodates both prior beliefs and empirical evidence, enabling accurate competition between inner-task and inter-task solutions, ultimately leading to the adaptive use of promising solutions while effectively suppressing inferior ones. The effectiveness of our method in boosting various SAS algorithms for both multi-task and many-task problems is empirically validated, complemented by comparative studies that demonstrate its superiority over peer algorithms and its applicability to real-world scenarios. The source code of our method is available at https://github.com/XmingHsueh/MSAS-BCKT.

Paper Structure

This paper contains 29 sections, 25 equations, 13 figures, 14 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multi-task Surrogate-Assisted Search (MSAS)
  4. When to Transfer
  5. A Priori Methods
  6. A Posteriori Approaches
  7. Hybrid Methods
  8. Motivations
  9. Proposed Methods
  10. Transferability in CKT
  11. Bayesian Inference of Transferability
  12. Prior Belief
  13. A Priori Criterion
  14. Likelihood
  15. Bayesian CKT for MSAS
  16. ...and 14 more sections

Figures (13)

  • Figure 1: High-level structure of MSAS.
  • Figure 2: Taxonomy of the existing techniques for when to transfer: an epistemological perspective.
  • Figure 3: Flowcharts of MSAS-BCKT and BCKT: (a) the overall structure of MSAS-BCKT; (b) the workflow of BCKT.
  • Figure 4: Illustration of the internal and external improvements.
  • Figure 5: Averaged convergence curves of MSAS-BCKT and MSAS on three selected problems: (a) MTOP 1 (Task 1); (b) MTOP 6 (Task 1); (c) MTOP 6 (Task 2); (d) MTOP 8 (Task 2).
  • ...and 8 more figures