Alessandro Alla
An Efficient Policy Iteration Algorithm for Dynamic Programming Equations
Alla, Alessandro; Falcone, Maurizio; Kalise, Dante
Authors
Maurizio Falcone
Dante Kalise
Abstract
© 2015 Society for Industrial and Applied Mathematics. We present an accelerated algorithm for the solution of static Hamilton–Jacobi–Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear convergence in many relevant cases provided the initial guess is sufficiently close to the solution. This limitation often degenerates into a behavior similar to a value iteration method, with an increased computation time. The new scheme circumvents this problem by combining the advantages of both algorithms with an efficient coupling. The method starts with a coarse-mesh value iteration phase and then switches to a fine-mesh policy iteration procedure when a certain error threshold is reached. A delicate point is to determine this threshold in order to avoid cumbersome computations with the value iteration and at the same time to ensure the convergence of the policy iteration method to the optimal solution. We analyze the methods and efficient coupling in a number of examples in different dimensions, illustrating their properties.
Citation
Alla, A., Falcone, M., & Kalise, D. (2015). An Efficient Policy Iteration Algorithm for Dynamic Programming Equations. SIAM Journal on Scientific Computing, 37(1), A181-A200. https://doi.org/10.1137/130932284
Journal Article Type | Article |
---|---|
Acceptance Date | Oct 13, 2014 |
Online Publication Date | Jan 20, 2015 |
Publication Date | Jan 20, 2015 |
Deposit Date | Nov 12, 2019 |
Publicly Available Date | Mar 28, 2024 |
Journal | SIAM Journal on Scientific Computing |
Print ISSN | 1064-8275 |
Electronic ISSN | 1095-7197 |
Publisher | Society for Industrial and Applied Mathematics |
Peer Reviewed | Peer Reviewed |
Volume | 37 |
Issue | 1 |
Pages | A181-A200 |
DOI | https://doi.org/10.1137/130932284 |
Keywords | Applied Mathematics; Computational Mathematics |
Public URL | https://nottingham-repository.worktribe.com/output/3220244 |
Publisher URL | https://epubs.siam.org/doi/10.1137/130932284 |
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