In large systems, it is important for agents to learn to act effectively, but sophisticated multi-agent learning algorithms generally do not scale. An alternative approach is to find restricted classes of games where simple, efficient algorithms converge. It is shown that stage learning efficiently converges to Nash equilibria in large anonymous games if best-reply dynamics converge. Two features are identified that improve convergence. First, rather than making learning more difficult, more agents are actually beneficial in many settings. Second, providing agents with statistical information about the behavior of others can significantly reduce the number of observations needed.
One approach to learning to play games is to generalize reinforcement learning algorithms such as Q-learning @cite_10 . One nice feature of this approach is that it can handle games with state, which is important in distributed systems. In Q-learning, an agent associates a value with each state-action pair. When he chooses action @math in state @math , he updates the value @math based on the reward he received and the best value he can achieve in the resulting state @math ( @math ). When generalizing to multiple agents, @math and @math become vectors of the state and action of every agent and the @math is replaced by a prediction of the behavior of other agents. Different algorithms use different predictions; for example, Nash-Q uses a Nash equilibrium calculation @cite_19 . See @cite_12 for a survey.
@cite_19 @cite_10 @cite_12
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We extend Q-learning to a noncooperative multiagent context, using the framework of general-sum stochastic games. A learning agent maintains Q-functions over joint actions, and performs updates based on assuming Nash equilibrium behavior over the current Q-values. This learning protocol provably converges given certain restrictions on the stage games (defined by Q-values) that arise during learning. Experiments with a pair of two-player grid games suggest that such restrictions on the game structure are not necessarily required. Stage games encountered during learning in both grid environments violate the conditions. However, learning consistently converges in the first grid game, which has a unique equilibrium Q-function, but sometimes fails to converge in the second, which has three different equilibrium Q-functions. In a comparison of offline learning performance in both games, we find agents are more likely to reach a joint optimal path with Nash Q-learning than with a single-agent Q-learning method. When at least one agent adopts Nash Q-learning, the performance of both agents is better than using single-agent Q-learning. We have also implemented an online version of Nash Q-learning that balances exploration with exploitation, yielding improved performance. This research describes a study into the ability of a state of the art reinforcement learning algorithm to learn to perform multiple tasks. We demonstrate that the limitation of learning to performing two tasks can be mitigated with a competitive training method. We show that this approach results in improved generalization of the system when performing unforeseen tasks. The learning agent assessed is an altered version of the DeepMind deep Q–learner network (DQN), which has been demonstrated to outperform human players for a number of Atari 2600 games. The key findings of this paper is that there were significant degradations in performance when learning more than one game, and how this varies depends on both similarity and the comparative complexity of the two games. The single-agent multi-armed bandit problem can be solved by an agent that learns the values of each action using reinforcement learning. However, the multi-agent version of the problem, the iterated normal form game, presents a more complex challenge, since the rewards available to each agent depend on the strategies of the others. We consider the behavior of value-based learning agents in this situation, and show that such agents cannot generally play at a Nash equilibrium, although if smooth best responses are used, a Nash distribution can be reached. We introduce a particular value-based learning algorithm, which we call individual Q-learning, and use stochastic approximation to study the asymptotic behavior, showing that strategies will converge to Nash distribution almost surely in 2-player zero-sum games and 2-player partnership games. Player-dependent learning rates are then considered, and it is shown that this extension converges in some games for which many algorithms, including the basic algorithm initially considered, fail to converge. In this paper, we propose a reinforcement learning method called a fuzzy Q-learning where an agent determines its action based on the inference result by a fuzzy rule-based system. We apply the proposed method to a soccer agent that intercepts a passed ball by another agent. In the proposed method, the state space is represented by internal information the learning agent maintains such as the relative velocity and the relative position of the ball to the learning agent. We divide the state space into several fuzzy subspaces. A fuzzy if-then rule in the proposed method represents a fuzzy subspace in the state space. The consequent part of the fuzzy if-then rules is a motion vector that suggests the moving direction and velocity of the learning agent. A reward is given to the learning agent if the distance between the ball and the agent becomes smaller or if the agent catches up with the ball. It is expected that the learning agent finally obtains the efficient positioning skill.