Prediction, Learning, and Games

Cesa-Bianchi, Nicolò; Lugosi, Gábor

doi:10.1017/cbo9780511546921

Cited by 2,216 publications

(2,265 citation statements)

References 230 publications

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“…While alternative update algorithms such as polynomial weighting have been studied, exponential weighting schemes have been found to provide lower error in empirical and analytical studies [26]. The following proposition characterizes the regret of Randomized-experts.…”

Section: : End Proceduresmentioning

confidence: 99%

“…First, when the objective function is submodular, locally optimal solutions, in which node follows an optimal strategy given the actions of the other nodes, are within a provable bound of the global optimum [96]. Second, even when the objective function is time-varying and unknown, each node can approximate the optimal strategy over time via prediction and learning algorithms [26].…”

Section: Distributed Online Submodular Maximizationmentioning

confidence: 99%

“…An example of a MAB algorithm, denoted Exponential Weighted Average (EWA) [26], that will be used as a subroutine in our distributed submodular maximization approach is given as Algorithm 1.…”

Section: Background On Multi-armed Bandit Algorithmsmentioning

confidence: 99%

“…For the EWA algorithm, we chose γ = 0.01, η = 1/M M SE(∅), and β = 0.03, based on the discussion of parameter selection in [26].…”

Section: M Se(∅)mentioning

confidence: 99%

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Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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Submodularity in Dynamics and Control of Networked Systems Andrew ClarkCo-Chairs of the Supervisory Committee:Radha Poovendran Electrical Engineering Linda Bushnell Electrical EngineeringControlling a networked dynamical system to reach a desired state is a fundamental challenge in applications including transportation, energy, social, and biological systems. One scalable approach to controlling such systems is to directly control the states of a subset of leader nodes, while relying on local interactions to steer the remaining nodes towards their desired states. The choice of leader nodes is known to affect system metrics including robustness to noise, rate of convergence to a desired state, and controllability of the system.Selecting an optimal subset of leader nodes, however, is inherently a combinatorial problem, making optimal leader node selection intractable in general.This thesis presents a submodular optimization framework to selecting leader nodes for control of networked systems. We investigate the problem of selecting a subset of leader nodes in order to minimize node state errors due to noise in the communication links between nodes. We prove that the error due to link noise is a supermodular function of the set of leader nodes, leading to the first polynomial-time algorithms for minimizing error due to link noise with provable optimality bounds. We develop our approach for networks with static topologies, as well as dynamic topologies due to random link failures, switching between predefined topologies, and arbitrary mobility.We study selecting leader nodes in order to minimize convergence error, defined as the error in the intermediate node states prior to reaching their desired values. We derive upper bounds for a class of convergence error metrics based on the hitting time of random walk on the network, which we prove to be a supermodular function of the set of input nodes.We present polynomial-time algorithms for minimizing convergence error with provable optimality bounds, for static as well as dynamic networks.Efficient algorithms have recently been proposed for selecting leader nodes to satisfy controllability, defined as the ability to drive the non-input nodes from any initial state to any desired state in finite time. These algorithms, however, do not incorporate performance criteria including robustness to noise and convergence rate. We study the problem of leader selection for joint performance and controllability, and prove that controllability can be formulated as a matroid constraint on the set of leader nodes. We propose efficient algorithms with provable optimality gap for selecting leader nodes for joint performance and controllability, and characterize the submodular structure of the largest controllable subgraph of a network.We also investigate selecting input nodes for guaranteeing synchronization in networked systems. Using the widely-studied Kuramoto model of nonlinear phase-coupled oscillators, we develop novel threshold-based conditions for a set of input nodes to ...

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Section: : End Proceduresmentioning

confidence: 99%

Section: Distributed Online Submodular Maximizationmentioning

confidence: 99%

Section: Background On Multi-armed Bandit Algorithmsmentioning

confidence: 99%

“…For the EWA algorithm, we chose γ = 0.01, η = 1/M M SE(∅), and β = 0.03, based on the discussion of parameter selection in [26].…”

Section: M Se(∅)mentioning

confidence: 99%

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Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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“…Having no-regret means that no deviating action would significantly improve the firm's utility. Several learning algorithms are known to provide such guarantees ( [3,25] and references therein). More importantly, the assumption is not tied to any specific algorithmic procedure, but instead captures successful long-term behavior.…”

Section: Introductionmentioning

confidence: 99%

Coalition Formation and Price of Anarchy in Cournot Oligopolies

Immorlica

Markakis

Piliouras

2010

Lecture Notes in Computer Science

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Non-cooperative game theory purports that economic agents behave with little regard towards the negative externalities they impose on each other. Such behaviors generally lead to inefficient outcomes where the social welfare is bounded away from its optimal value. However, in practice, self-interested individuals explore the possibility of circumventing such negative externalities by forming coalitions. What sort of coalitions should we expect to arise? How do they affect the social welfare?We study these questions in the setting of Cournot markets, one of the most prevalent models of firm competition. Our model of coalition formation has two dynamic aspects. First, agents choose strategically how to update the current coalition partition. Furthermore, coalitions compete repeatedly between themselves trying to minimize their long-term regret. We prove tight bounds on the social welfare, which are significantly higher than that of the Nash equilibria of the original game. Furthermore, this improvement in performance is robust across different supply-demand curves and depends only on the size of the market.

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Quantifying the Uncertainties in an Ensemble of Decadal Climate Predictions

Strobach

Bel

2017

JGR Atmospheres

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Meaningful climate predictions must be accompanied by their corresponding range of uncertainty. Quantifying the uncertainties is nontrivial, and different methods have been suggested and used in the past. Here we propose a method that does not rely on any assumptions regarding the distribution of the ensemble member predictions. The method is tested using the Coupled Model Intercomparison Project Phase 5 1981–2010 decadal predictions and is shown to perform better than two other methods considered here. The improved estimate of the uncertainties is of great importance both for practical use and for better assessing the significance of the effects seen in theoretical studies.

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Prediction, Learning, and Games

Cited by 2,216 publications

References 230 publications

Submodularity in Dynamics and Control of Networked Systems

Submodularity in Dynamics and Control of Networked Systems

Coalition Formation and Price of Anarchy in Cournot Oligopolies

Quantifying the Uncertainties in an Ensemble of Decadal Climate Predictions

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