Idempotent method for dynamic games and complexity reduction in min-max expansions
William M. McEneaney
- pp 163-168
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TLDR
It is shown that a similar, albeit more abstract, approach can be applied to deterministic game problems by finding reduced-complexity approximations to min-max sums of max-plus affine functions.Abstract:
In recent years, idempotent methods (specifically, max-plus methods) have been developed for solution of nonlinear control problems. It was thought that idempotent linearity of the associated semigroup was required for application of these techniques. It is now known that application of the max-plus distributive property allows one to apply the max-plus curse-of-dimensionality-free approach to stochastic control problems. Here, we see that a similar, albeit more abstract, approach can be applied to deterministic game problems. The main difficulty is a curse-of-complexity growth in the computational cost. Attenuation of this effect requires finding reduced-complexity approximations to min-max sums of max-plus affine functions. We demonstrate that this problem can be reduced to a pruning problem.read more
Citations
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Idempotent Expansions for Continuous-Time Stochastic Control
TL;DR: This paper explores min-plus methods for continuous-time stochastic control on a finite-time horizon and obtains an algorithm for recursive computation of the time-discretized values under the idempotent distributed dynamic programming principle (IDDPP).
Proceedings ArticleDOI
Idempotent expansions for continuous-time stochastic control: compact control space
TL;DR: It has recently been discovered that idempotent methods are applicable to stochastic control and games and a min-max method was discovered for games.
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Min-Max Spaces and Complexity Reduction in Min-Max Expansions
TL;DR: In this article, the authors consider functions which may be represented using infima (i.e., min-max sums) of max-plus affine functions and obtain a solution to this complexity-reduction problem in the case of minmax expansions.
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