The problem of Learning from Demonstration is targeted at learning to perform tasks based on observed examples. One approach to Learning from Demonstration is Inverse Reinforcement Learning, in which actions are observed to infer rewards. This work combines a feature based state evaluation approach to Inverse Reinforcement Learning with neuroevolution, a paradigm for modifying neural networks based on their performance on a given task. Neural networks are used to learn from a demonstrated expert policy and are evolved to generate a policy similar to the demonstration. The algorithm is discussed and evaluated against competitive feature-based Inverse Reinforcement Learning approaches. At the cost of execution time, neural networks allow for non-linear combinations of features in state evaluations. These valuations may correspond to state value or state reward. This results in better correspondence to observed examples as opposed to using linear combinations. This work also extends existing work on Bayesian Non-Parametric Feature Construction for Inverse Reinforcement Learning by using non-linear combinations of intermediate data to improve performance. The algorithm is observed to be specifically suitable for a linearly solvable non-deterministic Markov Decision Processes in which multiple rewards are sparsely scattered in state space. A conclusive performance hierarchy between evaluated algorithms is presented.
Since the function to be generated is unknown, so is its complexity. This implies uncertainty about the optimal number of layers and nodes in each layer to be used. Nodes in later layers of a neural network may be able to define a function for which it may take several nodes in the earlier layers of the neural network to define. There is therefore a trade-off between the number of hidden layers and the number of nodes in each layer. Because of this, using a fixed structure for the neural network in this scenario may be sub-optimal. Neuroevolution solves this problem by generating the optimal neural network using techniques such as Genetic Programming (GP) @cite_9 , Evolutionary Programming (EP) @cite_25 , Simulated Annealing (SA) @cite_36 , Genetic Algorithms (GA) @cite_28 @cite_23 , Evolution Strategies (ES) @cite_19 @cite_17 , Evolutionary Algorithms (EA) @cite_42 and Memetic Algorithms (MA) @cite_37 .
@cite_37 @cite_36 @cite_28 @cite_9 @cite_42 @cite_19 @cite_23 @cite_25 @cite_17
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In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to @math in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation functions satisfy the distilled properties, including rectified linear units (ReLUs), leaky ReLUs, squared ReLUs and sigmoids. For activation functions that are also smooth, we show @math guarantees of gradient descent under a resampling rule. For homogeneous activations, we show tensor methods are able to initialize the parameters to fall into the local strong convexity region. As a result, tensor initialization followed by gradient descent is guaranteed to recover the ground truth with sample complexity @math and computational complexity @math for smooth homogeneous activations with high probability, where @math is the dimension of the input, @math ( @math ) is the number of hidden nodes, @math is a conditioning property of the ground-truth parameter matrix between the input layer and the hidden layer, @math is the targeted precision and @math is the number of samples. To the best of our knowledge, this is the first work that provides recovery guarantees for 1NNs with both sample complexity and computational complexity @math in the input dimension and @math in the precision. We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. Under these conditions, it is also possible to construct networks that provide a geometric order of approximation for analytic target functions. The permissible activation functions include the squashing function (1-e-x)-1 as well as a variety of radial basis functions. Our proofs are constructive. The weights and thresholds of our networks are chosen independently of the target function; we give explicit formulas for the coefficients as simple, continuous, linear functionals of the target function. Neuromorphic algorithms, which are comprised of highly complex, large-scale networks of artificial neurons, are increasingly used for a variety of recognition, classification, search and vision tasks. However, their computational and energy requirements can be quite high, and hence their energy-efficient implementation is of great interest. We propose a new approach to design energy-efficient hardware implementations of large-scale neural networks (NNs) using approximate computing. Our work is motivated by the observations that (i) NNs are used in applications where less-than-perfect results are acceptable, and often inevitable, and (ii) they are highly resilient to inexactness in many (but not all) of their constituent computations. We make two key contributions. First, we propose a method to transform any given NN into an Approximate Neural Network (AxNN). This is performed by (i) adapting the backpropagation technique, which is commonly used to train these networks, to quantify the impact of approximating each neuron to the overall network quality (e.g., classification accuracy), and (ii) selectively approximating those neurons that impact network quality the least. Further, we make the key observation that training is a naturally error-healing process that can be used to mitigate the impact of approximations to neurons. Therefore, we incrementally retrain the network with the approximations in-place, reclaiming a significant portion of the quality ceded by approximations. As a second contribution, we propose a programmable and quality-configurable neuromorphic processing engine (qcNPE), which utilizes arrays of specialized processing elements that execute neuron computations with dynamically configurable accuracies and can be used to execute AxNNs from diverse applications. We evaluated the proposed approach by constructing AXNNs for 6 recognition applications (ranging in complexity from 12–47,818 neurons and 160–3,155,968 connections) and executing them on two different platforms - qcNPE implementation containing 272 processing elements in 45nm technology and a commodity Intel Xeon server. Our results demonstrate 1.14X–1.92X energy benefits for virtually no loss (< 0.5 ) in output quality, and even higher improvements (upto 2.3X) when some loss (upto 7.5 ) in output quality is acceptable. We consider learning two layer neural networks using stochastic gradient descent. The mean-field description of this learning dynamics approximates the evolution of the network weights by an evolution in the space of probability distributions in @math (where @math is the number of parameters associated to each neuron). This evolution can be defined through a partial differential equation or, equivalently, as the gradient flow in the Wasserstein space of probability distributions. Earlier work shows that (under some regularity assumptions), the mean field description is accurate as soon as the number of hidden units is much larger than the dimension @math . In this paper we establish stronger and more general approximation guarantees. First of all, we show that the number of hidden units only needs to be larger than a quantity dependent on the regularity properties of the data, and independent of the dimensions. Next, we generalize this analysis to the case of unbounded activation functions, which was not covered by earlier bounds. We extend our results to noisy stochastic gradient descent. Finally, we show that kernel ridge regression can be recovered as a special limit of the mean field analysis.