Stochastic meta-descent (SMD) is a new technique for online adaptation of local learning rates in arbitrary twice-differentiable systems. Like matrix momentum it uses full second-order information while retaining O(n) computational complexity by exploiting the efficient computation of Hessian-vector products. Here we apply SMD to independent component analysis, and employ the resulting algorithm for the blind separation of time-varying mixtures. By matching individual learning rates to the rate of change in each source signal's mixture coefficients, our technique is capable of simultaneously tracking sources that move at very different, a priori unknown speeds.

Recent theoretical results suggest that the effectiveness of these algorithms is due to their tendency to produce large margin classifiers [1, 18]. Loosely speaking, if a combination of classifiers correctly classifies most of the training data with a large margin, then its error probability is small. In [14] we gave improved upper bounds on the misclassification probability of a combined classifier in terms of the average over the training data of a certain cost function of the margins.

Stochastic meta-descent (SMD) is a new technique for online adaptation of local learning rates in arbitrary twice-differentiable systems. Like matrix momentum it uses full second-order information while retaining O(n) computational complexity by exploiting the efficient computation of Hessian-vector products. Here we apply SMD to independent component analysis, and employ the resulting algorithm for the blind separation of time-varying mixtures. By matching individual learning rates to the rate of change in each source signal's mixture coefficients, our technique is capable of simultaneously tracking sources that move at very different, a priori unknown speeds.

Recent theoretical results suggest that the effectiveness of these algorithms is due to their tendency to produce large margin classifiers [1, 18]. Loosely speaking, if a combination of classifiers correctly classifies most of the training data with a large margin, then its error probability is small. In [14] we gave improved upper bounds on the misclassification probability of a combined classifier in terms of the average over the training data of a certain cost function of the margins.

Stochastic meta-descent (SMD) is a new technique for online adaptation oflocal learning rates in arbitrary twice-differentiable systems. Like matrix momentum it uses full second-order information while retaining O(n) computational complexity by exploiting the efficient computation of Hessian-vector products. Here we apply SMD to independent component analysis, and employ the resulting algorithmfor the blind separation of time-varying mixtures. By matching individual learning rates to the rate of change in each source signal's mixture coefficients, our technique is capable of simultaneously trackingsources that move at very different, a priori unknown speeds. 1 Introduction Independent component analysis (ICA) methods are typically run in batch mode in order to keep the stochasticity of the empirical gradient low. Often this is combined with a global learning rate annealing scheme that negotiates the tradeoff between fast convergence and good asymptotic performance.

Recent theoretical results suggest that the effectiveness of these algorithms is due to their tendency to produce large margin classifiers [1, 18]. Loosely speaking, if a combination of classifiers correctly classifies most of the training data with a large margin, then its error probability is small. In [14] we gave improved upper bounds on the misclassification probability of a combined classifier in terms of the average over the training data of a certain cost function of the margins. That paper also described DOOM, an algorithm for directly minimizingthe margin cost function by adjusting the weights associated with Boosting Algorithms as Gradient Descent 513 each base classifier (the base classifiers are suppiled to DOOM). DOOM exhibits performance improvements over AdaBoost, even when using the same base hypotheses, whichprovides additional empirical evidence that these margin cost functions are appropriate quantities to optimize. In this paper, we present a general class of algorithms (called AnyBoost) which are gradient descent algorithms for choosing linear combinations of elements of an inner product function space so as to minimize some cost functional. The normal operation of a weak learner is shown to be equivalent to maximizing a certain inner product. We prove convergence of AnyBoost under weak conditions. In Section 3, we show that this general class of algorithms includes as special cases nearly all existing voting methods.

A simple learning rule is derived, the VAPS algorithm, which can be instantiated to generate a wide range of new reinforcementlearning algorithms. These algorithms solve a number of open problems, define several new approaches to reinforcement learning, and unify different approaches to reinforcement learning under a single theory. These algorithms all have guaranteed convergence, and include modifications of several existing algorithms that were known to fail to converge on simple MOPs. These include Q learning, SARSA, and advantage learning. In addition to these value-based algorithms it also generates pure policy-search reinforcement-learning algorithms, which learn optimal policies without learning a value function. In addition, it allows policysearch and value-based algorithms to be combined, thus unifying two very different approaches to reinforcement learning into a single Value and Policy Search (V APS) algorithm.

A simple learning rule is derived, the VAPS algorithm, which can be instantiated to generate a wide range of new reinforcementlearning algorithms. These algorithms solve a number of open problems, define several new approaches to reinforcement learning, and unify different approaches to reinforcement learning under a single theory. These algorithms all have guaranteed convergence, and include modifications of several existing algorithms that were known to fail to converge on simple MOPs. These include Q learning, SARSA, and advantage learning. In addition to these value-based algorithms it also generates pure policy-search reinforcement-learning algorithms, which learn optimal policies without learning a value function. In addition, it allows policysearch and value-based algorithms to be combined, thus unifying two very different approaches to reinforcement learning into a single Value and Policy Search (V APS) algorithm.

We describe a new iterative method for parameter estimation of Gaussian mixtures. The new method is based on a framework developed by Kivinen and Warmuth for supervised online learning. In contrast to gradient descent and EM, which estimate the mixture's covariance matrices, the proposed method estimates the inverses of the covariance matrices. Furthennore, the new parameter estimation procedure can be applied in both online and batch settings. We show experimentally that it is typically faster than EM, and usually requires about half as many iterations as EM.

The inverse of the Fisher information matrix is used in the natural gradient descent algorithm to train single-layer and multi-layer perceptrons. We have discovered a new scheme to represent the Fisher information matrix of a stochastic multi-layer perceptron. Based on this scheme, we have designed an algorithm to compute the natural gradient. When the input dimension n is much larger than the number of hidden neurons, the complexity of this algorithm is of order O(n). It is confirmed by simulations that the natural gradient descent learning rule is not only efficient but also robust.