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Cheung and Piliouras (2020) recently showed that two variants of the Multiplicative Weights Update method - OMWU and MWU - display opposite convergence properties depending on whether the game is zero-sum or cooperative.
Games with Randomly Disturbed Payoffs: a New Rationale for Mixed-strategy Equilibrium points
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Regularity and Stability of Equilibrium Points of Bimatrix Games
Jansen, M. J. M · 1981
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Matrix Analysis
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Bimatrix games have quasi-strict equilibria
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Rational and Convergent Learning in Stochastic Games
Bowling, M. and Veloso, M · 2001
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On the hardness and existence of quasi-strict equilibria
Brandt, F. and Fischer, F · 2008
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Settling the complexity of computing two-player nash equilibria
Chen, X., Deng, X., and Teng, S · 2009
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The complexity of computing a nash equilibrium
Daskalakis, C., Goldberg, P. W., and Papadimitriou, C. H · 2009
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Flows and Decompositions of Games: Harmonic and Potential Games
Candogan, O., Menache, I., Ozdaglar, A., and Parrilo, P. A · 2011
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Learning to learn by gradient descent by gradient descent
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A Unified Game Theoretic Approach to Multiagent Reinforcement Learning
Lanctot, M., Zambaldi, V., Gruslys, A., Lazaridou, A., Tuyls, K., Perolat, J., Silver, D., , and Graepel, T · 2017
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Learning to Optimize
Li, K. and Malik, J · 2017
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A unified approach to interpreting model predictions
Lundberg, S. M. and Lee, S.-I · 2017
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The Numerics of GANs
Mescheder, L., Nowozin, S., and Geiger, A · 2017
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Proximal Policy Optimization Algorithms
Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O · 2017
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The Mechanics of n-Player Differentiable Games
Balduzzi, D., Racaniere, S., Martens, J., Foerster, J., Tuyls, K., and Graepel, T · 2018
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Training GANs with Optimism
Daskalakis, C., Ilyas, A., Syrgkanis, V., and Zeng, H · 2018
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On the convergence of single-call stochastic extra-gradient methods
Hsieh, Y.-G., Iutzeler, F., Malick, J., and Mertikopoulos, P · 2019
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Differentiable Game Mechanics
Letcher, A., Balduzzi, D., Racaniere, S., Martens, J., Foerster, J., Tuyls, K., and Graepel, T · 2019
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Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile
Mertikopoulos, P., Lecouat, B., Zenati, H., Foo, C.-S., Chandrasekhar, V., and Piliouras, G · 2019
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A Tight and Unified Analysis of Gradient-Based Methods for a Whole Spectrum of Differentiable Games
Azizian, W., Mitliagkas, I., Lacoste-Julien, S., and Gidel, G · 2020
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Training Stronger Baselines for Learning to Optimize
Chen, T., Zhang, W., Zhou, J., Chang, S., Liu, S., Amini, L., and Wang, Z · 2020
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Chaos, Extremism and Optimism: Volume Analysis of Learning in Games
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RLlib: Abstractions for distributed reinforcement learning
Liang, E., Liaw, R., Nishihara, R., Moritz, P., Fox, R., Goldberg, K., Gonzalez, J., Jordan, M., and Stoica, I · 2018
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Open-ended learning in symmetric zero-sum games
Balduzzi, D., Garnelo, M., Bachrach, Y., Czarnecki, W., Perolat, J., Jaderberg, M., and Graepel, T · 2019
Cited alongside, same era.
Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization
Daskalakis, C. and Panageas, I · 2019
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Negative Momentum for Improved Game Dynamics
Gidel, G., Hemmat, R. A., Pezeshki, M., Lepriol, R., Huang, G., Lacoste-Julien, S., and Mitliagkas., I · 2019
Cited alongside, same era.
Cheung, Y. K. and Piliouras, G · 2020
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Strategic decompositions of normal form games: Zero-sum games and potential games
Hwang, S.-H. and Rey-Bellet, L · 2020
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Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes
Lei, Q., Nagarajan, S. G., Panageas, I., and Wang, X · 2021
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Learning a Minimax Optimizer: A Pilot study
Shen, J., Chen, X., Heaton, H., Chen, T., Liu, J., Yin, W., and Wang, Z · 2021
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Linear Last-iterate convergence in constrained saddle-point optimization
Wei, C.-Y., Lee, C.-W., Zhang, M., and Luo, H · 2021
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