We describe a probabilistic approach to the task of placing objects, described by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribution as well as possible when the same operation is performed on the low-dimensional "images" of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional images. Unlike other dimensionality reduction methods, this probabilistic framework makes it easy to represent each object by a mixture of widely separated low-dimensional images. This allows ambiguous objects, like the document count vector for the word "bank", to have versions close to the images of both "river" and "finance" without forcing the images of outdoor concepts to be located close to those of corporate concepts.

We present a novel, flexible statistical approach for modelling music and text jointly. The approach is based on multi-modal mixture models and maximum a posteriori estimation using EM. The learned models can be used to browse databases with documents containing music and text, to search for music using queries consisting of music and text (lyrics and other contextual information), to annotate text documents with music, and to automatically recommend or identify similar songs.

Machine learning has reached a point where many probabilistic methods can be understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms customized for different models.

In Slow Feature Analysis (SFA [1]), it has been demonstrated that high-order invariant properties can be extracted by projecting inputs into a nonlinear space and computing the slowest changing features in this space; this has been proposed as a simple general model for learning nonlinear invariances in the visual system. However, this method is highly constrained by the curse of dimensionality which limits it to simple theoretical simulations. This paper demonstrates that by using a different but closely-related objective function for extracting slowly varying features ([2, 3]), and then exploiting the kernel trick, this curse can be avoided. Using this new method we show that both the complex cell properties of translation invariance and disparity coding can be learnt simultaneously from natural images when complex cells are driven by simple cells also learnt from the image. The notion of maximising an objective function based upon the temporal predictability of output has been progressively applied in modelling the development of invariances in the visual system.

A longstanding goal of reinforcement learning is to develop nonparametric representations of policies and value functions that support rapid learning without suffering from interference or the curse of dimensionality. We have developed a trajectory-based approach, in which policies and value functions are represented nonparametrically along trajectories. These trajectories, policies, and value functions are updated as the value function becomes more accurate or as a model of the task is updated. We have applied this approach to periodic tasks such as hopping and walking, which required handling discount factors and discontinuities in the task dynamics, and using function approximation to represent value functions at discontinuities. We also describe extensions of the approach to make the policies more robust to modeling error and sensor noise.

We introduce efficient learning equilibrium (ELE), a normative approach to learning in non cooperative settings. In ELE, the learning algorithms themselves are required to be in equilibrium. In addition, the learning algorithms arrive at a desired value after polynomial time, and deviations from a prescribed ELE become irrational after polynomial time. We prove the existence of an ELE in the perfect monitoring setting, where the desired value is the expected payoff in a Nash equilibrium. We also show that an ELE does not always exist in the imperfect monitoring case. Yet, it exists in the special case of common-interest games. Finally, we extend our results to general stochastic games.

Convergence for iterative reinforcement learning algorithms like TD(O) depends on the sampling strategy for the transitions. However, in practical applications it is convenient to take transition data from arbitrary sources without losing convergence. In this paper we investigate the problem of repeated synchronous updates based on a fixed set of transitions. Our main theorem yields sufficient conditions of convergence for combinations of reinforcement learning algorithms and linear function approximation. This allows to analyse if a certain reinforcement learning algorithm and a certain function approximator are compatible.

Given is a problem sequence and a probability distribution (the bias) on programs computing solution candidates. We present an optimally fast way of incrementally solving each task in the sequence. Bias shifts are computed by program prefixes that modify the distribution on their suffixes by reusing successful code for previous tasks (stored in non-modifiable memory). No tested program gets more runtime than its probability times the total search time.

We developed a robust control policy design method in high-dimensional state space by using differential dynamic programming with a minimax criterion. As an example, we applied our method to a simulated five link biped robot. The results show lower joint torques from the optimal control policy compared to a hand-tuned PD servo controller. Results also show that the simulated biped robot can successfully walk with unknown disturbances that cause controllers generated by standard differential dynamic programming and the hand-tuned PD servo to fail. Learning to compensate for modeling error and previously unknown disturbances in conjunction with robust control design is also demonstrated.

Many control problems take place in continuous state-action spaces, e.g., as in manipulator robotics, where the control objective is often defined as finding a desired trajectory that reaches a particular goal state. While reinforcement learning offers a theoretical framework to learn such control policies from scratch, its applicability to higher dimensional continuous state-action spaces remains rather limited to date. Instead of learning from scratch, in this paper we suggest to learn a desired complex control policy by transforming an existing simple canonical control policy. For this purpose, we represent canonical policies in terms of differential equations with well-defined attractor properties. By nonlinearly transforming the canonical attractor dynamics using techniques from nonparametric regression, almost arbitrary new nonlinear policies can be generated without losing the stability properties of the canonical system. We demonstrate our techniques in the context of learning a set of movement skills for a humanoid robot from demonstrations of a human teacher. Policies are acquired rapidly, and, due to the properties of well formulated differential equations, can be reused and modified online under dynamic changes of the environment. The linear parameterization of nonparametric regression moreover lends itself to recognize and classify previously learned movement skills.