Itwas demonstrated in the simulation of a pendulum swing-up task that the value-gradient based control scheme requires much less learning trials than the conventional "actor-critic"control scheme (Barto et al., 1983). In the actor-critic scheme, the actor, a direct feedback controller, improves its control policystochastically using the TD error as the effective reinforcement (Figure 1a). Despite its relatively slow learning, the actor-critic architecture has the virtue of simple computation in generating control command. In order to train a direct controller while making efficient use of the value function, we propose a new reinforcement learning scheme which we call the "actor-tutor" architecture (Figure 1b).

Policy iteration is known to have rapid and robust convergence properties, and for Markov tasks with lookup-table state-space representations, it is guaranteed to convergence to the optimal policy. Online Policy Improvement using Monte-Carlo Search 1069 In typical uses of policy iteration, the policy improvement step is an extensive off-line procedure. For example, in dynamic programming, one performs a sweep through all states in the state space. Reinforcement learning provides another approach topolicy improvement; recently, several authors have investigated using RL in conjunction with nonlinear function approximators to represent the value functions and/orpolicies (Tesauro, 1992; Crites and Barto, 1996; Zhang and Dietterich, 1996). These studies are based on following actual state-space trajectories rather than sweeps through the full state space, but are still too slow to compute improved policies in real time.

In many optimization problems, the structure of solutions reflects complex relationships between the different input parameters. For example, experience may tell us that certain parameters are closely related and should not be explored independently. Similarly, experience mayestablish that a subset of parameters must take on particular values. Any search of the cost landscape should take advantage of these relationships. We present MIMIC, a framework in which we analyze the global structure of the optimization landscape. Anovel and efficient algorithm for the estimation of this structure is derived. We use knowledge of this structure to guide a randomized search through the solution space and, in turn, to refine ourestimate ofthe structure.

A modification is described to the use of mean field approximations inthe E step of EM algorithms for analysing data from latent structure models, as described by Ghahramani (1995), among others. Themodification involves second-order Taylor approximations to expectations computed in the E step. The potential benefits of the method are illustrated using very simple latent profile models. 1 Introduction Ghahramani (1995) advocated the use of mean field methods as a means to avoid the heavy computation involved in the E step of the EM algorithm used for estimating parameters within a certain latent structure model, and Ghahramani & Jordan (1995) used the same ideas in a more complex situation. Dunmur & Titterington (1996a) identified Ghahramani's model as a so-called latent profile model, they observed that Zhang (1992,1993) had used mean field methods for a similar purpose, and they showed, in a simulation study based on very simple examples, that the mean field version of the EM algorithm often performed very respectably. By this it is meant that, when data were generated from the model under analysis, the estimators of the underlying parameters were efficient, judging by empirical results, especially in comparison with estimators obtained by employing the'correct' EM algorithm: the examples therefore had to be simple enough that the correct EM algorithm is numerically feasible, although any success reported for the mean field 432 A. P. Dunmur and D. M. Titterington version is, one hopes, an indication that the method will also be adequate in more complex situations in which the correct EM algorithm is not implementable because of computational complexity. In spite of the above positive remarks, there were circumstances in which there was a perceptible, if not dramatic, lack of efficiency in the simple (naive) mean field estimators, and the objective of this contribution is to propose and investigate ways of refining the method so as to improve performance without detracting from the appealing, and frequently essential, simplicity of the approach. The procedure used here is based on a second order correction to the naive mean field well known in statistical physics and sometimes called the cavity or TAP method (Mezard, Parisi & Virasoro, 1987). It has been applied recently in cluster analysis (Hofmann & Buhmann, 1996). In Section 2 we introduce the structure of our model, Section 3 explains the refined mean field approach, Section 4 provides numerical results, and Section 5 contains a statement of our conclusions.

The optimal control problem reduces to a boundary value problem for a fully nonlinear second-order elliptic differential equation of Hamilton Jacobi-Bellman (HJB-) type. Numerical analysis provides multigrid methodsfor this kind of equation. In the case of Learning Control, however,the systems of equations on the various grid-levels are obtained using observed information (transitions and local cost). To ensure consistency, special attention needs to be directed toward thetype of time and space discretization during the observation. Analgorithm for multi-grid observation is proposed. The multi-grid algorithm is demonstrated on a simple queuing problem. 1 Introduction Controlled Diffusion Processes (CDP) are the analogy to Markov Decision Problems in continuous state space and continuous time.

To obtain classification systems with both good generalization performance andefficiency in space and time, we propose a learning method based on combinations of weak classifiers, where weak classifiers arelinear classifiers (perceptrons) which can do a little better than making random guesses. A randomized algorithm is proposed to find the weak classifiers. They· are then combined through a majority vote.As demonstrated through systematic experiments, the method developed is able to obtain combinations of weak classifiers with good generalization performance and a fast training time on a variety of test problems and real applications.

Support Vector Learning Machines (SVM) are finding application in pattern recognition, regression estimation, and operator inversion forill-posed problems. Against this very general backdrop, any methods for improving the generalization performance, or for improving the speed in test phase, of SVMs are of increasing interest. Inthis paper we combine two such techniques on a pattern recognition problem. The method for improving generalization performance (the"virtual support vector" method) does so by incorporating known invariances of the problem. This method achieves a drop in the error rate on 10,000 NIST test digit images of 1.4% to 1.0%.

We study the spatiotemporal correlation in natural time-varying images and explore the hypothesis that the visual system is concerned withthe optimal coding of visual representation through spatiotemporal decorrelation of the input signal. Based on the measured spatiotemporal power spectrum, the transform needed to decorrelate input signal is derived analytically and then compared with the actual processing observed in psychophysical experiments.

Further im- 528 F.Leisch and K. Hornik provements should be possible based on a better understanding of the theoretical properties of resample and combine techniques. These issues are currently being investigated.

A new method to calculate the full training process of a neural network isintroduced. No sophisticated methods like the replica trick are used. The results are directly related to the actual number of training steps. Some results are presented here, like the maximal learning rate, an exact description of early stopping, and the necessary numberof training steps. Further problems can be addressed with this approach.