SMGO-$\Delta$: Balancing Caution and Reward in Global Optimization with Black-Box Constraints

TL;DR

SMGO-$\Delta$ is a global optimization method for black-box problems with constraints, balancing caution and reward through a tunable risk parameter, and validated on benchmarks and a control tuning case study.

Contribution

The paper introduces SMGO-$\Delta$, a novel set membership-based algorithm for constrained black-box optimization with adjustable safety and exploration trade-offs.

Findings

Theoretical convergence properties are established.

Performance surpasses existing methods on benchmark problems.

Effective in practical control system tuning scenarios.

Abstract

In numerous applications across all science and engineering areas, there are optimization problems where both the objective function and the constraints have no closed-form expression or are too complex to be managed analytically, that they can only be evaluated through experiments. To address such issues, we design a global optimization technique for problems with black-box objective and constraints. Assuming Lipschitz continuity of the cost and constraint functions, a Set Membership framework is adopted to build a surrogate model of the optimization program, that is used for exploitation and exploration routines. The resulting algorithm, named Set Membership Global Optimization With Black-Box Constraints (SMGO-$\Delta$), features one tunable risk parameter, which the user can intuitively adjust to trade-off safety, exploitation, and exploration. The theoretical properties of the algorithm are derived, and the optimization performance is compared with representative techniques from the literature in several benchmarks. Lastly, it is tested and compared with constrained Bayesian optimization in a case study pertaining to model predictive control tuning for a servomechanism with disturbances and plant uncertainties, addressing practically-motivated task-level constraints.