Paper Info
Title
Convex Analysis in Decentralized Stochastic Control, Strategic Measures, and Optimal Solutions.
Abstract
This paper is concerned with the properties of the sets of strategic measures induced by admissible team policies in decentralized stochastic control and the convexity properties in dynamic team problems. To facilitate a convex analytical approach, strategic measures for team problems are introduced. Properties such as convexity, compactness, and Borel measurability under weak convergence topology are studied, and sufficient conditions for each of these properties are presented. These lead to existence of and structural results for optimal policies. It will be shown that the set of strategic measures for teams which are not classical is in general nonconvex, but the extreme points of a relaxed set consist of deterministic team policies, which lead to their optimality for a given team problem under an expected cost criterion. Externally provided independent common randomness for static teams or private randomness for dynamic teams do not improve the team performance. The problem of when a sequential team problem is convex is studied and necessary and sufficient conditions for problems which include teams with a nonclassical information structure are presented. Implications of this analysis in identifying probability and information structure dependent convexity properties are presented.
Year
DOI
Venue
2017
10.1137/15M1049129
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
stochastic control,decentralized control,optimal control,convex analysis
Extreme point,Information structure,Weak convergence,Mathematical optimization,Convexity,Compact space,Convex analysis,Mathematics,Randomness,Stochastic control
Journal
Volume
Issue
ISSN
55
1
0363-0129
Citations 
PageRank 
References 
4
0.45
11
Authors
2
Name
Order
Citations
PageRank
Serdar Yüksel145753.31
Naci Saldi22910.27