This is a monograph at the forefront of research on reinforcement learning, also referred to by other names such as approximate dynamic programming and neuro-dynamic programming. It focuses on the fundamental idea of policy iteration, i.e., start from some policy, and successively generate one or more improved policies. If just one improved policy is generated, this is called rollout, which, based on broad and consistent computational experience, appears to be one of the most versatile and reliable of all reinforcement learning methods. Among others, it can be applied on-line using easily implementable simulation, and it can be used for discrete deterministic combinatorial optimization, as well as for stochastic Markov decision problems. Approximate policy iteration is more ambitious than rollout, but it is a strictly off-line method, and it is generally far more computationally intensive. This motivates the use of parallel and distributed computation. One of the purposes of the monograph is to discuss distributed (possibly asynchronous) methods that relate to rollout and policy iteration, both in the context of an exact and an approximate implementation involving neural networks or other approximation architectures. Several of the ideas that we develop in some depth in this monograph have been central in the implementation of recent high profile successes, such as the AlphaZero program for playing chess, Go, and other games. In addition to the fundamental process of successive policy iteration/improvement, this program includes the use of deep neural networks for representation of both value functions and policies, the extensive use of large scale parallelization, and the simplification of lookahead minimization, through methods involving Monte Carlo tree search and pruning of the lookahead tree. In this monograph, we also focus on policy iteration, value and policy neural network representations, parallel and distributed computation, and lookahead simplification. Thus while there are significant differences, the principal design ideas that form the core of this monograph are shared by the AlphaZero architecture, except that we develop these ideas in a broader and less application-specific framework. Among its special features, the book: a) Presents new research relating to distributed asynchronous computation, partitioned architectures, and multiagent systems, with application to challenging large scale optimization problems, such as combinatorial/discrete optimization, as well as partially observed Markov decision problems. b) Describes variants of rollout and policy iteration for problems with a multiagent structure, which allow a dramatic reduction of the computational requirements for lookahead minimization. c) Establishes a connection of rollout with model predictive control, one of the most prominent control system design methodologies. d) Expands the coverage of some research areas discussed in 2019 textbook Reinforcement Learning and Optimal Control by the same author. See the author’s website for selected sections, instructional videos and slides, and other supporting material.

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