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16
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 21 (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.
ABSTRACT Title of dissertation: LEARNING IN ENGINEERED MULTIAGENT SYSTEMS
"... Consider the problem of maximizing the total power produced by a wind farm. Due to aerodynamic interactions between wind turbines, each turbine maximizing its individual power—as is the case in presentday wind farms—does not lead to optimal farmlevel power capture. Further, there are no good model ..."
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Consider the problem of maximizing the total power produced by a wind farm. Due to aerodynamic interactions between wind turbines, each turbine maximizing its individual power—as is the case in presentday wind farms—does not lead to optimal farmlevel power capture. Further, there are no good models to capture the said aerodynamic interactions, rendering model based optimization techniques ineffective. Thus, modelfree distributed algorithms are needed that help turbines adapt their power production online so as to maximize farmlevel power capture. Motivated by such problems, the main focus of this dissertation is a distributed modelfree optimization problem in the context of multiagent systems. The setup comprises of a fixed number of agents, each of which can pick an action and observe the value of its individual utility function. An individual’s utility function may depend on the collective action taken by all agents. The exact functional form (or model) of the agent utility functions, however, are unknown; an agent can only measure the numeric value of its utility. The objective of the multiagent system is to optimize the welfare function (i.e. sum of the individual utility functions).
From Weak Learning to Strong Learning in Fictitious Play Type Algorithms
"... accepted for inclusion in Department of Electrical and Computer Engineering by an authorized administrator of Research Showcase @ CMU. For more information, please contact ..."
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accepted for inclusion in Department of Electrical and Computer Engineering by an authorized administrator of Research Showcase @ CMU. For more information, please contact
ScienceDirect A behavioral study of "noise" in coordination gamesNCND license (http://creativecommons.org/licenses/byncnd/4.0/)
"... Abstract 'Noise' in this study, in the sense of evolutionary game theory, refers to deviations from prevailing behavioral rules. Analyzing data from a laboratory experiment on coordination in networks, we tested 'what kind of noise' is supported by behavioral evidence. This empi ..."
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Abstract 'Noise' in this study, in the sense of evolutionary game theory, refers to deviations from prevailing behavioral rules. Analyzing data from a laboratory experiment on coordination in networks, we tested 'what kind of noise' is supported by behavioral evidence. This empirical analysis complements a growing theoretical literature on 'how noise matters' for equilibrium selection. We find that the vast majority of decisions (96%) constitute myopic best responses, but deviations continue to occur with probabilities that are sensitive to their costs, that is, less frequent when implying larger payoff losses relative to the myopic best response. In addition, deviation rates vary with patterns of realized payoffs that are related to trialanderror behavior. While there is little evidence that deviations are clustered in time or space, there is evidence of individual heterogeneity.
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.
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.