Cooperative Games with Overlapping Coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions--or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

Scaling reinforcement learning to the unconstrained multi-agent domain

Reinforcement learning is a machine learning technique designed to mimic the way animals learn by receiving rewards and punishment. It is designed to train intelligent agents when very little is known about the agent’s environment, and consequently the agent’s designer is unable to hand-craft an appropriate policy. Using reinforcement learning, the agent’s designer can merely give reward to the agent when it does something right, and the algorithm will craft an appropriate policy automatically. In many situations it is desirable to use this technique to train systems of agents (for example, to train robots to play RoboCup soccer in a coordinated fashion). Unfortunately, several significant computational issues occur when using this technique to train systems of agents. This dissertation introduces a suite of techniques that overcome many of these difficulties in various common situations. First, we show how multi-agent reinforcement learning can be made more tractable by forming coalitions out of the agents, and training each coalition separately. Coalitions are formed by using information-theoretic techniques, and we find that by using a coalition-based approach, the computational complexity of reinforcement-learning can be made linear in the total system agent count. Next we look at ways to integrate domain knowledge into the reinforcement learning process, and how this can signifi-cantly improve the policy quality in multi-agent situations. Specifically, we find that integrating domain knowledge into a reinforcement learning process can overcome training data deficiencies and allow the learner to converge to acceptable solutions when lack of training data would have prevented such convergence without domain knowledge. We then show how to train policies over continuous action spaces, which can reduce problem complexity for domains that require continuous action spaces (analog controllers) by eliminating the need to finely discretize the action space. Finally, we look at ways to perform reinforcement learning on modern GPUs and show how by doing this we can tackle significantly larger problems. We find that by offloading some of the RL computation to the GPU, we can achieve almost a 4.5 speedup factor in the total training process