loans given that are repaid, or criminals that are apprehended). loans or police officers) amongst several groups, in order to maximize some objective (e.g. Settings such as lending and policing can be modeled by a centralized agent allocating a scarce resource (e.g. With hundreds of worked examples and exercises, this text is intended both for courses and for self-study by graduate students and researchers in statistics, machine learning, and related fields who must understand, apply, and adapt modern statistical methods suited to large-scale data. It includes chapters that are focused on core methodology and theory - including tail bounds, concentration inequalities, uniform laws and empirical process, and random matrices - as well as chapters devoted to in-depth exploration of particular model classes - including sparse linear models, matrix models with rank constraints, graphical models, and various types of non-parametric models. This book provides a self-contained introduction to the area of high-dimensional statistics, aimed at the first-year graduate level. Such massive data sets present a number of challenges to researchers in statistics and machine learning. Recent years have witnessed an explosion in the volume and variety of data collected in all scientific disciplines and industrial settings. In a 2D navigation example, we find the algorithm effectively learn feasible policies without assumptions on the feasibility of initial policies, even with non-Markovian objective functions and con

In a constrained linear quadratic regulator example, we observe that the algorithm converges to the global optimum with high probability. At last, we show the performance of the proposed algorithm in two simulation examples. Then we give sufficient conditions on the properties of this differential equation for the convergence of the proposed algorithm.

We show that the asymptotic behavior of the proposed algorithm can be almost-surely described by that of an ordinary differential equation. The method explicitly tracks its performance with respect to constraint satisfaction and thus is well-suited for safety-critical applications. The key idea is to transform the original constrained optimization problem into an unconstrained one with a surrogate objective. We propose a constrained cross-entropy-based method to solve this problem. We study a safe reinforcement learning problem in which the constraints are defined as the expected cost over finite-length trajectories.

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