In the real world, the environment is constantly changing with the input variables under the effect of noise. However, few algorithms were shown to be able to work under those circumstances. Here, Novelty-Organizing Team of Classifiers (NOTC) is applied to the continuous action mountain car as well as two variations of it: a noisy mountain car and an unstable weather mountain car. These problems take respectively noise and change of problem dynamics into account. Moreover, NOTC is compared with NeuroEvolution of Augmenting Topologies (NEAT) in these problems, revealing a trade-off between the approaches. While NOTC achieves the best performance in all of the problems, NEAT needs less trials to converge. It is demonstrated that NOTC achieves better performance because of its division of the input space (creating easier problems). Unfortunately, this division of input space also requires a bit of time to bootstrap.
In the following, there is a brief review of the LCS's and Neuroevolution's literature's related with this article. Here, we will restrain the review to only continuous action LCS algorithms and some of most salient Neuroevolution methods. For a complete review of both LCS's and Neuroevolution's literature please refer to @cite_6 @cite_37 and @cite_12 , respectively.
@cite_37 @cite_12 @cite_6
2100543212 2002196558 2170821486 2010260400
While evidence indicates that neural systems may be employing sparse approximations to represent sensed stimuli, the mechanisms underlying this ability are not understood. We describe a locally competitive algorithm (LCA) that solves a collection of sparse coding principles minimizing a weighted combination of mean-squared error and a coefficient cost function. LCAs are designed to be implemented in a dynamical system composed of many neuron-like elements operating in parallel. These algorithms use thresholding functions to induce local (usually one-way) inhibitory competitions between nodes to produce sparse representations. LCAs produce coefficients with sparsity levels comparable to the most popular centralized sparse coding algorithms while being readily suited for neural implementation. Additionally, LCA coefficients for video sequences demonstrate inertial properties that are both qualitatively and quantitatively more regular (i.e., smoother and more predictable) than the coefficients produced by greedy algorithms. Neuroevolution, the artificial evolution of neural networks, has shown great promise on continuous reinforcement learning tasks that require memory. However, it is not yet directly applicable to realistic embedded agents using high-dimensional (e.g. raw video images) inputs, requiring very large networks. In this paper, neuroevolution is combined with an unsupervised sensory pre-processor or compressor that is trained on images generated from the environment by the population of evolving recurrent neural network controllers. The compressor not only reduces the input cardinality of the controllers, but also biases the search toward novel controllers by rewarding those controllers that discover images that it reconstructs poorly. The method is successfully demonstrated on a vision-based version of the well-known mountain car benchmark, where controllers receive only single high-dimensional visual images of the environment, from a third-person perspective, instead of the standard two-dimensional state vector which includes information about velocity. This study assesses the relative performance characteristics of five established classification techniques on data collected using the P300 Speller paradigm, originally described by Farwell and Donchin (1988 Electroenceph. Clin. Neurophysiol. 70 510). Four linear methods: Pearson's correlation method (PCM), Fisher's linear discriminant (FLD), stepwise linear discriminant analysis (SWLDA) and a linear support vector machine (LSVM); and one nonlinear method: Gaussian kernel support vector machine (GSVM), are compared for classifying offline data from eight users. The relative performance of the classifiers is evaluated, along with the practical concerns regarding the implementation of the respective methods. The results indicate that while all methods attained acceptable performance levels, SWLDA and FLD provide the best overall performance and implementation characteristics for practical classification of P300 Speller data. The problems of finding shortest common supersequences (SCS) and longest common subsequences (LCS) are two well-known NP -hard problems that have applications in many areas including computational molecular biology, data compression, robot motion planning and scheduling, text editing, etc. A lot of fruitless effort has been spent in searching for good approximation algorithms for these problems. In this paper, we show that these problems are inherently hard to approximate in the worst case. In particular, we prove that (i) SCS does not have a polynomial time linear approximation algorithm, unless P = NP ; (ii) There exists a constant @math such that, if SCS has a polynomial time approximation algorithm with ratio @math , where @math is the number of input sequences, then NP is contained in DTIME @math ; (iii) There exists a constant @math such that, if LCS has a polynomial time approximation algorithm with performance ratio @math , then P = NP . The proofs utilize the recent results of [Proc. 23rd IEEE Symposium on Foundations of Computer Science, 1992, pp. 14-23] on the complexity of approximation problems. In the second part of the paper, we introduce a new method for analyzing the average-case performance of algorithms for sequences, based on Kolmogorov complexity. Despite the above nonapproximability results, we show that near optimal solutions for both SCS and LCS can be found on the average. More precisely, consider a fixed alphabet @math and suppose that the input sequences are generated randomly according to the uniform probability distribution and are of the same length @math . Moreover, assume that the number of input sequences is polynomial in @math . Then, there are simple greedy algorithms which approximate SCS and LCS with expected additive errors @math and @math for any @math , respectively. Incidentally, our analyses also provide tight upper and lower bounds on the expected LCS and SCS lengths for a set of random sequences, solving a generalization of another well-known open question on the expected LCS length for two random sequences [K. Alexander, The rate of convergence of the mean length of the longest common subsequence, 1992, manuscript],[V. Chvatal and D. Sankoff, J. Appl. Probab., 12 (1975), pp. 306-315], [D. Sankoff and J. Kruskall, eds., Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison-Wesley, Reading, MA, 1983].