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Machine learning system design frequently necessitates balancing multiple objectives, such as prediction error and energy consumption, for deep neural networks (DNNs). Typically, no single design performs well across all objectives; thus, finding Pareto-optimal designs is of interest. Measuring different objectives frequently incurs different costs; for example, measuring the prediction error of DNNs is significantly more expensive than measuring the energy consumption of a pre-trained DNN because it requires re-training the DNN. Current state-of-the-art methods do not account for this difference in objective evaluation cost, potentially wasting costly evaluations of objective functions for little information gain. To address this issue, we propose a novel cost-aware decoupled approach that weights the improvement of the hypervolume of the Pareto region by the measurement cost of each objective. To evaluate our approach, we perform experiments on several machine learning systems deployed on energy constraints environments.