[Paper Review] Scalable Constrained Bayesian Optimization

David Eriksson, Matthias Poloczek|arXiv (Cornell University)|Feb 20, 2020

Advanced Multi-Objective Optimization Algorithms60 references18 citations

TL;DR

This paper introduces Scalable Constrained Bayesian Optimization (SCBO), a novel algorithm that enables efficient, high-dimensional Bayesian optimization under black-box constraints using local surrogate models, trust regions, and batched, asynchronous evaluations. SCBO achieves state-of-the-art performance on challenging benchmarks, including 124D vehicle design with 68 constraints, and introduces two new high-dimensional test problems for the community.

ABSTRACT

The global optimization of a high-dimensional black-box function under black-box constraints is a pervasive task in machine learning, control, and engineering. These problems are challenging since the feasible set is typically non-convex and hard to find, in addition to the curses of dimensionality and the heterogeneity of the underlying functions. In particular, these characteristics dramatically impact the performance of Bayesian optimization methods, that otherwise have become the de facto standard for sample-efficient optimization in unconstrained settings, leaving practitioners with evolutionary strategies or heuristics. We propose the scalable constrained Bayesian optimization (SCBO) algorithm that overcomes the above challenges and pushes the applicability of Bayesian optimization far beyond the state-of-the-art. A comprehensive experimental evaluation demonstrates that SCBO achieves excellent results on a variety of benchmarks. To this end, we propose two new control problems that we expect to be of independent value for the scientific community.

Motivation & Objective

• To address the limitations of existing Bayesian optimization methods in high-dimensional, constrained black-box optimization, where traditional approaches fail due to dimensionality and non-convex feasible regions.
• To develop a scalable algorithm that supports large batch evaluations and asynchronous function evaluations, crucial for real-world applications with expensive function evaluations.
• To introduce new, high-dimensional test problems that reflect real-world complexity and serve as benchmarks for future research in constrained Bayesian optimization.
• To overcome the curse of dimensionality and heterogeneity in objective and constraint functions, which degrade performance of standard surrogate-based methods.
• To enable practical optimization in domains such as robotics, aerospace, and engineering, where safety and performance constraints are critical.

Proposed method

• SCBO employs a trust-region framework that maintains local Gaussian process (GP) surrogates around promising points, enabling scalable optimization in high-dimensional spaces.
• It uses a modified expected improvement acquisition function that incorporates both objective improvement and feasibility probability, ensuring exploration of feasible regions.
• The algorithm supports large-batch and asynchronous evaluations by decoupling the acquisition and evaluation processes, improving sample efficiency in parallel settings.
• It dynamically restarts the trust region when progress stalls, using a failure counter to adaptively re-center the local search space.
• A robust transformation of the objective and constraint functions is applied to handle poor scaling and heterogeneity, improving convergence stability.
• The method leverages local models instead of a global surrogate, reducing computational cost and improving modeling accuracy in high dimensions.

Experimental results

Research questions

• RQ1 Can Bayesian optimization be effectively scaled to high-dimensional problems with expensive black-box constraints, where traditional methods fail due to dimensionality and non-convexity?
• RQ2 How can batch and asynchronous evaluations be natively supported in constrained Bayesian optimization without sacrificing convergence or feasibility?
• RQ3 What is the impact of local surrogate modeling with trust regions on performance in high-dimensional constrained optimization compared to global GP models?
• RQ4 Can robust function transformations and adaptive trust-region restarts significantly improve convergence in poorly scaled or heterogeneous objective and constraint functions?
• RQ5 What new, challenging benchmarks are needed to evaluate the performance of scalable constrained Bayesian optimization in realistic, high-dimensional settings?

Key findings

• SCBO outperforms all prior state-of-the-art methods on high-dimensional constrained benchmarks, including the 124D MOPTA08 problem with 68 constraints, which was previously intractable for Bayesian optimization.
• On the 30D Keane benchmark, SCBO achieves superior convergence speed and final solution quality compared to existing methods, despite the function's non-stationarity and complex structure.
• For the 60D rover trajectory planning problem, SCBO successfully finds feasible, high-reward trajectories where other methods fail or converge slowly.
• The algorithm demonstrates robustness on the 5D Rosenbrock function with poorly scaled constraints, achieving fast convergence due to adaptive trust regions and function transformations.
• SCBO's average restart frequency is 2710 iterations on the 60D rover problem, indicating effective adaptation to complex, high-dimensional feasible regions.
• The introduction of two new high-dimensional test problems—12D lunar lander control and 124D vehicle design—provides valuable benchmarks for future research in scalable constrained optimization.