53rd IEEE Conference on Decision and Control 2014
DOI: 10.1109/cdc.2014.7040433
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Bounds for approximate dynamic programming based on string optimization and curvature

Abstract: In this paper, we will develop a systematic approach to deriving guaranteed bounds for approximate dynamic programming (ADP) schemes in optimal control problems. Our approach is inspired by our recent results on bounding the performance of greedy strategies in optimization of string functions over a finite horizon. The approach is to derive a string-optimization problem, for which the optimal strategy is the optimal control solution and the greedy strategy is the ADP solution. Using this approach, we show that… Show more

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Cited by 3 publications
(5 citation statements)
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“…This extension introduces a number of issues that have to be addressed, which we do so here. Moreover, in the current paper, we introduce a new bounding result based on two curvature parameters, which is stronger than the bound used in [31]. This new bounding result is of interest in its own right.…”
Section: Prior Workmentioning
confidence: 94%
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“…This extension introduces a number of issues that have to be addressed, which we do so here. Moreover, in the current paper, we introduce a new bounding result based on two curvature parameters, which is stronger than the bound used in [31]. This new bounding result is of interest in its own right.…”
Section: Prior Workmentioning
confidence: 94%
“…In our previous work [31], we had described bounding deterministic ADP schemes using a preliminary version of what is presented in this paper. The current paper goes well beyond [31] by treating the nontrivial extension to the stochastic case. This extension introduces a number of issues that have to be addressed, which we do so here.…”
Section: Prior Workmentioning
confidence: 99%
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“…In [36] and [37], Zhang et al generalized the notions of total curvature and elemental curvature to string submodular functions where the objective function value depends on the order of the elements in the set. This framework is further extended to approximate dynamic programming problems by Liu et al in [38].…”
Section: A Related Workmentioning
confidence: 99%
“…Therefore, it significantly reduces the search space, i.e., it does not search over all possible combinations of open expansion valves. When the expansion valve optimization problem (3.3) is extended to multi-stage optimization, a greedy algorithm achieves the same suboptimality bound using adaptive (or string) submodularity and monotonicity of the value function [8,2,15].…”
Section: Theorem 3 ([18]mentioning
confidence: 99%