ADMMBO: Bayesian Optimization with Unknown Constraints using ADMM.

Area of Science:

• Engineering
• Computer Science
• Applied Mathematics

Background:

• Bayesian Optimization (BO) is effective for optimizing expensive black-box functions.
• Optimizing functions with unknown constraints is a significant challenge with existing method limitations.

Purpose of the Study:

• To present a novel constrained Bayesian optimization framework for unknown objective functions and unknown constraints.
• To address limitations of current methods in handling constrained optimization problems.

Main Methods:

• Developed a constrained Bayesian optimization framework by augmenting the objective function with constraints and auxiliary variables.
• Proposed ADMM-Bayesian Optimization (ADMMBO), an iterative approach based on the Alternating Direction Method of Multipliers (ADMM).
• Solved multiple unconstrained subproblems using Bayesian Optimization (BO).

Main Results:

• ADMMBO demonstrates superior performance compared to state-of-the-art methods on challenging benchmark problems.
• The framework achieves faster feasible solution acquisition and improved convergence to the global optimum.
• ADMMBO effectively minimizes the total number of objective and constraint function evaluations.

Conclusions:

• ADMMBO offers a robust solution for constrained Bayesian optimization, overcoming challenges like infeasible starting points and initialization sensitivity.
• The method provides a concrete stopping criterion and efficiently handles decoupled problems.
• ADMMBO represents a significant advancement in optimizing complex, real-world problems with unknown constraints.