One of the key challenges in designing machine learning systems is to determine the right balance amongst several objectives, which also oftentimes are incommensurable and conflicting. For example, when designing deep neural networks (DNNs), one often has to trade-off between multiple objectives, such as accuracy, energy consumption, and inference time. Typically, there is no single configuration that performs equally well for all objectives. Consequently, one is interested in identifying Pareto-optimal designs. Although different multi-objective optimization algorithms have been developed to identify Pareto-optimal configurations, state-of-the-art multi-objective optimization methods do not consider the different evaluation costs attending the objectives under consideration. This is particularly important for optimizing DNNs: the cost arising on account of assessing the accuracy of DNNs is orders of magnitude higher than that of measuring the energy consumption of pre-trained DNNs. We propose FlexiBO, a flexible Bayesian optimization method, to address this issue. We formulate a new acquisition function based on the improvement of the Pareto hyper-volume weighted by the measurement cost of each objective. Our acquisition function selects the next sample and objective that provides maximum information gain per unit of cost. We evaluated FlexiBO on 7 state-of-theart DNNs for object detection, natural language processing, and speech recognition. Our results indicate that, when compared to other state-of-theart methods across the 7 architectures we tested, the Pareto front obtained using FlexiBO has, on average, a 28.44% higher contribution to the true Pareto front and achieves 25.64% better diversity.

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