The design of machine learning systems often requires trading off different objectives, for example, prediction error and energy consumption for deep neural networks (DNNs). Typically, no single design performs well in all objectives; therefore, finding Pareto-optimal designs is of interest. The search for Pareto-optimal designs involves evaluating designs in an iterative process, and the measurements are used to evaluate an acquisition function that guides the search process. However, measuring different objectives incurs different costs. For example, the cost of measuring the prediction error of DNNs is orders of magnitude higher than that of measuring the energy consumption of a pre-trained DNN as it requires re-training the DNN. Current state-of-the-art methods do not consider this difference in objective evaluation cost, potentially incurring expensive evaluations of objective functions in the optimization process. In this paper, we develop a novel decoupled and cost-aware multi-objective optimization algorithm, which we call Flexible Multi-Objective Bayesian Optimization (FlexiBO) to address this issue. For evaluating each design, FlexiBO selects the objective with higher relative gain by weighting the improvement of the hypervolume of the Pareto region with the measurement cost of each objective. This strategy, therefore, balances the expense of collecting new information with the knowledge gained through objective evaluations, preventing FlexiBO from performing expensive measurements for little to no gain. We evaluate FlexiBO on seven state-of-the-art DNNs for image recognition, natural language processing (NLP), and speech-to-text translation. Our results indicate that, given the same total experimental budget, FlexiBO discovers designs with 4.8% to 12.4% lower hypervolume error than the best method in state-of-the-art multi-objective optimization.
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BOKEI: Bayesian optimization using knowledge of correlated torsions and expected improvement for conformer generation
A key challenge in conformer sampling is finding low-energy conformations with a small number of energy evaluations. We recently demonstrated the Bayesian Optimization Algorithm (BOA) is an effective method for finding the lowest energy conformation of a small molecule. Our approach balances between exploitation and exploration, and is more efficient than exhaustive or random search methods. Here, we extend strategies used on proteins and oligopeptides ( e.g. Ramachandran plots of secondary structure) and study correlated torsions in small molecules. We use bivariate von Mises distributions to capture correlations, and use them to constrain the search space. We validate the performance of our new method, Bayesian Optimization with Knowledge-based Expected Improvement (BOKEI), on a dataset consisting of 533 diverse small molecules, using (i) a force field (MMFF94); and (ii) a semi-empirical method (GFN2), as the objective function. We compare the search performance of BOKEI, BOA with Expected Improvement (BOA-EI), and a genetic algorithm (GA), using a fixed number of energy evaluations. In more than 60% of the cases examined, BOKEI finds lower energy conformations than global optimization with BOA-EI or GA. More importantly, we find correlated torsions in up to 15% of small molecules in larger data sets, up to 8 times more often than previously reported. The BOKEI patterns not only describe steric clashes, but also reflect favorable intramolecular interactions such as hydrogen bonds and π–π stacking. Increasing our understanding of the conformational preferences of molecules will help improve our ability to find low energy conformers efficiently, which will have impact in a wide range of computational modeling applications.
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- Award ID(s):
- 1800435
- NSF-PAR ID:
- 10177038
- Date Published:
- Journal Name:
- Physical Chemistry Chemical Physics
- Volume:
- 22
- Issue:
- 9
- ISSN:
- 1463-9076
- Page Range / eLocation ID:
- 5211 to 5219
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/C9CP06688H
