Many complex domains, such as robotics control and real-time strategy (RTS) games, require an agent to learn a continuous control. In the former, an agent learns a policy over $\mathbb{R}^d$ and in the latter, over a discrete set of actions each of which is parametrized by a continuous parameter. Such problems are naturally solved using policy based reinforcement learning (RL) methods, but unfortunately these often suffer from high variance leading to instability and slow convergence. We show that in many cases a substantial portion of the variance in policy gradient estimators is completely unnecessary and can be eliminated without introducing bias. Unnecessary variance is introduced whenever policies over bounded action spaces are modeled using distributions with unbounded support, by applying a transformation $T$ to the sampled action before execution in the environment. Recent works have studied variance reduced policy gradients for actions in bounded intervals, but to date no variance reduced methods exist when the action is a direction -- constrained to the unit sphere -- something often seen in RTS games. To address these challenges we: (1) introduce a stochastic policy gradient method for directional control; (2) introduce the marginal policy gradient framework, a powerful technique to obtain variance reduced policy gradients for arbitrary $T$; (3) show that marginal policy gradients are guaranteed to reduce variance, quantifying that reduction exactly; (4) validate our framework by applying the methods to a popular RTS game and a navigation task, demonstrating improvement over a policy gradient baseline.

Deep Neural Networks (DNN) are increasingly deployed in highly energy-constrained environments such as autonomous drones and wearable devices while at the same time must operate in real-time. Therefore, reducing the energy consumption has become a major design consideration in DNN training. This paper proposes the first end-to-end DNN training framework that provides quantitative energy guarantees. The key idea is to formulate the DNN training as an optimization problem in which the energy budget imposes a previously unconsidered optimization constraint. We integrate the quantitative DNN energy estimation into the DNN training process to assist the constraint optimization. We prove that an approximate algorithm can be used to efficiently solve the optimization problem. Compared to the best prior energy-saving techniques, our framework trains DNNs that provide higher accuracies under same or lower energy budgets.

The positive-unlabeled (PU) classification is a common scenario in real-world applications such as healthcare, text classification, and bioinformatics, in which we only observe a few samples labeled as "positive" together with a large volume of "unlabeled" samples that may contain both positive and negative samples. Building robust classifier for the PU problem is very challenging, especially for complex data where the negative samples overwhelm and mislabeled samples or corrupted features exist. To address these three issues, we propose a robust learning framework that unifies AUC maximization (a robust metric for biased labels), outlier detection (for excluding wrong labels), and feature selection (for excluding corrupted features). The generalization error bounds are provided for the proposed model that give valuable insight into the theoretical performance of the method and lead to useful practical guidance, e.g., to train a model, we find that the included unlabeled samples are sufficient as long as the sample size is comparable to the number of positive samples in the training process. Empirical comparisons and two real-world applications on surgical site infection (SSI) and EEG seizure detection are also conducted to show the effectiveness of the proposed model.

The cardinality constraint is an intrinsic way to restrict the solution structure in many domains, for example, sparse learning, feature selection, and compressed sensing. To solve a cardinality constrained problem, the key challenge is to solve the projection onto the cardinality constraint set, which is NP-hard in general when there exist multiple overlapped cardinality constraints. In this paper, we consider the scenario where the overlapped cardinality constraints satisfy a Three-view Cardinality Structure (TVCS), which reflects the natural restriction in many applications, such as identification of gene regulatory networks and task-worker assignment problem. We cast the projection into a linear programming, and show that for TVCS, the vertex solution of this linear programming is the solution for the original projection problem. We further prove that such solution can be found with the complexity proportional to the number of variables and constraints. We finally use synthetic experiments and two interesting applications in bioinformatics and crowdsourcing to validate the proposed TVCS model and method.