Symmetric team problems and multi access wire communication

Schoute, F.C.

doi:10.1016/0005-1098(78)90090-0

Cited by 8 publications

(8 citation statements)

References 5 publications

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“…As mentioned earlier, if attention is restricted to identical control laws, then randomized strategies may perform better than pure strategies [15,Theorem 2.3]. Our results extend naturally to randomized strategies by considering ∆(U ), the space of probability distributions on U , as the action space.…”

Section: A Randomized Strategiessupporting

confidence: 61%

“…Although assuming identical control laws (Assumption 1) leads to loss in performance, it is a standard assumption in the literature on large scale systems for reasons of simplicity, fairness, and robustness. For example, similar assumption has been made in [15], [16], [17].…”

Section: Salient Features Of the Modelmentioning

confidence: 75%

“…In general, randomized strategies are not considered in team problems because randomization does not improve performance [18,Theorem 1.6]. However, if attention is restricted to identical strategies, randomized strategies may perform better than pure strategies [15,Theorem 2.3]. In the above model, we assume that the control strategies are pure, primarily for the ease of exposition.…”

Section: Salient Features Of the Modelmentioning

confidence: 99%

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Team optimal control of coupled subsystems with mean-field sharing

Arabneydi

Mahajan

2014

53rd IEEE Conference on Decision and Control

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We investigate team optimal control of stochastic subsystems that are weakly coupled in dynamics (through the mean-field of the system) and are arbitrary coupled in the cost. The controller of each subsystem observes its local state and the mean-field of the state of all subsystems. The system has a nonclassical information structure. Exploiting the symmetry of the problem, we identify an information state and use that to obtain a dynamic programming decomposition. This dynamic program determines a globally optimal strategy for all controllers. Our solution approach works for arbitrary number of controllers and generalizes to the setup when the mean-field is observed with noise. The size of the information state is time-invariant; thus, the results generalize to the infinite-horizon control setups as well. In addition, when the mean-field is observed without noise, the size of the corresponding information state increases polynomially (rather than exponentially) with the number of controllers which allows us to solve problems with moderate number of controllers. We illustrate our approach by an example motivated by smart grids that consists of 100 coupled subsystems.

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Section: A Randomized Strategiessupporting

confidence: 61%

Section: Salient Features Of the Modelmentioning

confidence: 75%

Section: Salient Features Of the Modelmentioning

confidence: 99%

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Team optimal control of coupled subsystems with mean-field sharing

Arabneydi

Mahajan

2014

53rd IEEE Conference on Decision and Control

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“…Proof. This proof follows a proof by Schoute (1978). It is possible to convert a Dec-POMDP to an extensive game and thus to a strategic game, in which the actions are pure policies for the Dec-POMDP (Oliehoek & Vlassis, 2006).…”

Section: Appendix a Proofsmentioning

confidence: 80%

Optimal and Approximate Q-value Functions for Decentralized POMDPs

Oliehoek¹,

Spaan²,

Vlassis³

2008

jair

257

186

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Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q*. Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem

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“…In general, randomization can improve the performance of a fair strategy [31]. On the other hand, any parametrized randomized strategy can be formulated as a deterministic one wherein the randomization is embedded into the transition probability and cost function, and the action space is replaced by the parameter space.…”

Section: B Admissible Strategymentioning

confidence: 99%

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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Symmetric team problems and multi access wire communication

Cited by 8 publications

References 5 publications

Team optimal control of coupled subsystems with mean-field sharing

Team optimal control of coupled subsystems with mean-field sharing

Optimal and Approximate Q-value Functions for Decentralized POMDPs

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

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