The Linear Programming Approach to Approximate Dynamic Programming
TLDR
In this article, an efficient method based on linear programming for approximating solutions to large-scale stochastic control problems is proposed. But the approach is not suitable for large scale queueing networks.Abstract:
The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits" a linear combination of pre-selected basis functions to the dynamic programming cost-to-go function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and "state-relevance weights" that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology.read more
Citations
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An Improved Dynamic Programming Decomposition Approach for Network Revenue Management
TL;DR: This work considers a nonlinear nonseparable functional approximation to the value function of a dynamic programming formulation for the network revenue management (RM) problem with customer choice and shows that it leads to a tighter upper bound on optimal expected revenue than some known bounds in the literature.
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Robust Markov Decision Process: Beyond Rectangularity
TL;DR: The robust counterpart of important structural results of classical MDPs, including the maximum principle and Blackwell optimality, are introduced and a computational study is provided to demonstrate the effectiveness of the approach in mitigating the conservativeness of robust policies.
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A Cost-Shaping Linear Program for Average-Cost Approximate Dynamic Programming with Performance Guarantees
TL;DR: A bound is established on the performance of the resulting policy that scales gracefully with the number of states without imposing the strong Lyapunov condition required by its counterpart in de Farias and Van Roy.
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Structural Properties of Optimal Transmission Policies Over a Randomly Varying Channel
TL;DR: By casting the problem of transmitting packets over a randomly varying point to point channel as a constrained Markov decision process in discrete time with time-averaged costs, structural results about the dependence of the optimal policy on buffer occupancy, number of packet arrivals in the previous slot and the channel fading state are proved.
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A Distributed Decision-Making Structure for Dynamic Resource Allocation Using Nonlinear Functional Approximations
TL;DR: This paper proposes a distributed solution approach to a certain class of dynamic resource allocation problems and develops a dynamic programming-based multiagent decision-making, learning, and communication mechanism.
References
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Dynamic Programming and Optimal Control
TL;DR: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization.
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Learning to Predict by the Methods of Temporal Differences
TL;DR: This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior – and proves their convergence and optimality for special cases and relation to supervised-learning methods.
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Neuro-dynamic programming
TL;DR: This is the first textbook that fully explains the neuro-dynamic programming/reinforcement learning methodology, which is a recent breakthrough in the practical application of neural networks and dynamic programming to complex problems of planning, optimal decision making, and intelligent control.