Kernelizing LSPE λ

We propose the use of kernel-based methods as underlying function approximator in the least-squares based policy evaluation framework of LSPE(λ) and LSTD(λ). In particular we present the ‘kernelization’ of model-free LSPE(λ). The ‘kernelization’ is computationally made possible by using the subset of regressors approximation, which approximates the kernel using a vastly reduced number of basis functions. The core of our proposed solution is an efficient recursive implementation with automatic supervised selection of the relevant basis functions. The LSPE method is well-suited for optimistic policy iteration and can thus be used in the context of online reinforcement learning. We use the high-dimensional Octopus benchmark to demonstrate this

On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems

The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well as numerical experiments show that a projection does usually not satisfy both objectives at once. In a standard classification problem we determine projections on the input data that balance the objectives and compare subsequent results. Next, we extend our application of orthogonal projections to deep learning tasks and introduce a general framework of augmented target loss functions. These loss functions integrate additional information via transformations and projections of the target data. In two supervised learning problems, clinical image segmentation and music information classification, the application of our proposed augmented target loss functions increase the accuracy