Data Collection Versus Data Estimation: A Fundamental Trade-Off in Dynamic Networks

Arabneydi, Jalal; Aghdam, Amir G.

doi:10.1109/tnse.2020.2966504

Cited by 6 publications

(5 citation statements)

References 34 publications

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“…For more details on the connection with deep neural networks, the interested reader is referred to [32], [34].…”

Section: A Deep Chapman-kolmogorov (Dck) Equationmentioning

confidence: 99%

“…Note that the complexity of computing ˆ t (d t , γ t ) in time is exponential with respect to the number of agents. However, this computation can be carried out off-line by machine learning methods or circumvented by reinforcement learning techniques [34], [37]. In general, the exploration space of an arbitrarily asymmetric cost function grows exponentially with the number of agents while that of its deep state projection grows polynomially, according to Proposition 2, which is a considerable reduction in complexity.…”

Section: Infinite Horizon Discounted Costmentioning

confidence: 99%

“…According to equation (39), Proposition 1 holds at initial time t = 1. Suppose p 1:t is adapted to the filtration (d p,k 1:t ) k∈S at time t. From Assumption 4 and equation (34), the following equality holds for any d ∈ E, p ∈ P S and γ ∈ G at any time t ∈ N T ,…”

Section: A a Mixed Statementioning

confidence: 99%

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Deep Teams: Decentralized Decision Making With Finite and Infinite Number of Agents

Arabneydi

Aghdam

2020

IEEE Trans. Automat. Contr.

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Inspired by the concepts of deep learning in artificial intelligence and fairness in behavioural economics, we introduce deep teams in this paper. In such systems, agents are partitioned into a few sub-populations so that the dynamics and cost of agents in each sub-population is invariant to the indexing of agents. The goal of agents is to minimize a common cost function in such a manner that the agents in each sub-population are not discriminated or privileged by the way they are indexed. Two non-classical information structures are studied. In the first one, each agent observes its local state as well as the empirical distribution of the states of agents in each sub-population, called deep state, whereas in the second one, the deep states of a subset (possibly all) of sub-populations are not observed. Novel dynamic programs are developed to identify globally optimal and sub-optimal solutions for the first and second information structures, respectively. The computational complexity of finding the optimal solution in both space and time is polynomial (rather than exponential) with respect to the number of agents in each sub-population and is linear (rather than exponential) with respect to the control horizon. This complexity is further reduced in time by introducing a forward equation, that we call deep Chapman-Kolmogorov equation, described by multiple convolutional layers of Binomial probability distributions. Two different prices are defined for computation and communication, and it is shown that under mild assumptions they converge to zero as the quantization level and the number of agents tend to infinity. In addition, the main results are extended to the infinite-horizon discounted model and arbitrarily asymmetric cost function. Finally, a service-management example with 200 users is presented.

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“…For more details on the connection with deep neural networks, the interested reader is referred to [32], [34].…”

Section: A Deep Chapman-kolmogorov (Dck) Equationmentioning

confidence: 99%

Section: Infinite Horizon Discounted Costmentioning

confidence: 99%

See 1 more Smart Citation

Deep Teams: Decentralized Decision Making With Finite and Infinite Number of Agents

Arabneydi

Aghdam

2020

IEEE Trans. Automat. Contr.

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“…Notice that z t is not necessarily the best possible estimate, but it is always measurable with respect to PDSS information structure. The interested reader is referred to [20] for more details on the above Kalman-like filter that emerges in the trade-off between data collection and data estimation.…”

Section: A Finite-model Strategy For Problemmentioning

confidence: 99%

Deep Structured Teams with Linear Quadratic Model: Partial Equivariance and Gauge Transformation

Arabneydi,

Aghdam

2019

Preprint

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Motivated from invariance principle and recent developments in artificial intelligence, we introduce a risk-sensitive linear quadratic optimal control whose solution resembles a deep neural network, called deep teams. Two notions of equivariant and partially equivariant systems are defined for linear quadratic models. It is shown that such systems can be partitioned into a few sub-populations of decision makers wherein the decision makers in each sub-population are coupled in both dynamics and cost function through a number of linear regressions of the states and actions of the decision makers. Two non-classical information structures are considered: deep-state sharing and partial deepstate sharing, where deep state refers to the linear regression of the states of the decision makers in each sub-population. For deep-state sharing structure, a closed-form representation of the globally optimal strategy is obtained in terms of a deep Riccati equation, whose dimension is independent of the number of decision makers in each sub-population, i.e., the solution is scalable. In addition, two sub-optimal sequential strategies under partial deep-state sharing information structure are proposed by introducing two Kalman-like filters, one based on the finite-population model and the other one based on the infinite-population model. It is shown that the prices of information associated with the above sub-optimal solutions converge to zero as the number of decision makers goes to infinity. Furthermore, an explicit connection between optimal control theory and deep learning is established wherein it is proved that a simple deep neural network can incorporate an arbitrary number of orthonormal features, substantiating the fact that deep neural networks are structurally rich enough to model complex dynamical systems. Finally, two numerical examples of a supply-chain management system are presented to demonstrate the efficacy of the obtained results.

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“…Furthermore, we demonstrate in [9] that today's most common feed-forward deep neural networks (i.e., those with rectified linear unit activation function) may be viewed as a special case of deep structured teams, where layers are time steps and neurons are simple integrator agents whose goal is to collaborate in order to minimize a common loss (cost) function. For more applications of deep structured models, the reader is referred to reinforcement learning [8], [13], [14], nonzerosum game [12], [15], minmax optimization [17], leaderfollowers [18], [19], epidemics [20], smart grids [21], meanfield teams [22]- [25], and networked estimation [26], [27].…”

Section: Introductionmentioning

confidence: 99%

Deep Structured Teams in Arbitrary-Size Linear Networks: Decentralized Estimation, Optimal Control and Separation Principle

Arabneydi¹,

Aghdam²

2021

Preprint

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Data Collection Versus Data Estimation: A Fundamental Trade-Off in Dynamic Networks

Cited by 6 publications

References 34 publications

Deep Teams: Decentralized Decision Making With Finite and Infinite Number of Agents

Deep Teams: Decentralized Decision Making With Finite and Infinite Number of Agents

Deep Structured Teams with Linear Quadratic Model: Partial Equivariance and Gauge Transformation

Deep Structured Teams in Arbitrary-Size Linear Networks: Decentralized Estimation, Optimal Control and Separation Principle

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