Recursive Learning

Increasingly, multi-agent systems are being designed for a variety of complex, dynamic domains. Effective agent learning in such domains raise some of most fundamental research challenges for agent-based systems. An agent in such domains may often need to model other agents’ behaviors, or learn/adapt from its interactions, or form teams and act effectively in a team, or negotiate with other agents, and so on. The typical assumption in most of the studies on learning is that the data is uniformly distributed. However, real data and real environments overwhelmingly disobey these assumptions. Recognized groups of data typically are skewed and exhibit fractal dimensionalities. Almost all biological systems contain self-similar structures that are made through recurrent processes, while many physical systems contain a form of functional self-similarity that owes its richness to recursion. Human brains, economic markets, network data, agent behavior, WWW browsing behavior and nature create enormously complex behavior that is much richer than the behavior of the individual component units. Complex systems with emergent properties are often highly parallel collections of similar units. A parallel system is inherently more efficient than a sequential system, since tasks can be performed simultaneously and more readily via specialization. Parallel systems that are redundant have fault tolerance and subtle variation among the parts of a parallel system allows for multiple problem solutions to be attempted simultaneously .

Self-similar structures similar to many recognized group of human activity, applied systems, engineering mechanisms, time series and agents behavior consists of a collection of behavior stored in a hierarchy. A macro point of view suggests system behavior is more a trajectory among higher level units or super behaviors. The notion of super behavior comes with the idea of granularity, organization and hierarchy. The concept of granulation and organization play fundamental role in human cognition as well as in the nature and in a large group of real application domains. A model structure could be considered as a set of smaller models at one time and a group of such structures may make a new bigger entity in a higher level. In more specific terms, information granulation relates to partitioning a class of points, objects, states etc into granules, with a granule being a clump of objects or states drawn together by locality, similarity, or functionality. An observed sequence of a system might be considered as a collection of a certain behaviors (rather than a big collection of states inside each behavior), and it might provide enough information for reasoning or be guidance for further details. While there have been much effort on observing self-similar structures in scientific databases and natural structures there are few works on using self-similar structure and fractal dimension for data mining, learning, predictive modeling and forecasting. Amongthese works, using fractal dimension and self-similarity for managing the dimensionally curse, learning association rules and application in spatial joint are considerable.

This work is motivated by the open question of agent learning in a complex, dynamic environment that are extremely difficult for predictive modeling.In this body of work er we introduce a novel technique which use the self-similar structure for learning and predictive modeling using a layered Hidden Markov Model . We believe agents can learn form their experience and leverage such knowledge in two major categories through using self-similarity information in the environment. First, they are enable to learn other part of the model through the assumption of self-similarity in horizontal level. Second, they can extend their knowledge to learn macro rules, macro plans and high level structure using the self-similarity in vertical dimension. In addition we study, discuss and analyze Self-Similar Hidden Markov as a novel technique for recursive learning and illustrate it is a better estimation than flat HMM when data shows self-similar property. Moreover, we study different types of self-similarity along with some result on synthetic data and experiments on Network data. Since SSLHMM has hierarchical structures and abstract states into phases, it overcomes, to a certain extent, the difficulty of dealing with larger number of states at the same layer, thus making the learning process move efficient and effective.