Bounce: Reliable High-Dimensional Bayesian Optimization for Combinatorial and Mixed Spaces

Core Concepts

Bounce proposes a reliable algorithm for optimizing high-dimensional black-box functions in combinatorial and mixed spaces, outperforming state-of-the-art methods.

Abstract

This paper introduces Bounce, a novel algorithm for Bayesian optimization in high-dimensional spaces. It addresses the limitations of current methods by leveraging nested embeddings and trust region management. The experimental evaluation demonstrates Bounce's robust performance across various benchmarks, surpassing existing algorithms like BODi and COMBO. The algorithm's ability to handle mixed variable spaces efficiently makes it a valuable tool for real-world applications. Abstract: Impactful applications require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. Current state-of-the-art methods are unreliable when the unknown optima lack structure. Bounce proposes a novel algorithm that achieves reliable performance on high-dimensional problems. Introduction: Bayesian optimization is crucial for optimizing expensive-to-evaluate black-box functions with numerous applications. Challenges arise from high-dimensionality and different variable types in real-world problems. Recent efforts extend Bayesian optimization to combinatorial and mixed spaces. Algorithm Overview: Bounce uses nested embeddings to model GP in low-dimensional subspaces efficiently. Trust region management allows focusing on promising regions of high-dimensional target spaces. Batch parallelism enables parallel evaluations of the objective function, improving sample efficiency. Experimental Evaluation: Empirical evaluation shows Bounce outperforms state-of-the-art algorithms on diverse benchmarks. Sensitivity analysis reveals shortcomings of existing methods like BODi and COMBO. Bounce demonstrates robust performance across various tasks, making it a reliable optimizer for practitioners. Conclusion: Bounce offers a scalable solution for optimizing high-dimensional black-box functions in combinatorial and mixed spaces. The algorithm's reliability and performance superiority make it a valuable tool for practical applications.

Stats

"BODi is more susceptible to the location of the optimizer than COMBO." "COMBO's implementation suffers from a bug explained in Appendix H.2."

Quotes

"Bounce leverages parallel function evaluations efficiently." "The proposed algorithm is reliable for high-dimensional black-box optimization."

Key Insights Distilled From

Bounce

by Leonard Pape... at arxiv.org 03-21-2024

https://arxiv.org/pdf/2307.00618.pdf

Deeper Inquiries

How can the concept of nested embeddings be applied to other optimization problems

The concept of nested embeddings, as demonstrated in the Bounce algorithm for high-dimensional Bayesian optimization, can be applied to various other optimization problems. By mapping variables into nested embeddings of increasing dimensionality, it becomes possible to handle high-dimensional spaces more efficiently and effectively. This approach can be particularly useful in tasks where there are multiple types of input variables with different characteristics or when dealing with combinatorial and mixed spaces. For example, in machine learning model hyperparameter tuning, nested embeddings could help optimize over a large set of hyperparameters that include both continuous and categorical variables. By organizing these variables into nested subspaces based on their type, the optimization process can be streamlined and made more robust. Similarly, in materials discovery or chemical engineering applications, where optimizing complex compositions is crucial, using nested embeddings can enhance the search efficiency by structuring the search space intelligently. Overall, applying the concept of nested embeddings to other optimization problems allows for better handling of high-dimensional spaces with diverse variable types while improving performance and reliability.

What implications does the sensitivity of existing algorithms to optimal locations have on real-world applications

The sensitivity of existing algorithms to optimal locations has significant implications for real-world applications across various domains. When algorithms like BODi and COMBO show degradation in performance due to changes in the location or structure of optima within a problem space, it raises concerns about their reliability and applicability. In practical scenarios such as drug discovery or materials design where precise optimizations are critical for success, relying on algorithms that are sensitive to optimal locations poses risks. A small change in the structure or position of an optimum could lead these algorithms astray from finding truly optimal solutions. This sensitivity may result in suboptimal outcomes or even failure to converge on satisfactory solutions within a reasonable time frame. Therefore, understanding this sensitivity underscores the importance of developing more robust optimization algorithms that are resilient to variations in optimal locations. It highlights the need for advanced techniques like Bounce that demonstrate reliable performance across different scenarios without being heavily influenced by specific structures within problem spaces.

How can the findings of this study impact the development of future optimization algorithms

The findings from this study have several implications for future developments in optimization algorithms: Robustness: The study emphasizes the importance of developing robust optimization algorithms that can perform consistently across different scenarios without being overly sensitive to specific structures within problem spaces. Efficiency: The success of Bounce demonstrates how efficient parallel function evaluations through batch acquisition strategies can significantly improve sample efficiency during optimization processes. Adaptability: Future algorithms should aim at incorporating adaptive strategies like dynamic TR management seen in Bounce to adjust parameters based on evaluation budgets effectively. Diverse Applications: The study's impact extends beyond Bayesian Optimization; future research could explore applying similar concepts like nested embeddings across various fields requiring complex optimizations involving mixed-variable types. By leveraging these insights from current research findings such as those presented by Bounce's development and evaluation process will pave the way towards more effective and reliable optimization methods suitable for a wide range of real-world applications."