Neuroevolution has yet to scale up to complex reinforcement learning tasks that require large networks. Networks with many inputs (e.g. raw video) imply a very high dimensional search space if encoded directly. Indirect methods use a more compact genotype representation that is transformed into networks of potentially arbitrary size. In this paper, we present an indirect method where networks are encoded by a set of Fourier coefficients which are transformed into network weight matrices via an inverse Fourier-type transform. Because there often exist network solutions whose weight matrices contain regularity (i.e. adjacent weights are correlated), the number of coefficients required to represent these networks in the frequency domain is much smaller than the number of weights (in the same way that natural images can be compressed by ignore high-frequency components). This "compressed" encoding is compared to the direct approach where search is conducted in the weight space on the high-dimensional octopus arm task. The results show that representing networks in the frequency domain can reduce the search-space dimensionality by as much as two orders of magnitude, both accelerating convergence and yielding more general solutions.
@cite_6 @cite_8 used a simple set of program instructions to describe perceptron weight matrix showing that short programs can represent scalable solutions to problems that require a regular weight vector.
@cite_6 @cite_8
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Approximation of the permanent of a matrix with nonnegative entries is a well studied problem. The most successful approach to date for general matrices uses Markov chains to approximately sample from a distribution on weighted permutations, and Jerrum, Sinclair, and Vigoda developed such a method they proved runs in polynomial time in the input. The current bound on the running time of their method is O(n7(log n)4). Here we present a very different approach using sequential acceptance rejection, and show that for a class of dense problems this method has an O(n4 log n) expected running time. We introduce new Perceptron-based algorithms for the online multitask binary classification problem. Under suitable regularity conditions, our algorithms are shown to improve on their baselines by a factor proportional to the number of tasks. We achieve these improvements using various types of regularization that bias our algorithms towards specific notions of task relatedness. More specifically, similarity among tasks is either measured in terms of the geometric closeness of the task reference vectors or as a function of the dimension of their spanned subspace. In addition to adapting to the online setting a mix of known techniques, such as the multitask kernels of , our analysis also introduces a matrix-based multitask extension of the p-norm Perceptron, which is used to implement spectral co-regularization. Experiments on real-world data sets complement and support our theoretical findings.