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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. 

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.