Partially nested information structures with a common past

Casalino, Giuseppe; Davoli, Franco; Minciardi, R.; Puliafito, P. P.; Zoppoli, R.

doi:10.1109/tac.1984.1103653

Cited by 21 publications

(16 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When signaling is present, the problem has a communications flavour and any communication problem is inherently non-convex, see Theorem 4.3.1 in [61]. It is known that quasi-classical information structures eliminate the incentive for signaling, since the future decision makers already have access to the information at the signaling decision maker (see [43], but also [18], [50], [9] and [44] among other papers). On the other hand, one can also put a probabilistic flavor: [60] identified such a probabilistic, but rather restrictive, characterization; see also [36].…”

Section: Stochastic Partial Nestednessmentioning

confidence: 99%

Convex Analysis in Decentralized Stochastic Control, Strategic Measures, and Optimal Solutions

Yüksel¹,

Saldi²

2017

SIAM J. Control Optim.

View full text Add to dashboard Cite

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 non-convex, 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 non-classical information structure are presented. Implications of this analysis in identifying probability and information structure dependent convexity properties are presented.Key words. Stochastic control, decentralized control, optimal control, convex analysis.AMS subject classifications. 93E03, 90B99, 49J551. Introduction. Team decision theory has its roots in control theory and economics. Marschak [37] was perhaps the first to introduce the basic elements of teams, and to provide the first steps toward the development of a team theory. Radner [42] provided foundational results for static teams, establishing connections between person-by-person optimality, stationarity, and team-optimality [38]. Contributions of Witsenhausen [56,57,58,54,53] on dynamic teams and characterization of information structures have been crucial in the progress of our understanding of dynamic teams. We refer the reader to Section 1.1, where Witsenhausen's intrinsic model, and characterization of information structures are discussed in detail. Further discussion on design of information structures in the context of team theory is available in [5,48,61].Convexity is a very important property for optimization problems. A property related to convex analysis that is relevant in team problems is the characterization of the sets of strategic measures; these are the probability measures induced on the exogenous variables, and measurement and action spaces by admissible control policies. In the context of single decision maker control problems, such measures have been studied extensively in [45,41,24,27]. A study of strategic measures for team problems has not been made to our knowledge, and it will be observed in this paper that many of the properties that are natural for fully-observed single-decision-maker stochastic control problems, such as convexity, do not generally extend to a large class of stochastic team problem...

show abstract

Section: Stochastic Partial Nestednessmentioning

confidence: 99%

Convex Analysis in Decentralized Stochastic Control, Strategic Measures, and Optimal Solutions

Yüksel¹,

Saldi²

2017

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

“…Variations of this approach have been used for various information structures, including delayed state sharing [64], partially nested systems with common past [65], teams with sequential partitions [66], coupled subsystems with control sharing [67], periodic sharing information structure [68], and belief sharing information structure [21].…”

Section: Dynamic Programming Approach To Team Problems and Limitedmentioning

confidence: 99%

Information structures in optimal decentralized control

Mahajan

Martins

Rotkowitz

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

137

153

View full text Add to dashboard Cite

Abstract-This tutorial paper provides a comprehensive characterization of information structures in team decision problems and their impact on the tractability of team optimization. Solution methods for team decision problems are presented in various settings where the discussion is structured in two foci: The first is centered on solution methods for stochastic teams admitting state-space formulations. The second focus is on norm-optimal control for linear plants under information constraints.

show abstract

“…Due to the static nature of the problem, one shows that the optimization is jointly convex in the decision variables and there is a person-by-person optimal solution, which turns out to be a linear set of solutions. Partially nested structures can also have a dynamic evolution [11], and as a special case, this includes the case where information propagation is faster than dynamics propagation, where in the above definition, delay is also considered [11], [26], [37].…”

Section: B Relevant Literature and Information Patternsmentioning

confidence: 99%

Stochastic Nestedness and the Belief Sharing Information Pattern

Yüksel

2009

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-Solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the time-horizon, thus leading to non-tractability of classical dynamic programming. A common joint information state supplied to each of the agents leads to a tractable recursion, as is evident in the one-step-delayed information sharing structure case or when deterministic nestedness in information holds when there is a causality relationship as in the case of partially nested information structure. However, communication requirements for such conditions require exchange of very large data noiselessly, hence these assumptions are generally impractical. In this paper, we present a weaker notion of nestedness, which we term as stochastic nestedness, which is characterized by a sequence of Markov chain conditions. It is shown that if the information structure is stochastically nested, then an optimization problem is tractable, and in particular for LQG problems, the team optimal solution is linear, despite the lack of deterministic nestedness or partial nestedness. One other contribution of this paper is that, by regarding the multiple decision makers as a single decision maker and using Witsenhausen's equivalent model for discrete-stochastic control, it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions; a pattern we refer to as -stage belief sharing pattern. We discuss the minimum amount of information exchange required to achieve such an information pattern for = 1.The information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies. In view of nestedness, we present a discussion on the monotone values of information channels.

show abstract

Partially nested information structures with a common past

Cited by 21 publications

References 9 publications

Convex Analysis in Decentralized Stochastic Control, Strategic Measures, and Optimal Solutions

Convex Analysis in Decentralized Stochastic Control, Strategic Measures, and Optimal Solutions

Information structures in optimal decentralized control

Stochastic Nestedness and the Belief Sharing Information Pattern

Contact Info

Product

Resources

About