# Reinforcement Learning, Neural Networks and PI Control Applied to a Heating Coil

Save this PDF as:

Size: px
Start display at page:

Download "Reinforcement Learning, Neural Networks and PI Control Applied to a Heating Coil"

## Transcription

2 Heating Coil with Dual Controller T ai Temp Air In f a Mass Flow Air T ao Temp Air Out Duct Temp H20 In T wi c P Controller Temp H20 Out f w Mass Flow Rate H20 T wo Neural Network Temp Set Point Other Variables Figure 1: The simulated heating coil. Also shown is the control system composed of a feedback controller and a neural network whose outputs are summed to form the control signal. disturbances and changing conditions that would occur in actual heating and air conditioning systems. The bounds on the random walks were 4 T ai 10 o C, 73 T wi 81 o C, and 0:7 f a 0:9 kg/s. A PI controller was tuned to control the simulated heating coil. The best proportional and integral gains were determined by measuring the sum of the absolute value of the difference between the set point and actual exiting air temperature under a variety of disturbances. 3 Training with a Simple Inverse Model The most immediate problem that arises when designing a procedure for training a neural-network controller is that a desired output for the network is usually not available. One way to obtain such an error is to transform the error in the controlled state variable, which is usually a difference from a set point, into a control-signal error, and use this error to train the network. An inverse model of the controlled system is needed for this transformation. In addition to an inverse model, one must consider which error in time is to be minimized. Ideally, a sum of the error over time is minimized. This is addressed in Section 5. Here the error n steps ahead is minimized. A neural network was trained to reduce the error in the output air temperature n steps ahead. For the simulated heating coil, a step is five seconds. This is the assumed sampling interval for a digital controller that implements any of the control schemes tried here. The network was used as an independent controller, with the output of the network being the control signal. To train an n-step ahead network, a simple inverse model was assumed: the error of the network s output at time step t was defined to be proportional to the difference between the output air temperature and the set point at time t + n. Inputs to the network were T ai, T ao, T wi, T wo, f a, f w, and the set point at time t. The network had these seven inputs, 30 hidden units, and one output unit. Training data was generated by randomly changing the set point and system disturbances every 30 time steps. Neural networks were trained to minimize the error from two to eight steps ahead. All were found to reduce the error in comparison to the PI controller by itself. For n =1, 2, and 3, the RMS error between T ao and its set point was about 0.6 over a 300-step test sequence. For n =5and 6, the error increased to approximately 0.7 and 0.65, respectively. Figure 2 shows a 60-step portion of the test sequence. Smaller values of n result in more overshoot of the set point. The performance of the PI controller as shown is significantly damped. Recall that the PI proportional and integral gains were chosen to minimize the RMS error over a wide variety of disturbances.

4 0.12 Average Squared Error Hidden Units 3 Hidden Units 6 Hidden Units Hidden Unit 2 Hidden Units Epochs Figure 3: Average squared error versus epochs for various numbers of hidden units. component is missing. When combined with a proportional controller, whose gain is optimized for this case, performance was significantly better than the original PI controller s performance. Figure 4 shows the behavior of the exiting air temperature when controlled with PI controller, the neural network alone, and with the combined neural network and proportional controller. This successful simulation result in not surprising, since well-behaved physical models are modeled well by statistical methods. However, our approach is more general than an analytical solution. It can be used for systems for which a model is not well known and for situations where systems constants need to be determined by regression. 5 Optimal Control with Q-Learning Reinforcement learning methods embody a general Monte Carlo approach to dynamic programming for solving optimal control problems. Q-learning procedures converge on value functions for state-action pairs that estimate the expected sum of future reinforcements, which reflect behavior goals that might involve costs, errors, or profits. To define the Q-learning algorithm, we start by representing a system to be controlled as consisting of a discrete state space, S, and a finite set of actions, A, that can be taken in all states. A policy is defined by the probability, (s t ;a), that action a will be taken in state s t. Let the reinforcement resulting from applying action a t while the system is in state s t be R(s t ;a t ). Q (s t ;a t ) is the value function given state s t and action a t, assuming policy governs action selection from then on. The optimal value of Q (s t ;a t )is Q (s t ;a t )=E ( TX k=0 k R(s t+k ;a t+k ) where is a discount factor between 0 and 1 that weights reinforcement received sooner more heavily than reinforcement received later. This expression can be rewritten as an immediate reinforcement plus a sum of future reinforcement: Q (s t ;a t ) = E (R(s t ;a t )+ = E (R(s t ;a t )+ TX k=1 T,1 X k=0 ) k R(s t+k ;a t+k ) ; ) k R(s t+k+1 ;a t+k+1 ) In dynamic programming, policy evaluation is conducted by iteratively updating the value function until it converges on the desired sum. By substituting the estimated value function for the sum in the above equation, the iterative policy evaluation method from dynamic programming results in the following update to the current estimate of the value function: Q (s t ;a t ) = E fr(s t ;a t )+Q (s t+1 ;a t+1 )g,q (s t ;a t ); ; ) :

5 50 T 45 ao a. PI Controller T ao T 45 ao 40 b. Neural Network Controller 35 c. Combined Neural Network and PI Controller Figure 4: Set Point and actual temperature versus time as the system is controlled with a) the PI controller, b) the neural network, steady-state predictor, and c) the combined neural network predictor and proportional controller.

