Extended Predictable Feature Analysis (PFAx) [Richthofer and Wiskott, 2017] is an extension of PFA [Richthofer and Wiskott, 2015] that allows generating a goal-directed control signal of an agent whose dynamics has previously been learned during a training phase in an unsupervised manner. PFAx hardly requires assumptions or prior knowledge of the agent's sensor or control mechanics, or of the environment. It selects features from a high-dimensional input by intrinsic predictability and organizes them into a reasonably low-dimensional model. While PFA obtains a well predictable model, PFAx yields a model ideally suited for manipulations with predictable outcome. This allows for goal-directed manipulation of an agent and thus for local navigation, i.e. for reaching states where intermediate actions can be chosen by a permanent descent of distance to the goal. The approach is limited when it comes to global navigation, e.g. involving obstacles or multiple rooms. In this article, we extend theoretical results from [Sprekeler and Wiskott, 2008], enabling PFAx to perform stable global navigation. So far, the most widely exploited characteristic of Slow Feature Analysis (SFA) was that slowness yields invariances. We focus on another fundamental characteristics of slow signals: They tend to yield monotonicity and one significant property of monotonicity is that local optimization is sufficient to find a global optimum. We present an SFA-based algorithm that structures an environment such that navigation tasks hierarchically decompose into subgoals. Each of these can be efficiently achieved by PFAx, yielding an overall global solution of the task. The algorithm needs to explore and process an environment only once and can then perform all sorts of navigation tasks efficiently. We support this algorithm by mathematical theory and apply it to different problems.
@cite_46 suggests how a hierarchical decomposition of a problem space can be achieved using the successor representation and its eigenvalue decomposition. That work draws a number of links to studies of animal behavior, observations in the hippocampus and to cognitive maps. It contains many interesting notes regarding biological plausibility of decomposition approaches.
@cite_46
2152404340 2037348066 36903255 2110371102
Considers the problem of robot motion planning using an approximate cell decomposition method for Cspace representation. By means of a hierarchical multilevel discretization the authors are able to reduce the complexity of the problem and to provide a practically feasible procedure for its solution. Hierarchical discretization is based on the use of a multisource distance field that is introduced and described in the paper. The developed procedure, used as an heuristic, systematically reduces the amount of memory needed for implementing the motion planning algorithm. Using such a procedure, several instances of the motion planning problem, involving for example two three-links manipulators acting in the same tridimensional environment, have been solved in a reasonable amount of time. > Hierarchical approximate cell decomposition is a popular approach to the geometric robot motion planning problem. In many cases, the search effort expended at a particular iteration can be greatly reduced by exploiting the work done during previous iterations. In this paper, we describe how this exploitation of past computation can be effected by the use of a dynamically maintained single-source shortest paths tree. We embed a single-source shortest paths tree in the connectivity graph of the approximate representation of the robot configuration space. This shortest paths tree records the most promising path to each vertex in the connectivity graph from the vertex corresponding to the robot's initial configuration. At each iteration, some vertex in the connectivity graph is replaced with a new set of vertices, corresponding to a more detailed representation of the configuration space. Our new, dynamic algorithm is then used to update the single-source shortest paths tree to reflect these changes to the underlying connectivity graph. > In recent years, variants of a neural network architecture for statistical language modeling have been proposed and successfully applied, e.g. in the language modeling component of speech recognizers. The main advantage of these architectures is that they learn an embedding for words (or other symbols) in a continuous space that helps to smooth the language model and provide good generalization even when the number of training examples is insufficient. However, these models are extremely slow in comparison to the more commonly used n-gram models, both for training and recognition. As an alternative to an importance sampling method proposed to speed-up training, we introduce a hierarchical decomposition of the conditional probabilities that yields a speed-up of about 200 both during training and recognition. The hierarchical decomposition is a binary hierarchical clustering constrained by the prior knowledge extracted from the WordNet semantic hierarchy. Cooperative coevolution decomposes a problem into subcomponents and employs evolutionary algorithms for solving them. Cooperative coevolution has been effective for evolving neural networks. Different problem decomposition methods in cooperative coevolution determine how a neural network is decomposed and encoded which affects its performance. A good problem decomposition method should provide enough diversity and also group interacting variables which are the synapses in the neural network. Neural networks have shown promising results in chaotic time series prediction. This work employs two problem decomposition methods for training Elman recurrent neural networks on chaotic time series problems. The Mackey-Glass, Lorenz and Sunspot time series are used to demonstrate the performance of the cooperative neuro-evolutionary methods. The results show improvement in performance in terms of accuracy when compared to some of the methods from literature.