Structure d’information, stratégies de communication et application aux réseaux distribués

Abstract : This thesis studies distributed optimization problems with different observation structuresand application to wireless network and Smart Grids problems. Specifically, an asymmetricobservation structure between two agents is considered, where a first agent has full knowledgeabout the realization of a random state, and the other agent does not know anything about thisstate. In this context, the question is how to transmit information from the first agent to thesecond agent in order to use in an optimal way the communication resources. Several modelsare studied in this thesis. For all of them, a common element is that the information source hasto be encoded in an appropriate manner to optimize the use of the system’s configuration. Afirst model is studied where no dedicated channel for communication is available between agentsand they have the same objective function. Therefore, the only way communication is possible isthrough the actions chosen by agents. As actions are payoff relevant, the first agent has to findthe optimal tradeoff between transmission of information and payoff maximization. The informedagent encodes his knowledge about the state into his actions, which will be imperfectly observedby the second agent. The latter will decode the information and choose his actions in order tomaximize the common objective function. We use tools from information theory to characterizethis optimal tradeoff by an information constraint, and apply this scenario to a power controlproblem in an interference channel setting. Our new strategy (the coded power control ) givessome promising gains compare to classical approaches.In a second part, we consider that there exists a dedicated channel for communication, that isto say the actions of the informed agent are not payoff relevant and are only useful for transmissionof information. Furthermore, agents are supposed to have diverging interests, so that the informedagent does not necessarily have an incentive to send all his knowledge to the uninformed agent.Game theory and Cheap talk game in particular appears to be the right framework to analyzethis problem. We characterize the signal scheme that agents will agree on. This scheme willlead to a Nash Equilibrium, thus will optimize the way communication is done. This model is ofparticular interest for electrical vehicles networks where an electrical vehicle has to send his needin term of power to an aggregator which will choose an effective charging level for the electricalvehicle. The latter only cares about his need in term of power whereas the aggregator also takesinto account the network status. The considered model help to optimize the way the network isused.We finally consider a model with more than two agents, where the main goal is for all agentsto retrieve perfect observations of all past actions of all agents. This is of particular interest ina game theory point of view to characterize the long term expected utilities of the agents. Inthis model, we add an encoder who perfectly oberves all past actions and will help agents tohave perfect monitoring. In fact, this is possible if the right information constraint is satisfied.We thus characterized the latter, using a hybrid coding scheme combining classical informationtheoretic scheme and tools from graph theory.
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Benjamin Larrousse. Structure d’information, stratégies de communication et application aux réseaux distribués. Théorie de l'information [cs.IT]. Université Paris Sud - Paris XI, 2014. Français. ⟨NNT : 2014PA112373⟩. ⟨tel-01135076⟩

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