Targeted Adaptive Design
Carlo Graziani, Marieme Ngom
TL;DR
Targeted Adaptive Design (TAD) addresses the problem of locating a high-dimensional target design $f_T$ within tolerance $\tau$ using expensive, noisy mappings $f:X\to Y$. It builds a vector-valued Gaussian process surrogate and employs a closed-form ELPPD-based acquisition, coupled with the expected information gain, to batch-sample control settings and adaptively balance exploration and exploitation. The framework includes rigorous model validation, dynamic complexity adjustment, and stopping rules that declare either convergence to a solution within tolerance or global convergence failure when the target is unlikely. Empirically, TAD demonstrates robust convergence on twin-peak and DTLZ4 benchmarks and outperforms an $L_2$-based baseline by exploiting directional uncertainty, with practical implications for efficient design of advanced manufacturing processes. The approach advances Bayesian optimization and adaptive experimental design by explicitly incorporating per-output tolerances and information-theoretic stopping criteria in a scalable, gradient-friendly, batch-sequential setting.
Abstract
Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. We abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate optimal control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated log-predictive likelihood of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.