Modern deep learning methods are very sensitive to many hyperparameters, and, due to the long training times of state-of-the-art models, vanilla Bayesian hyperparameter optimization is typically computationally infeasible. On the other hand, bandit-based configuration evaluation approaches based on random search lack guidance and do not converge to the best configurations as quickly. Here, we propose to combine the benefits of both Bayesian optimization and banditbased methods, in order to achieve the best of both worlds: strong anytime performance and fast convergence to optimal configurations. We propose a new practical state-of-the-art hyperparameter optimization method, which consistently outperforms both Bayesian optimization and Hyperband on a wide range of problem types, including high-dimensional toy functions, support vector machines, feed-forward neural networks, Bayesian neural networks, deep reinforcement learning, and convolutional neural networks. Our method is robust and versatile, while at the same time being conceptually simple and easy to implement.

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We revisit the one dimensional discrete time quantum walk with 3-states and the Grover coin, the simplest model that exhibits localization in a quantum walk. We derive analytic expressions for the localization and a long-time approximation for the entire probability density function (PDF). We also connect the time-averaged approximation of the PDF found by Inui et. al. to a spatial average of the walk. We show that this smoothed approximation predicts moments of the real PDF accurately.

While existing work on neural architecture search (NAS) tunes hyperparameters in a separate post-processing step, we demonstrate that architectural choices and other hyperparameter settings interact in a way that can render this separation suboptimal. Likewise, we demonstrate that the common practice of using very few epochs during the main NAS and much larger numbers of epochs during a post-processing step is inefficient due to little correlation in the relative rankings for these two training regimes. To combat both of these problems, we propose to use a recent combination of Bayesian optimization and Hyperband for efficient joint neural architecture and hyperparameter search.

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