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nonlinear function approximation: Computing smooth solutions with an adaptive greedy algorithm

JOURNAL OF approximation THEORY 2006年第2期143卷 159-175页

作者： Hofinger, Andreas Austrian Acad Sci Johann Radon Inst Computat & Appl Math Linz Austria

In contrast to linear schemes, nonlinear approximation techniques allow for dimension independent rates of convergence. Unfortunately, typical algorithms (such as, e.g., backpropagation) are not only computationally demanding, but also unstable in the presence of data noise. While we can show stability for a weak relaxed greedy algorithm, the resulting method has the drawback that it requires in practise unavailable smoothness information about the data. In this work we propose an adaptive greedy algorithm which does not need this information but rather recovers it iteratively from the available data. We show that the generated approximations are always at least as smooth as the original function and that the algorithm also remains stable, when it is applied to noisy data. Finally, the applicability of this algorithm is demonstrated by numerical experiments. (c) 2006 ***. All rights reserved.

关键词： greedy algorithm nonlinear function approximation data noise regularization theory

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A spiking neural network architecture for nonlinear function approximation

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NEURAL NETWORKS 2001年第6-7期14卷 933-939页

作者： Iannella, N Back, AD RIKEN Brain Sci Inst Wako Saitama 3510198 Japan

Multilayer perceptrons have received much attention in recent years due to their universal approximation capabilities. Normally, such models use real valued continuous signals, although they are loosely based on biological neuronal networks that encode signals using spike trains. Spiking neural networks are of interest both from a biological point of view and in terms of a method of robust signaling in particularly noisy or difficult environments. It is important to consider networks based on spike trains. A basic question that needs to be considered however, is what type of architecture can be used to provide universal function approximation capabilities in spiking networks? In this paper, we propose a spiking neural network architecture using both integrate-and-fire units as well as delays, that is capable of approximating a real valued function mapping to within a specified degree of accuracy. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： spiking neurons integrate-and-fire units delays neural architecture nonlinear function approximation

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Optimization and stabilization of sequential learning in RBF network for nonlinear function approximation

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IEICE ELECTRONICS EXPRESS 2008年第23期5卷 1030-1035页

作者： Lim, W. S. Yeoh, J. W. L. Multimedia Univ Fac Engn & Technol Jalan Ayer Keroh Lama 75450 Melaka Malaysia

This paper proposes a solution for inconsistency pruning of neurons within a sequential learning Radial Basis function (RBF) Network. This paper adopts the concept that a specific RBF neuron which continuously exhibits low output in a sequence of training patterns does not justify the proposition that the neuron is insignificant to the whole function to be approximated. We establish additional criterions to provide protection from error in pruning RBF neurons within the hidden layer, which we prove is able to improve consistency and stability of neuron evolution. With such stability within the sequential learning process, we also show how the convergence speed of the network can be improved by reducing the number of consecutive observations required to prune a neuron in the hidden layer.

关键词： feedforward neural networks Radial Basis Network (RBF) sequential learning nonlinear function approximation minimal resource allocation network

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VOQL: Towards Optimal Regret in Model-free RL with nonlinear function approximation 36

VOQL: Towards Optimal Regret in Model-free RL with Nonlinear...

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36th Annual Conference on Learning Theory (COLT)

作者： Agarwal, Alekh Jin, Yujia Zhang, Tong Google Res Mountain View CA 94043 USA Stanford Univ Stanford CA 94305 USA

We study time-inhomogeneous episodic reinforcement learning (RL) under general function approximation and sparse rewards. We design a new algorithm, Variance-weighted Optimistic Q-Learning (VOQL), based on Q-learning and bound its regret assuming closure under Bellman backups, and bounded Eluder dimension for the regression function class. As a special case, VOQL achieves (O) over tilde (d root TH + d(6)H(5)) regret over T episodes for a horizon H MDP under (d-dimensional) linear function approximation, which is asymptotically optimal. Our algorithm incorporates weighted regression-based upper and lower bounds on the optimal value function to obtain this improved regret. The algorithm is computationally efficient given a regression oracle over the function class, making this the first computationally tractable and statistically optimal approach for linear MDPs.

