A literature survey of low-rank tensor approximation techniques

During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey attempts to give a literature overview of current developments in this area, with an emphasis on function-related tensors

Reinforcement Learning: A Survey

This paper surveys the field of reinforcement learning from a computer-science perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem faced by an agent that learns behavior through trial-and-error interactions with a dynamic environment. The work described here has a resemblance to work in psychology, but differs considerably in the details and in the use of the word ``reinforcement.'' The paper discusses central issues of reinforcement learning, including trading off exploration and exploitation, establishing the foundations of the field via Markov decision theory, learning from delayed reinforcement, constructing empirical models to accelerate learning, making use of generalization and hierarchy, and coping with hidden state. It concludes with a survey of some implemented systems and an assessment of the practical utility of current methods for reinforcement learning.Comment: See http://www.jair.org/ for any accompanying file

Verifiable Reinforcement Learning via Policy Extraction

While deep reinforcement learning has successfully solved many challenging control tasks, its real-world applicability has been limited by the inability to ensure the safety of learned policies. We propose an approach to verifiable reinforcement learning by training decision tree policies, which can represent complex policies (since they are nonparametric), yet can be efficiently verified using existing techniques (since they are highly structured). The challenge is that decision tree policies are difficult to train. We propose VIPER, an algorithm that combines ideas from model compression and imitation learning to learn decision tree policies guided by a DNN policy (called the oracle) and its Q-function, and show that it substantially outperforms two baselines. We use VIPER to (i) learn a provably robust decision tree policy for a variant of Atari Pong with a symbolic state space, (ii) learn a decision tree policy for a toy game based on Pong that provably never loses, and (iii) learn a provably stable decision tree policy for cart-pole. In each case, the decision tree policy achieves performance equal to that of the original DNN policy

Computation and Learning in High Dimensions (hybrid meeting)

The most challenging problems in science often involve the learning and accurate computation of high dimensional functions. High-dimensionality is a typical feature for a multitude of problems in various areas of science. The so-called curse of dimensionality typically negates the use of traditional numerical techniques for the solution of high-dimensional problems. Instead, novel theoretical and computational approaches need to be developed to make them tractable and to capture fine resolutions and relevant features. Paradoxically, increasing computational power may even serve to heighten this demand, since the wealth of new computational data itself becomes a major obstruction. Extracting essential information from complex problem-inherent structures and developing rigorous models to quantify the quality of information in a high-dimensional setting pose challenging tasks from both theoretical and numerical perspective. This has led to the emergence of several new computational methodologies, accounting for the fact that by now well understood methods drawing on spatial localization and mesh-refinement are in their original form no longer viable. Common to these approaches is the nonlinearity of the solution method. For certain problem classes, these methods have drastically advanced the frontiers of computability. The most visible of these new methods is deep learning. Although the use of deep neural networks has been extremely successful in certain application areas, their mathematical understanding is far from complete. This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computational methods and to promote the exchange of ideas emerging in various disciplines about how to treat multiscale and high-dimensional problems