Computer Science Department
School of Computer Science, Carnegie Mellon University


Multiagent Learning in the Presence of Agents
with Limitations

Michael Bowling

May 2003

Ph.D. Thesis
(Color images)

Keywords: Machine learning, multiagent systems, game theory, reinforcement learning, multiagent learning, policy gradient methods, non-stationary environments, variable learning rate, game-playing, robot soccer

Learning to act in a multiagent environment is a challenging problem. Optimal behavior for one agent depends upon the behavior of the other agents, which are learning as well. Multiagent envi-ronments are therefore non-stationary, violating the traditional assumption underlying single-agent learning. In addition, agents in complex tasks may have limitations, such as physical constraints or designer-imposed approximations of the task that make learning tractable. Limitations prevent agents from acting optimally, which complicates the already challenging problem. A learning agent must effectively compensate for its own limitations while exploiting the limitations of the other agents. My thesis research focuses on these two challenges, namely multiagent learning and limitations, and includes four main contributions.

First, the thesis introduces the novel concepts of a variable learning rate and the WoLF (Win or Learn Fast) principle to account for other learning agents. The WoLF principle is capable of making rational learning algorithms converge to optimal policies, and by doing so achieves two properties, rationality and convergence, which had not been achieved by previous techniques. The converging effect of WoLF is proven for a class of matrix games, and demonstrated empirically for a wide-range of stochastic games.

Second, the thesis contributes an analysis of the effect of limitations on the game-theoretic con-cept of Nash equilibria. The existence of equilibria is important if multiagent learning techniques, which often depend on the concept, are to be applied to realistic problems where limitations are unavoidable. The thesis introduces a general model for the effect of limitations on agent behavior, which is used to analyze the resulting impact on equilibria. The thesis shows that equilibria do exist for a few restricted classes of games and limitations, but even well-behaved limitations do not preserve the existence of equilibria, in general.

Third, the thesis introduces GraWoLF, a general-purpose, scalable, multiagent learning algo-rithm. GraWoLF combines policy gradient learning techniques with the WoLF variable learning rate. The effectiveness of the learning algorithm is demonstrated in both a card game with an in-tractably large state space, and an adversarial robot task. These two tasks are complex and agent limitations are prevalent in both.

Fourth, the thesis describes the CMDragons robot soccer team strategy for adapting to an un-known opponent. The strategy uses a notion of plays as coordinated team plans. The selection of team plans is the decision point for adapting the team to its current opponent, based on the out-come of previously executed plays. The CMDragons were the first RoboCup robot team to employ online learning to autonomously alter its behavior during the course of a game.

These four contributions demonstrate that it is possible to effectively learn to act in the presence of other learning agents in complex domains when agents may have limitations. The introduced learning techniques are proven effective in a class of small games, and demonstrated empirically across a wide range of settings that increase in complexity.

172 pages

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