关键词： Reinforcement learning nonlinear function approximation model-free algorithms eluder dimension

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Forward Actor-Critic for nonlinear function approximation in Reinforcement Learning 16

Forward Actor-Critic for Nonlinear Function Approximation in...

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16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS)

作者： Veeriah, Vivek van Seijen, Harm Sutton, Richard S. Univ Alberta Dept Comp Sci Edmonton AB Canada Univ Alberta Edmonton AB Canada

ISBN: (纸本)9781510855076

Multi-step methods are important in reinforcement learning (RL). Eligibility traces, the usual way of handling them, works well with linear function approximators. Recently, van Seijen (2016) had introduced a delayed learning approach, without eligibility traces, for handling the multi-step lambda-return with nonlinear function approximators. However, this was limited to action-value methods. In this paper, we extend this approach to handle n-step returns, generalize this approach to policy gradient methods and empirically study the effect of such delayed updates in control tasks. Specifically, we introduce two novel forward actor-critic methods and empirically investigate our proposed methods with the conventional actor-critic method on mountain car and pole-balancing tasks. From our experiments, we observe that forward actor-critic dramatically outperforms the conventional actor-critic in these standard control tasks. Notably, this forward actor-critic method has produced a new class of multi-step RL algorithms without eligibility traces.

关键词： Reinforcement Learning Actor-Critic Policy Gradient nonlinear function approximation Incremental Learning

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Optimized algorithm for industrial process instrumentation calibration based on nonlinear function approximation

Optimized algorithm for industrial process instrumentation c...

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International Symposium on Logistics and Industrial Informatics

作者： Ukil, Abhisek Andenna, Andrea ABB Switzerland Ltd Integrated Sensor Syst RD S4 CH-5405 Baden Daettwil Switzerland

ISBN: (纸本)9781424414406

Calibration is an all important operation in the instrumentation industry for determining the relationship between the output(s) (or response) of a measuring instrument and the value of the input(s). Common industrial practice is to use a finite number of calibration points covering the entire calibration range. The common calibration method is to select the equidistant (over the calibration range) operating (calibration) points and performing linear interpolation operation between them. Although this ensures uniformity, but it does not guarantee effective and optimal composite modeling of the linearity and the non-linearity involved. In this paper, we propose a nonlinear function approximation-based optimized calibration technique which takes into account the composite effect of the underlying linear and nonlinear behavior of the process. Application examples are cited to substantiate the improved accuracy of the proposed algorithm over the common calibration practice.

关键词： calibration linear nonlinear modeling nonlinear function approximation optimization process instrumentation

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Forward Actor-Critic for nonlinear function approximation in Reinforcement Learning 17

Forward Actor-Critic for Nonlinear Function Approximation in...

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International Conference on Autonomous Agents and Multiagent Systems

作者： Vivek Veeriah Harm van Seijen Richard S. Sutton Dept. of Computing Science University of Alberta

ISBN: (纸本)9781510855076

Multi-step methods are important in reinforcement learning (RL). Eligibility traces, the usual way of handling them, works well with linear function approximators. Recently, van Seijen (2016) had introduced a delayed learning approach, without eligibility traces, for handling the multi-step λ-return with nonlinear function approximators. However, this was limited to action-value methods In this paper, we extend this approach to handle n-step returns, generalize this approach to policy gradient methods and empirically study the effect of such delayed updates in control tasks. Specifically, we introduce two novel forward actorcritic methods and empirically investigate our proposed methods with the conventional actor-critic method on mountain car and pole-balancing tasks. From our experiments, we observe that forward actor-critic dramatically outperforms the conventional actor-critic in these standard control tasks. Notably, this forward actor-critic method has produced a new class of multi-step RL algorithms without eligibility traces.

