Optimal Solutions to Infinite-Player Stochastic Teams and Mean-Field Teams

Sanjari, Sina; Yüksel, Serdar

doi:10.1109/tac.2020.2994899

Cited by 17 publications

(14 citation statements)

References 46 publications

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“…We note that if one also has convexity in the cost as well as action sets U i , then one can also establish that for every finite N , the optimal policies are symmetric and deterministic, but in the infinite limit, randomization may be required [121]. Similar results also hold for dynamic team problems [120].…”

Section: Policies Defined By Conditional Independence Given Measurementsmentioning

confidence: 62%

“…As a final example on the utility of placing a product topology on individual policies, we consider stochastic team problems with infinitely many decision makers. Such problems have seen a significant activity in the context of mean field theory [76,75,94] (see also more recent papers [60,29,9,89]) and in mean-field team problems [77, 131][8] [99] [121]. In the context of mean-field team problems [99] and [121] have shown that, under sufficient convexity conditions, a sequence of optimal policies for teams with N number of decision makers as N → ∞ converges to a team optimal policy for the static team with countably infinite number of decision makers, where the latter establishes the optimality of symmetric (i.e., identical for each DM) policies as well as existence of optimal team policies for both finite and infinite DM setups.…”

Section: Policies Defined By Conditional Independence Given Measurementsmentioning

confidence: 99%

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Geometry of Information Structures, Strategic Measures and associated Control Topologies

Saldi,

Yuksel

2020

Preprint

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In many areas of applied mathematics, engineering, and social and natural sciences, decentralization of information is a key aspect determining how to approach a problem. In this review article, we study information structures in a probability theoretic and geometric context. We define information structures, place various topologies on them, and study closedness, compactness and convexity properties on the strategic measures induced by information structures and decentralized control/decision policies under varying degree of relaxations with regard to access to private or common randomness. Ultimately, we present existence and tight approximation results for optimal decision/control policies. We discuss various lower bounding techniques, through relaxations and convex programs ranging from classically realizable and classically non-realizable (such as quantum and non-signaling) relaxations. For each of these, we establish closedness and convexity properties and also a hierarchy of correlation structures. As a second main theme, we review and introduce various topologies on decision/control strategies defined independent of information structures, but for which information structures determine whether the topologies entail utility in arriving at existence, compactness, convexification or approximation results. These approaches, which we term as the strategic measures approach and the control topology approach, lead to complementary results on existence, approximations and upper and lower bounds in optimal decentralized decision and control.

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Section: Policies Defined By Conditional Independence Given Measurementsmentioning

confidence: 62%

Section: Policies Defined By Conditional Independence Given Measurementsmentioning

confidence: 99%

Geometry of Information Structures, Strategic Measures and associated Control Topologies

Saldi,

Yuksel

2020

Preprint

Self Cite

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“…Figure 1: System diagram: A large number of decision makers in a remote estimation system communicating their observations to a base station or access point without coordination, and its block diagram abstraction considered for analytical problem formulation herein. Sanjari and Yüksel, 2021). Such problem formulations are very relevant in modern applications such as industrial internet of things, where many tiny, low-power devices sense the environment and communicate with a remote gateway, base-station or access point (Gatsis, 2021).…”

Section: Dmsmentioning

confidence: 99%

Learning distributed channel access policies for networked estimation: data-driven optimization in the mean-field regime

Vasconcelos¹

2021

Preprint

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The problem of communicating sensor measurements over shared networks is prevalent in many modern large-scale distributed systems such as cyber-physical systems, wireless sensor networks and the internet of things. Due to bandwidth constraints, the system designer must jointly design decentralized medium access transmission and estimation policies that accommodate a very large number of devices in extremely contested environments such that the collection of all observations is reproduced at the destination with the best possible fidelity. We formulate a remote estimation problem in the mean-field regime where a very large number of sensors communicate their observations to an access point, or base-station, under a strict constraint on the maximum fraction of transmitting devices. We show that in the mean-field regime, this problem exhibits a structure which enables tractable optimization algorithms. More importantly, we obtain a data-driven learning scheme that admits a finite sample-complexity guarantee on the performance of the resulting estimation system under minimal assumptions on the data's probability density function.

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“…Furthermore, our objective functional is defined as the expected rank-based reward minus effort and size costs while [5] and [11] mainly focus on the standard linear quadratic payoff. On the other hand, some recent work such as [13], [10] and [17] studied the mean field team problem for a single team with mean field interacting members, but the teamwise interaction and the equilibrium team size choice are not considered therein. The formulation of a mean field game of mean field games makes the present paper distinct from the existing literature and mathematically interesting.…”

Section: Introductionmentioning

confidence: 99%

Teamwise Mean Field Competitions

Zhang

Zhou

2020

Preprint

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This paper studies competitions with rank-based reward among a large number of teams. Within each sizable team, we consider a mean-field contribution game in which each team member contributes to the jump intensity of a common Poisson project process; across all teams, a mean field competition game is formulated on the rank of the completion time, namely the jump time of Poisson project process, and the reward to each team is paid based on its ranking. On the layer of teamwise competition game, three optimization problems are introduced when the team size is determined by: (i) the team manager; (ii) the central planner; (iii) the team members' voting as partnership. We propose a relative performance criteria for each team member to share the team's reward and formulate some mean field games of mean field games, which are new to the literature. In all problems with homogeneous parameters, the equilibrium control of each worker and the equilibrium or optimal team size can be computed in an explicit manner, allowing us to analytically examine the impacts of some model parameters and discuss their economic implications. Two numerical examples are also presented to illustrate the parameter dependence and comparison between different team size decision making.

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Optimal Solutions to Infinite-Player Stochastic Teams and Mean-Field Teams

Cited by 17 publications

References 46 publications

Geometry of Information Structures, Strategic Measures and associated Control Topologies

Geometry of Information Structures, Strategic Measures and associated Control Topologies

Learning distributed channel access policies for networked estimation: data-driven optimization in the mean-field regime

Teamwise Mean Field Competitions

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