In this paper we propose using machine learning to improve the design of deep neural network hardware accelerators. We show how to adapt multi-objective Bayesian optimization to overcome a challenging design problem: Optimizing deep neural network hardware accelerators for both accuracy and energy efficiency. DNN accelerators exhibit all aspects of a challenging optimization space: The landscape is rough, evaluating designs is expensive, the objectives compete with each other, and both design spaces (algorithmic and microarchitectural) are unwieldy. With multi-objective Bayesian optimization, the design space exploration is made tractable and the design points found vastly outperform traditional methods across all metrics of interest.