关键词： Reinforcement Learning Actor-Critic Policy Gradient nonlinear function approximation Incremental Learning learning (artificial intelligence) Learning eligibility nonlinear functions control task New classes function approximation

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Adaptive temporal-difference learning via deep neural network function approximation: a non-asymptotic analysis

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COMPLEX & INTELLIGENT SYSTEMS 2025年第2期11卷 1-19页

作者： Wang, Guoyong Fu, Tiange Zheng, Ruijuan Zhao, Xuhui Zhu, Junlong Zhang, Mingchuan Luoyang Inst Sci & Technol Sch Informat Engn Luoyang 471023 Peoples R China Longmen Lab Luoyang 471023 Peoples R China Henan Univ Sci & Technol Sch Informat Engn Luoyang 471023 Peoples R China

Although deep reinforcement learning has achieved notable practical achievements, its theoretical foundations have been scarcely explored until recent times. Nonetheless, the rate of convergence for current neural temporal-difference (TD) learning algorithms is constrained, largely due to their high sensitivity to stepsize choices. In order to mitigate this issue, we propose an adaptive neural TD algorithm (AdaBNTD) inspired by the superior performance of adaptive gradient techniques in training deep neural networks. Simultaneously, we derive non-asymptotic bounds for AdaBNTD within the Markovian observation framework. In particular, AdaBNTD is capable of converging to the global optimum of the mean square projection Bellman error (MSPBE) with a convergence rate of O(1/K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {O}}}(1/\sqrt{K})$$\end{document}, where K denotes the iteration count. Besides, the effectiveness AdaBNTD is also verified through several reinforcement learning benchmark domains.

关键词： Adaptive methods Non-asymptotic convergence nonlinear function approximation Reinforcement learning Temporal-difference learning

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On the hinge-finding algorithm for hinging hyperplanes

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IEEE TRANSACTIONS ON INFORMATION THEORY 1998年第3期44卷 1310-1319页

作者： Pucar, P Sjoberg, J Saab AB Saab Aerosp Gripen S-58188 Linkoping Sweden Chalmers Univ Technol Dept Signals & Syst S-41296 Gothenburg Sweden

This correspondence concerns the estimation algorithm for hinging hyperplane (HH) models, a piecewise-linear model for approximating functions of several variables, suggested in Breiman [1], The estimation algorithm is analyzed and it is shown that it is a special case of a Newton algorithm applied to a sum of squared error criterion. This insight is then used to suggest possible improvements of the algorithm so that convergence to a local minimum can be guaranteed. In addition, the way of updating the parameters in the HH model is discussed. In Breiman [1], a stepwise updating procedure is proposed where only a subset of the parameters are changed in each step. This connects closely to some recently suggested greedy algorithms and these greedy algorithms are discussed and compared to a simultaneous updating of all parameters.

关键词： hinging hyperplanes nonlinear function approximation numerical minimization

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Incorporating statistical and neural network approaches for student course satisfaction analysis and prediction

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EXPERT SYSTEMS WITH APPLICATIONS 2010年第4期37卷 3358-3365页

作者： Guo, William W. Cent Queensland Univ Fac Arts Business Informat & Educ Rockhampton Qld 4702 Australia

Students' perception on course satisfaction through student surveys has become more influential in institutional operations because their experience in study may affect not only the prospective student's decision in choosing the institution for their tertiary education, but also the retention of existing students. Student course satisfaction is a multivariate nonlinear problem. Neural network (NN) techniques have been successfully applied to approximating nonlinear functions in many disciplines, but there has been little information available in applying NN to the modelling of student course satisfaction. In this paper, based on the student survey results collected from 43 courses in 11 semesters from 2002 to 2007, statistical analysis and NN techniques are incorporated for establishing some dynamic models for analysing and predicting student course satisfaction. The factors identified from this process also allow new strategies to be drawn for improving course satisfaction in the future. This study shows that both the number of students (NS) enrolled to a course and the high distinction (HD) rate in final grading are the two most influential factors to student course satisfaction. The three-layer multilayer perceptron (MLP) models outperform the linear regressions in predicting student course satisfaction, with the best outcome being achieved by combining both NS and HD as the input to the networks. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Neural networks Multilayer perceptron Linear regression Student course satisfaction nonlinear function approximation

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