Introduction to analysis (3rd ed.)
Introduction to analysis (3rd ed.)
Using knowledge about the opponent in game-tree search
Using knowledge about the opponent in game-tree search
Learning to coordinate without sharing information
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Average reward reinforcement learning: foundations, algorithms, and empirical results
Machine Learning - Special issue on reinforcement learning
Competitive Markov decision processes
Competitive Markov decision processes
The dynamics of reinforcement learning in cooperative multiagent systems
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Bargaining with limited computation: deliberation equilibrium
Artificial Intelligence
Multiagent learning using a variable learning rate
Artificial Intelligence
Friend-or-Foe Q-learning in General-Sum Games
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
Automatic Discovery of Subgoals in Reinforcement Learning using Diverse Density
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
Multiagent Reinforcement Learning: Theoretical Framework and an Algorithm
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Intra-Option Learning about Temporally Abstract Actions
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Bounding the Suboptimality of Reusing Subproblem
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Reinforcement Learning in POMDP's via Direct Gradient Ascent
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Tree based hierarchical reinforcement learning
Tree based hierarchical reinforcement learning
Learning models of intelligent agents
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Hierarchical solution of Markov decision processes using macro-actions
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Reaching pareto-optimality in prisoner's dilemma using conditional joint action learning
Autonomous Agents and Multi-Agent Systems
A Design of Reward Function Based on Knowledge in Multi-agent Learning
ADMA '08 Proceedings of the 4th international conference on Advanced Data Mining and Applications
Perpetual learning for non-cooperative multiple agents
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
The Dynamics of Multi-Agent Reinforcement Learning
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Pareto-Q learning algorithm for cooperative agents in general-sum games
CEEMAS'05 Proceedings of the 4th international Central and Eastern European conference on Multi-Agent Systems and Applications
Seeking multiobjective optimization in uncertain, dynamic games
EPIA'05 Proceedings of the 12th Portuguese conference on Progress in Artificial Intelligence
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Multiagent learning is a necessary yet challenging problem as multiagent systems become more prevalent and environments become more dynamic. Much of the groundbreaking work in this area draws on notable results from game theory, in particular, the concept of Nash equilibria. Learners that directly learn an equilibrium obviously rely on their existence. Learners that instead seek to play optimally with respect to the other players also depend upon equilibria since equilibria are fixed points for learning. From another perspective, agents with limitations are real and common. These may be undesired physical limitations as well as self-imposed rational limitations, such as abstraction and approximation techniques, used to make learning tractable. This article explores the interactions of these two important concepts: equilibria and limitations in learning. We introduce the question of whether equilibria continue to exist when agents have limitations. We look at the general effects limitations can have on agent behavior, and define a natural extension of equilibria that accounts for these limitations. Using this formalization, we make three major contributions: (i) a counterexample for the general existence of equilibria with limitations, (ii) sufficient conditions on limitations that preserve their existence, (iii) three general classes of games and limitations that satisfy these conditions. We then present empirical results from a specific multiagent learning algorithm applied to a specific instance of limited agents. These results demonstrate that learning with limitations is feasible, when the conditions outlined by our theoretical analysis hold.