Parametric Polynomial Time Perceptron Rescaling Algorithm

Let us consider a linear feasibility problem with a possibly infinite number of inequality constraints posed in an on-line setting: an algorithm suggests a candidate solution, and the oracle either confirms its feasibility, or outputs a violated constraint vector. This model can be solved by subgradient optimisation algorithms for non-smooth functions, also known as the perceptron algorithms in the machine learning community, and its solvability depends on the problem dimension and the radius of the constraint set. The classical perceptron algorithm may have an exponential complexity in the worst case when the radius is infinitesimal [1]. To overcome this difficulty, the space dilation technique was exploited in the ellipsoid algorithm to make its running time polynomial [3]. A special case of the space dilation, the rescaling procedure is utilised in the perceptron rescaling algorithm [2] with a probabilistic approach to choosing the direction of dilation. A parametric version of the perceptron rescaling algorithm is the focus of this work. It is demonstrated that some fixed parameters of the latter algorithm (the initial estimate of the radius and the relaxation parameter) may be modified and adapted for particular problems. The generalised theoretical framework allows to determine convergence of the algorithm with any chosen set of values of these parameters, and suggests a potential way of decreasing the complexity of the algorithm which remains the subject of current research

Advances in quantum machine learning

Here we discuss advances in the field of quantum machine learning. The following document offers a hybrid discussion; both reviewing the field as it is currently, and suggesting directions for further research. We include both algorithms and experimental implementations in the discussion. The field's outlook is generally positive, showing significant promise. However, we believe there are appreciable hurdles to overcome before one can claim that it is a primary application of quantum computation.Comment: 38 pages, 17 Figure

Using Kernel Perceptrons to Learn Action Effects for Planning

Abstract — We investigate the problem of learning action effects in STRIPS and ADL planning domains. Our approach is based on a kernel perceptron learning model, where action and state information is encoded in a compact vector representation as input to the learning mechanism, and resulting state changes are produced as output. Empirical results of our approach indicate efficient training and prediction times, with low average error rates (< 3%) when tested on STRIPS and ADL versions of an object manipulation scenario. This work is part of a project to integrate machine learning techniques with a planning system, as part of a larger cognitive architecture linking a highlevel reasoning component with a low-level robot/vision system. I

Optimizing 0/1 Loss for Perceptrons by Random Coordinate Descent

The 0/1 loss is an important cost function for perceptrons. Nevertheless it cannot be easily minimized by most existing perceptron learning algorithms. In this paper, we propose a family of random coordinate descent algorithms to directly minimize the 0/1 loss for perceptrons, and prove their convergence. Our algorithms are computationally efficient, and usually achieve the lowest 0/1 loss compared with other algorithms. Such advantages make them favorable for nonseparable real-world problems. Experiments show that our algorithms are especially useful for ensemble learning, and could achieve the lowest test error for many complex data sets when coupled with AdaBoost