We study the reinforcement learning problem in the setting of finite-horizon episodic Markov Decision Processes (MDPs) with $S$ states, $A$ actions, and episode length $H$. We propose a model-free algorithm UCB-Advantage and prove that it achieves $\tilde{O}(\sqrt{H^2SAT})$ regret where $T = KH$ and $K$ is the number of episodes to play. Our regret bound improves upon the results of [Jin et al., 2018] and matches the best known model-based algorithms as well as the information theoretic lower bound up to logarithmic factors. We also show that UCB-Advantage achieves low local switching cost and applies to concurrent reinforcement learning, improving upon the recent results of [Bai et al., 2019].

Screening and working set techniques are important approaches to reducing the size of an optimization problem. They have been widely used in accelerating first-order methods for solving large-scale sparse learning problems. In this paper, we develop a new screening method called Newton screening (NS) which is a generalized Newton method with a built-in screening mechanism. We derive an equivalent KKT system for the Lasso and utilize a generalized Newton method to solve the KKT equations. Based on this KKT system, a built-in working set with a relatively small size is first determined using the sum of primal and dual variables generated from the previous iteration, then the primal variable is updated by solving a least-squares problem on the working set and the dual variable updated based on a closed-form expression. Moreover, we consider a sequential version of Newton screening (SNS) with a warm-start strategy. We show that NS possesses an optimal convergence property in the sense that it achieves one-step local convergence. Under certain regularity conditions on the feature matrix, we show that SNS hits a solution with the same signs as the underlying true target and achieves a sharp estimation error bound with high probability. Simulation studies and real data analysis support our theoretical results and demonstrate that SNS is faster and more accurate than several state-of-the-art methods in our comparative studies.

The learning of deep models, in which a numerous of parameters are superimposed, is known to be a fairly sensitive process and should be carefully done through a combination of several techniques that can help to stabilize it. We introduce an additional challenge that has never been explicitly studied: the heterogeneity of sparsity at the instance level due to missing values or the innate nature of the input distribution. We confirm experimentally on the widely used benchmark datasets that this variable sparsity problem makes the output statistics of neurons unstable and makes the learning process more difficult by saturating non-linearities. We also provide the analysis of this phenomenon, and based on our analysis, we present a simple technique to prevent this issue, referred to as Sparsity Normalization (SN). Finally, we show that the performance can be significantly improved with SN on certain popular benchmark datasets, or that similar performance can be achieved with lower capacity. Especially focusing on the collaborative filtering problem where the variable sparsity issue has been completely ignored, we achieve new state-of-the-art results on Movielens 100k and 1M datasets, by simply applying Sparsity Normalization (SN).

Gene expression profiles have been widely used to characterize patterns of cellular responses to diseases. As data becomes available, scalable learning toolkits become essential to processing large datasets using deep learning models to model complex biological processes. We present an autoencoder to capture nonlinear relationships recovered from gene expression profiles. The autoencoder is a nonlinear dimension reduction technique using an artificial neural network, which learns hidden representations of unlabeled data. We train the autoencoder on a large collection of tumor samples from the National Cancer Institute Genomic Data Commons, and obtain a generalized and unsupervised latent representation. We leverage a HPC-focused deep learning toolkit, Livermore Big Artificial Neural Network (LBANN) to efficiently parallelize the training algorithm, reducing computation times from several hours to a few minutes. With the trained autoencoder, we generate latent representations of a small dataset, containing pairs of normal and cancer cells of various tumor types. A novel measure called autoencoder node saliency (ANS) is introduced to identify the hidden nodes that best differentiate various pairs of cells. We compare our findings of the best classifying nodes with principal component analysis and the visualization of t-distributed stochastic neighbor embedding. We demonstrate that the autoencoder effectively extracts distinct gene features for multiple learning tasks in the dataset.