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Achieving Pareto Optimality Through Distributed Learning
, 2012
"... We propose a simple payoffbased learning rule that is completely decentralized, and that leads to an efficient configuration of actions in any nperson finite strategicform game with generic payoffs. The algorithm follows the theme of exploration versus exploitation and is hence stochastic in natu ..."
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Cited by 19 (5 self)
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We propose a simple payoffbased learning rule that is completely decentralized, and that leads to an efficient configuration of actions in any nperson finite strategicform game with generic payoffs. The algorithm follows the theme of exploration versus exploitation and is hence stochastic in nature. We prove that if all agents adhere to this algorithm, then the agents will select the action profile that maximizes the sum of the agents ’ payoffs a high percentage of time. The algorithm requires no communication. Agents respond solely to changes in their own realized payoffs, which are affected by the actions of other agents in the system in ways that they do not necessarily understand. The method can be applied to the optimization of complex systems with many distributed components, such as the routing of information in networks and the design and control of wind farms. The proof of the proposed learning algorithm relies on the theory of large deviations for perturbed Markov chains.
Game Theory and Distributed Control
, 2012
"... Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems fro ..."
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Cited by 3 (1 self)
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Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems from the parallels between the underlying decision making architectures in both societal systems and distributed engineered systems. In particular, both settings involve an interconnection of decision making elements whose collective behavior depends on a compilation of local decisions that are based on partial information about each other and the state of the world. Accordingly, there is extensive work in game theory that is relevant to the engineering agenda. Similarities notwithstanding, there remain important differences between the constraints and objectives in societal and engineered systems that require looking at game theoretic methods from a new perspective. This chapter provides an overview of selected recent developments of game theoretic methods in this role as a framework for distributed control in engineered systems.
Information Management in the Smart Grid: A Learning Game Approach
, 2013
"... In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the energy produc ..."
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Cited by 1 (0 self)
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In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the energy productions and the demand of the microgrids. The biases resulting from the decentralized learning might create imbalances between demand and supply, leading to penalties for the providers and for the producers. We determine analytically prices that provide to the producers a guarantee to avoid such penalties, reporting all the risk on the providers. Additionally, we prove that collaborative learning, through a grand coalition of providers where information is shared and forecasts aligned on a single value, minimizes their average risk. Simulations, run on a toy network, lead us to observe that the convergence rates of the collaborative learning strategy are clearly superior to rates resulting from distributed learning, using external and internal regret minimization.
Learning in Games
"... Abstract—In a Nash equilibrium, each player selects a strategy that is optimal with respect to the strategies of other players. This definition does not mention the process by which players reach a Nash equilibrium. The topic of learning in games seeks to address this issue in that it explores how s ..."
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Abstract—In a Nash equilibrium, each player selects a strategy that is optimal with respect to the strategies of other players. This definition does not mention the process by which players reach a Nash equilibrium. The topic of learning in games seeks to address this issue in that it explores how simplistic learning/adaptation rules can lead to Nash equilibrium. This article presents a selective sampling of learning rules and their longrun convergence properties, i.e., conditions under which player strategies converge or not to Nash equilibrium.
1Selecting Efficient Correlated Equilibria Through Distributed Learning
"... A learning rule is completely uncoupled if each player’s behavior is conditioned only on his own realized payoffs, and does not need to know the actions or payoffs of anyone else. We demonstrate a simple, completely uncoupled learning rule such that, in any finite normal form game with generic payof ..."
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A learning rule is completely uncoupled if each player’s behavior is conditioned only on his own realized payoffs, and does not need to know the actions or payoffs of anyone else. We demonstrate a simple, completely uncoupled learning rule such that, in any finite normal form game with generic payoffs, the players ’ realized strategies implements a Pareto optimal coarse correlated (Hannan) equilibrium a very high proportion of the time. A variant of the rule implements correlated equilibrium a very high proportion of the time. I.
Author manuscript, published in "ValueTools 2012, Cargèse: France (2012)" Distributed Learning in Hierarchical Networks
, 2012
"... Abstract—In this article, we propose distributed learning based approaches to study the evolution of a decentralized hierarchical system, an illustration of which is the smart grid. Smart grid management requires the control of nonrenewable energy production and the integration of renewable energie ..."
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Abstract—In this article, we propose distributed learning based approaches to study the evolution of a decentralized hierarchical system, an illustration of which is the smart grid. Smart grid management requires the control of nonrenewable energy production and the integration of renewable energies which might be highly unpredictable. Indeed, their production levels rely on uncontrolable factors such as sunshine, wind strength, etc. First, we derive optimal control strategies on the nonrenewable energy productions and compare competitive learning algorithms to forecast the energy needs of the end users. Second, we introduce an online learning algorithm based on regret minimization enabling the agents to forecast the production of renewable energies. Additionally, we define organizations of the market promoting collaborative learning which generate higher performance for the whole smart grid than full competition.
Game Theory and Distributed Control
, 2012
"... Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems fro ..."
Abstract
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Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems from the parallels between the underlying decision making architectures in both societal systems and distributed engineered systems. In particular, both settings involve an interconnection of decision making elements whose collective behavior depends on a compilation of local decisions that are based on partial information about each other and the state of the world. Accordingly, there is extensive work in game theory that is relevant to the engineering agenda. Similarities notwithstanding, there remain important differences between the constraints and objectives in societal and engineered systems that require looking at game theoretic methods from a new perspective. This chapter provides an overview of selected recent developments of game theoretic methods in this role as a framework for distributed control in engineered systems.
Coarse Resistance Tree Methods For Stochastic Stability Analysis
"... Abstract — Emergent behavior in natural and manmade systems can often be characterized by the limiting distribution of a special class of Markov processes termed regular perturbed processes. Resistance trees have gained popularity as a computationally efficient way to characterize the stochastically ..."
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Abstract — Emergent behavior in natural and manmade systems can often be characterized by the limiting distribution of a special class of Markov processes termed regular perturbed processes. Resistance trees have gained popularity as a computationally efficient way to characterize the stochastically stable states (i.e., support of the limiting distribution); however, there are three main limitations of this approach. First, it often requires finding a minimum weight spanning tree for each state in a potentially large state space. Second, perturbations to transition probabilities must decay at an exponentially smooth rate. Lastly, the approach is shown to hold purely in the context of finite Markov chains. In this paper we seek to address these limitations by developing new tools for characterizing the stochastically stable states. First, we provide necessary conditions for stochastic stability via a coarse, and less computationally intensive, state space analysis. Next, we identify necessary conditions for stochastic stability when smooth convergence requirements are relaxed. Lastly, we establish similar tools for stochastic stability analysis in Markov chains over a continuous state space.