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The design of machine learning systems often requires trading off differentobjectives, for example, prediction error and energy consumption for deepneural networks (DNNs). Typically, no single design performs well in allobjectives; therefore, finding Pareto-optimal designs is of interest. Thesearch for Pareto-optimal designs involves evaluating designs in an iterativeprocess, and the measurements are used to evaluate an acquisition function thatguides the search process. However, measuring different objectives incursdifferent costs. For example, the cost of measuring the prediction error ofDNNs is orders of magnitude higher than that of measuring the energyconsumption of a pre-trained DNN, as it requires re-training the DNN. Currentstate-of-the-art methods do not consider this difference in objectiveevaluation cost, potentially incurring expensive evaluations of objectivefunctions in the optimization process. In this paper, we develop a noveldecoupled and cost-aware multi-objective optimization algorithm, we callFlexible Multi-Objective Bayesian Optimization (FlexiBO) to address this issue.FlexiBO weights the improvement of the hypervolume of the Pareto region by themeasurement cost of each objective to balance the expense of collecting newinformation with the knowledge gained through objective evaluations, preventingus from performing expensive measurements for little to no gain. We evaluateFlexiBO on seven state-of-the-art DNNs for image recognition, natural languageprocessing (NLP), and speech-to-text translation. Our results indicate that,given the same total experimental budget, FlexiBO discovers designs with4.8$\%$ to 12.4$\%$ lower hypervolume error than the best method instate-of-the-art multi-objective optimization.

FlexiBO: A Decoupled Cost-Aware Multi-Objective Optimization Approach for Deep Neural Networks