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From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming

Peyman Mohajerin Esfahani(P.MohajerinEsfahani***at***tudelft.nl)
Tobias Sutter(sutter***at***control.ee.ethz.ch)
Daniel Kuhn(daniel.kuhn***at***epfl.ch)
John Lygeros(lygeros***at***control.ee.ethz.ch)

Abstract: We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite convex programs in which the performance of the approximation is quantified explicitly. To this end, we adopt the recent developments in two areas of randomized optimization and first order methods, leading to a priori as well as a posteriori performance guarantees. We illustrate the generality and implications of our theoretical results in the special case of the long-run average cost and discounted cost optimal control problems for Markov decision processes on Borel spaces. The applicability of the theoretical results is demonstrated through a constrained linear quadratic optimal control problem and a fisheries management problem.

Keywords: infinite-dimensional linear programming, Markov decision processes, approximate dynamic programming, randomized optimization, convex optimization

Category 1: Infinite Dimensional Optimization

Category 2: Other Topics (Dynamic Programming )

Category 3: Stochastic Programming

Citation:

Download: [PDF]

Entry Submitted: 02/20/2017
Entry Accepted: 03/01/2017
Entry Last Modified: 02/20/2017

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