The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
This book examines Gaussian processes in both model-based reinforcement learning (RL) and inference in nonlinear dynamic systems.First, we introduce PILCO, a fully Bayesian approach for efficient RL in continuous-valued state and action spaces when no expert knowledge is available. PILCO takes model uncertainties consistently into account during long-term planning to reduce model bias. Second, we propose principled algorithms for robust filtering and smoothing in GP dynamic systems.
The first comprehensive guide to distributional reinforcement learning, providing a new mathematical formalism for thinking about decisions from a probabilistic perspective. Distributional reinforcement learning is a new mathematical formalism for thinking about decisions. Going beyond the common approach to reinforcement learning and expected values, it focuses on the total reward or return obtained as a consequence of an agent's choices—specifically, how this return behaves from a probabilistic perspective. In this first comprehensive guide to distributional reinforcement learning, Marc G. Bellemare, Will Dabney, and Mark Rowland, who spearheaded development of the field, present its key concepts and review some of its many applications. They demonstrate its power to account for many complex, interesting phenomena that arise from interactions with one's environment. The authors present core ideas from classical reinforcement learning to contextualize distributional topics and include mathematical proofs pertaining to major results discussed in the text. They guide the reader through a series of algorithmic and mathematical developments that, in turn, characterize, compute, estimate, and make decisions on the basis of the random return. Practitioners in disciplines as diverse as finance (risk management), computational neuroscience, computational psychiatry, psychology, macroeconomics, and robotics are already using distributional reinforcement learning, paving the way for its expanding applications in mathematical finance, engineering, and the life sciences. More than a mathematical approach, distributional reinforcement learning represents a new perspective on how intelligent agents make predictions and decisions.
A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed.
A Survey on Policy Search for Robotics provides an overview of successful policy search methods in the context of robot learning, where high-dimensional and continuous state-action space challenge any Reinforcement Learning (RL) algorithm. It distinguishes between model-free and model-based policy search methods.
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