The complexity of dynamic programming
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TLDR
Tight lower bounds are provided on the computational complexity of discretetime, stationary, infinite horizon, discounted stochastic control problems, for the case where the state space is continuous and the problem is to be solved approximately, within a specified accuracy.About:
This article is published in Journal of Complexity.The article was published on 1989-12-01 and is currently open access. It has received 73 citations till now. The article focuses on the topics: Dynamic problem & State space.read more
Citations
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Book
Algorithms for Reinforcement Learning
TL;DR: This book focuses on those algorithms of reinforcement learning that build on the powerful theory of dynamic programming, and gives a fairly comprehensive catalog of learning problems, and describes the core ideas, followed by the discussion of their theoretical properties and limitations.
Journal ArticleDOI
Survey A survey of computational complexity results in systems and control
TL;DR: This paper considers problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, time-varying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
Journal Article
Finite-Time Bounds for Fitted Value Iteration
Rémi Munos,Csaba Szepesvári +1 more
TL;DR: A theoretical analysis of the performance of sampling-based fitted value iteration (FVI) to solve infinite state-space, discounted-reward Markovian decision processes (MDPs) under the assumption that a generative model of the environment is available.
Journal ArticleDOI
Using randomization to break the curse of dimensionality
TL;DR: In this paper, random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs) were introduced.
Book ChapterDOI
Chapter 14 Numerical dynamic programming in economics
TL;DR: This chapter explores the numerical methods for solving dynamic programming (DP) problems and focuses on continuous Markov decision processes (MDPs) because these problems arise frequently in economic applications.
References
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Book
Problem complexity and method efficiency in optimization
TL;DR: In this article, problem complexity and method efficiency in optimisation are discussed in terms of problem complexity, method efficiency, and method complexity in the context of OO optimization, respectively.
Book
Stochastic optimal control : the discrete time case
TL;DR: This research monograph is the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including thetreatment of the intricate measure-theoretic issues.
Journal ArticleDOI
The Complexity of Markov Decision Processes
TL;DR: All three variants of the classical problem of optimal policy computation in Markov decision processes, finite horizon, infinite horizon discounted, and infinite horizon average cost are shown to be complete for P, and therefore most likely cannot be solved by highly parallel algorithms.
Book
Dynamic Programming: Deterministic and Stochastic Models
TL;DR: As one of the part of book categories, dynamic programming deterministic and stochastic models always becomes the most wanted book.
Book
Information-Based Complexity
TL;DR: This book provides a comprehensive treatment of information-based complexity, the branch of computational complexity that deals with the intrinsic difficulty of the approximate solution of problems for which the information is partial, noisy, and priced.