First Layer : Expanded Input Representation Final Output

We consider the requirements of online learning|learning which must be done in-crementally and in realtime, with the results of learning available soon after each new example is acquired. Despite the abundance of methods for learning from examples, there are few that can be used eeectively for on-line learning, e.g., as components of reinforcement learning systems. Most of these few, including radial basis functions, CMACs, Ko-honen's self-organizing maps, and those developed in this paper, share the same structure. All expand the original input representation into a higher dimensional representation in an unsupervised way, and then map that representation to the nal answer using a relatively simple supervised learner, such as a perceptron or LMS rule. Such structures learn very rapidly and reliably, but have been thought either to scale poorly or to require extensive domain knowledge. have argued that the expanded representation can be chosen largely at random with good results. The main contribution of this paper is to develop and test this hypothesis. We show that simple random-representation methods can perform as well as nearest-neighbor methods (while being more suited to online learning), and signiicantly better than backprop-agation. We nd that the size of the random representation does increase with the dimensionality of the problem, but not unreasonably so, and that the required size can be reduced substantially using unsupervised-learning techniques. Our results suggest that randomness has a useful role to play in on-line supervised learning and constructive induction. 1 Online Learning Applications of supervised learning can be divided into two types: online and ooine. By ooine supervised learning we mean the classical task in machine learning and statistics: a set of examples is obtained and used to learn a good approximating function before the function is used in the application. In online learning, on the other hand, data gathered during the normal operation of the system is used to continually adapt the learned function. Online learning has several advantages over ooine learning. First, online learning is potentially more robust because errors or omissions in the training set can be corrected during operation. Second, training data can often be generated easily and in great quantities when a system is in operation, whereas it is usually scarce and precious before. Being able to use this data sometimes puts online learning at a great advantage ; for example, this was probably the most important reason for the success of Tesauro's (1992) champion …