ParetoUCB—Simple and Fast Multi-Objective Bayesian Optimization for Materials Synthesis Experiments

The objective of many new materials synthesis experiments is to simultaneously optimize two or more material properties, for example maximizing infrared/visible transparency while minimizing DC electrical resistivity in transparent conductors [1]. Often the physics and chemistry needed to optimize one property conflict with that needed for other properties, so attaining globally optimal values for all objectives as if they were independent is not possible. In such a case the experiment becomes a classic multi-objective optimization problem with the goal of determining the Pareto frontier: the set of objective values where further improvement in any one objective can only come at the expense of degrading one or more other objectives.<br/><br/>Many machine learning (ML) algorithms exist for finding the Pareto frontier of multi-objective optimization problems involving black-box functions using a Bayesian optimization approach. Most of these are based on general methods which in theory are scalable to the mathematically difficult problem of high dimensional spaces for both input predictors and output objectives and so are computationally intensive and non-intuitive. Such ML methods may be overkill for many if not most real materials synthesis experiments involving predictor space dimensions ≤ 6 and only two or three objectives. This work describes a ML Bayesian optimization approach to determine the Pareto frontier that is computationally simple, intuitive, easily extendible to batch sample acquisition, and converges rapidly for the relatively low dimensional problems typically encountered in materials synthesis experiments. We nicknamed this method “ParetoUCB” because it uses as the acquisition function upper confidence bound (UCB) values evaluated solely over the Pareto frontier of a Gaussian process regression model generated from sampled data. In several trials using synthetic data generated by common test functions on problems with predictor dimensions ≤ 4 and two or three objectives, ParetoUCB (coded in Matlab running on a desktop Apple M2 CPU) converged onto the Pareto frontier more accurately, with the same or fewer number of data evaluations, and as fast or faster in real computational time benchmarked against the widely used BoTorch Python package using its qEHVI or qNEHVI multi-objective acquisition functions (coded in Python running on either a desktop Apple M2 GPU core or an Nvidia GPU via Colab). Limitations of ParetoUCB when extended to higher dimensional problems and its use with actual experimental data will be discussed.<br/><br/>This work is supported by NSF CMMI-2109554.<br/><br/>References<br/>[1] M. Lee, et al., ACS Appl. Nano Mater. 6, 17364 (2023), doi.org/10.1021/acsanm.3c03599