6 50 T ai 40 c (control 1000 signal) Figure 5: Performance of PI controller. The top graph shows the set point and the actual output air temperature over time. The bottom graph shows the PI output control signal. where the expectation is taken over possible next states, s t+1, given that the current state is s t and action a t was taken. This expectation requires a model of state transition probabilities. If such a model does not exist, a Monte Carlo approach can be used in which the expectation is replaced by a single sample and the value function is updated by a fraction of the difference. Q (s t ;a t ) = [R(s t ;a t )+Q (s t+1 ;a t+1 ), Q (s t ;a t )] ; where 0 1. The term within brackets is often referred to as a temporal-difference error, defined by Sutton [8]. To improve the action-selection policy and achieve optimal control, the dynamic programming method called value iteration can be applied. This method combines steps of policy evaluation with policy improvement. Assuming we want to maximize total reinforcement, as would be the case if reinforcements are positive, such as profits or proximity to a destination, the Monte Carlo version of value iteration for the Q function is Q (s t ;a t )= R(s t ;a t )+max Q (s t+1 ;a 0 ),Q (s t ;a t ) a 0 2A This is what has become known as the Q-learning algorithm. Watkins [10] proves that it does converge to the optimal value function, meaning that selecting the action, a, that maximizes Q(s t ;a)for any state s t will result in the optimal sum of reinforcement over time. 5.1 Experiment Reinforcement at time step t is determined by the squared error plus a term proportionalto the magnitude of the action change from one time step to the next. Formally, this reinforcement is calculated by R(t) =(T ao (t), T ao (t)) 2 ; where T ao is the set point. Input to the reinforcement-learning agent consist of the variables T ai, T ao, T wi, T wo, f a, f w,andtheset point, all at time t. The output of the network is directly added to the integrated output of the PI controller. The allowed output actions are,100,,50,,20,,10, 0, 10, 20, 50, and 100. The selected action is added to the PI control signal. The Q function is implemented by the network in a quantized, or table look-up, method. Each of the seven input variables are divided into six intervals, which quantize the 7-dimensional input space into 6 7 hypercubes. In each hypercube is stored the Q values for the nine possible actions. The parameter was decreased during training from 0.1 to The reinforcement-learning agent is trained repeatedly on 500 time steps of feedback interactions between the PI controller and the simulated heating coil. Figure 5 shows the set point and actual temperatures and the control signal over these 500 steps. The RMS error between the set point and actual output air temperature over these 500 steps is :

7 RMS Error Between Setpoint and Tao PI Controller RMS Error Epochs Figure 6: Reduction in error with multiple training epochs. The amount of exploration is reduced during training. 5.2 Result The reduction in RMS error while training the reinforcement-learning agent is shown in Figure 6. After approximately 500 epochs of training, the average error between the set point and actual temperature was reduced to below the level achieved by the PI controller alone. It appears that further error reduction will not occur. This remaining error is probably due to the random walk taken by the disturbances and, if so, cannot be reduced. The resulting behavior of the controlled air temperature is shown in Figure 7. The middle graph shows the output of the reinforcement-learningagent. It has learned to be silent (an output of 0) for most time steps. It produces large outputs at set point changes, and at several other time steps. The combined reinforcementlearning agent output and PI output is shown in the bottom graph. 6 Conclusions Three independent strategies for combining neural network learning algorithms with PI controllers were successfully shown to result in more accurate tracking of the temperature set point of a simulated heating coil. Variations of each strategy are being studied further and ways of combining them are being developed. For example, the reinforcement learner can be added to any existing control system, including the combined steady-state predictor and PI controller. Additional investigations continue on the state representation [1, 2], the set of possible reinforcementlearning agent actions, different neural network architectures, and on strategies for slowly decreasing the amount of exploration performed by the reinforcement-learning agent during learning. Plans include the evaluation of this technique on a physical heating coil being controlled with a PC and control hardware. Acknowledgements This work was supported by the National Science Foundation through grant CMS References [1] Charles W. Anderson. Q-learning with hidden-unit restarting. In Stephen Jose Hanson, Jack D. Cowan, and C. Lee Giles, editors, Advances in Neural Information Processing Systems 5, pages Morgan Kaufmann Publishers, San Mateo, CA, [2] Charles W. Anderson and S. G. Crawford-Hines. Multigrid Q-learning. Technical Report CS , Colorado State University, Fort Collins, CO, [3] Peter S. Curtiss. Experimental results from a network-assisted PID controller. ASHRAE Transactions, 102(1), 1996.

8 50 T 40 ao Output of Reinforcement Learning Agent c (PI Control output plus 1000 output of RLA) 500 Figure 7: Performance of combined reinforcement-learning agent and PI controller. Top graph shows the set point and the actual output air temperature over time. The second graph shows the output of the reinforcement-learning agent. The third graph shows the combined PI output and reinforcement-learning agent output. [4] Peter S. Curtiss, Gideon Shavit, and Jan F. Krieder. Neural networks applied to buildings a tutorial and case studies in prediction and adaptive control. ASHRAE Transactions, 102(1), [5] S. J. Hepworth and A. L. Dexter. Neural control of a non-linear HVAC plant. Proceedings 3rd IEEE Conference on Control Applications, [6] S. J. Hepworth, A. L. Dexter, and S. T. P. Willis. Control of a non-linear heater battery using a neural network. Technical report, University of Oxford, [7] Minoru Kawashima, Charles E. Dorgan, and John W. Mitchell. Optimizing system control with load prediction by neural networks for an ice-storage system. ASHRAE Transactions, 102(1), [8] R. S. Sutton. Learning to predict by the method of temporal differences. Machine Learning, 3:9 44, [9] David M. Underwood and Roy R. Crawford. Dynamic nonlinear modeling of a hot-water-to-air heat exchanger for control applications. ASHRAE Transactions, 97(1): , [10] C. Watkins. Learning with Delayed Rewards. PhD thesis, