TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) and Maximum A Posteriori estimation problems, especially for models with latent variables. It is also the algorithm of choice to fit mixture models: generative models that represent unlabelled points originating from $k$ different processes, as samples from $k$ multivariate distributions. In this work we define and use a quantum version of EM to fit a Gaussian Mixture Model. Given quantum access to a dataset of $n$ vectors of dimension $d$, our algorithm has convergence and precision guarantees similar to the classical algorithm, but the runtime is only polylogarithmic in the number of elements in the training set, and is polynomial in other parameters - as the dimension of the feature space, and the number of components in the mixture. We generalize further the algorithm by fitting any mixture model of base distributions in the exponential family. We discuss the performance of the algorithm on datasets that are expected to be classified successfully by those algorithms, arguing that on those cases we can give strong guarantees on the runtime.

SOLUTION: It's the quantum algorithm for Expectation Maximization. It's fast: the runtime depends only polylogarithmically on the number of elements in the dataset. 

PROBLEM: Transfer and adaptation to new unknown environmental dynamics is a key challenge for reinforcement learning (RL). An even greater challenge is performing near-optimally in a single attempt at test time, possibly without access to dense rewards, which is not addressed by current methods that require multiple experience rollouts for adaptation. To achieve single episode transfer in a family of environments with related dynamics, we propose a general algorithm that optimizes a probe and an inference model to rapidly estimate underlying latent variables of test dynamics, which are then immediately used as input to a universal control policy. This modular approach enables integration of state-of-the-art algorithms for variational inference or RL. Moreover, our approach does not require access to rewards at test time, allowing it to perform in settings where existing adaptive approaches cannot. In diverse experimental domains with a single episode test constraint, our method significantly outperforms existing adaptive approaches and shows favorable performance against baselines for robust transfer.

SOLUTION: Single episode policy transfer in a family of environments with related dynamics, via optimized probing for rapid inference of latent variables and immediate execution of a universal policy.

PROBLEM: In deep learning, performance is strongly affected by the choice of architecture
 and hyperparameters. While there has been extensive work on automatic hyperpa-
 rameter optimization for simple spaces, complex spaces such as the space of deep
 architectures remain largely unexplored. As a result, the choice of architecture is
 done manually by the human expert through a slow trial and error process guided
 mainly by intuition. In this paper we describe a framework for automatically
 designing and training deep models. We propose an extensible and modular lan-
 guage that allows the human expert to compactly represent complex search spaces
 over architectures and their hyperparameters. The resulting search spaces are tree-
 structured and therefore easy to traverse. Models can be automatically compiled to
 computational graphs once values for all hyperparameters have been chosen. We
 can leverage the structure of the search space to introduce different model search
 algorithms, such as random search, Monte Carlo tree search (MCTS), and sequen-
 tial model-based optimization (SMBO). We present experiments comparing the
 different algorithms on CIFAR-10 and show that MCTS and SMBO outperform
 random search. We also present experiments on MNIST, showing that the same
 search space achieves near state-of-the-art performance with a few samples. These
 experiments show that our framework can be used effectively for model discov-
 ery, as it is possible to describe expressive search spaces and discover competitive
 models without much effort from the human expert. Code for our framework and
 experiments has been made publicly available

SOLUTION:
We describe a modular and composable language for describing expressive search spaces over architectures and simple model search algorithms applied to these search spaces.