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We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical systems theory.
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Dynamic Noncooperative Game Theory
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The theory of learning in games , volume 2
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Nonlinear Systems
S. Sastry · 1999
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Nash convergence of gradient dynamics in general-sum games
Satinder P. Singh, Michael J. Kearns, and Yishay Mansour · 2000
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Online convex optimization in the bandit setting: Gradient descent without a gradient
Abraham Flaxman, Adam Kalai, and Brendan McMahan · 2005
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Individual Q-Learning in Normal Form Games
David S. Leslie and E. J. Collins · 2005
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Gradient descent only converges to minimizers
J. D. Lee, M. Simchowitz, M. I. Jordan, and B. Recht · 2016
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Gradient descent only converges to minimizers: Non-isolated critical points and invariant regions
Ioannis Panageas and Georgios Piliouras · 2016
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On the Characterization of Local Nash Equilibria in Continuous Games
L. J. Ratliff, S. A. Burden, and S. S Sastry · 2016
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Hopf bifurcations in delayed rock–paper–scissors replicator dynamics
Elizabeth Wesson and Richard Rand · 2016
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A lyapunov analysis of momentum methods in optimization
Ashia C. Wilson, Benjamin Recht, and Michael I. Jordan · 2016
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Adversarial learning games with deep learning models
A. S. Chivukula and W. Liu · 2017
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Stochastic Approximation: A Dynamical Systems Viewpoint
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Multiple equilibria and limit cycles in evolutionary games with logit dynamics
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Traning GANs with Optimism
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Deep decentralized multi-task multi-agent reinforcement learning under partial observability
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Reinforcement Learning: An Introduction
Richard S. Sutton and Andrew G. Barto · 2017
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Bandit learning in concave n-person games
Mario Bravo, David Leslie, and Panayotis Mertikopoulos · 2018
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The limit points of (optimistic) gradient descent in min-max optimization
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Learning with opponent-learning awareness
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