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Multi-agent learning is intrinsically harder, more unstable and unpredictable than single agent optimization.
Period three implies chaos
Li, T.-Y. and Yorke, J. A · 1975
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Global Stability of Dynamical Systems
Shub, M · 1987
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The weighted majority algorithm
Littlestone, N. and Warmuth, M. K · 1994
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Adaptive game playing using multiplicative weights
Freund, Y. and Schapire, R. E · 1999
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Nash convergence of gradient dynamics in general-sum games
Singh, S., Kearns, M. J., and Mansour, Y · 2000
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Multiagent learning using a variable learning rate
Bowling, M. and Veloso, M · 2002
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How bad is selfish routing?
Roughgarden, T. and Tardos, É · 2002
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Adaptive policy gradient in multiagent learning
Banerjee, B. and Peng, J · 2003
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Uncoupled dynamics do not lead to nash equilibrium
Hart, S. and Mas-Colell, A · 2003
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Convergence and no-regret in multiagent learning
Bowling, M · 2004
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The complexity of computing a nash equilibrium
Daskalakis, C., Goldberg, P. W., and Papadimitriou, C. H · 2006
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Study on chaos induced by turbulent maps in noncompact sets
Shi, Y. and Yu, P · 2006
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Algorithmic Game Theory
Nisan, N., Roughgarden, T., Tardos, E., and Vazirani, V. V · 2007
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A multiagent reinforcement learning algorithm with non-linear dynamics
Abdallah, S. and Lesser, V · 2008
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An evolutionary model of multi-agent learning with a varying exploration rate
Kaisers, M., Tuyls, K., Parsons, S., and Thuijsman, F · 2009
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Online learning and online convex optimization
Shalev-Shwartz, S. et al · 2011
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The multiplicative weights update method: a meta-algorithm and applications
Arora, S., Hazan, E., and Kale, S · 2012
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Complex dynamics in learning complicated games
Galla, T. and Farmer, J. D · 2013
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Evolutionary dynamics of multi-agent learning: A survey
Bloembergen, D., Tuyls, K., Hennes, D., and Kaisers, M · 2015
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Multiplicative weights update with constant step-size in congestion games: Convergence, limit cycles and chaos
Palaiopanos, G., Panageas, I., and Piliouras, G · 2017
Finite regret and cycles with fixed step-size via alternating gradient descent-ascent
Bailey, J. P., Gidel, G., and Piliouras, G · 2020
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Chaos, extremism and optimism: Volume analysis of learning in games
Cheung, Y. K. and Piliouras, G · 2020
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The route to chaos in routing games: When is price of anarchy too optimistic?
Chotibut, T., Falniowski, F., Misiurewicz, M., and Piliouras, G · 2020
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No-regreet learning and mixed nash equilibria: They do not mix
Flokas, L., Vlatakis-Gkaragkounis, E.-V., Lianeas, T., Mertikopoulos, P., and Piliouras, G · 2020
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Learning in matrix games can be arbitrarily complex
Andrade, G. P., Frongillo, R., and Piliouras, G · 2021
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Follow-the-regularized-leader routes to chaos in routing games
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Proximal policy optimization algorithms
Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O · 2017
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Multiplicative weights update in zero-sum games
Bailey, J. P. and Piliouras, G · 2018
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The mechanics of n-player differentiable games
Balduzzi, D., Racanière, S., Martens, J., Foerster, J. N., Tuyls, K., and Graepel, T · 2018
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Cycles in adversarial regularized learning
Mertikopoulos, P., Papadimitriou, C., and Piliouras, G · 2018
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The prevalence of chaotic dynamics in games with many players
Sanders, J. B. T., Farmer, J. D., and Galla, T · 2018
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Fast and furious learning in zero-sum games: Vanishing regret with non-vanishing step sizes
Bailey, J. P. and Piliouras, G · 2019
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Bielawski, J., Chotibut, T., Falniowski, F., Kosiorowski, G., Misiurewicz, M., and Piliouras, G · 2021
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Chaos of learning beyond zero-sum and coordination via game decompositions
Cheung, Y. K. and Tao, Y · 2021
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Learning in markets: Greed leads to chaos but following the price is right
Cheung, Y. K., Leonardos, S., and Piliouras, G · 2021
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Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information
Giannou, A., Vlatakis-Gkaragkounis, E. V., and Mertikopoulos, P · 2021
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The limits of min-max optimization algorithms: Convergence to spurious non-critical sets
Hsieh, Y.-P., Mertikopoulos, P., and Cevher, V · 2021
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Dynamical analysis of the eip-1559 ethereum fee market
Leonardos, S., Monnot, B., Reijsbergen, D., Skoulakis, E., and Piliouras, G · 2021
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On the impossibility of global convergence in multi-loss optimization, 2021
Letcher, A · 2021
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Exploration-exploitation in multi-agent learning: Catastrophe theory meets game theory
Leonardos, S. and Piliouras, G · 2022
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Multi-agent performative prediction: From global stability and optimality to chaos
Piliouras, G. and Yu, F.-Y · 2022
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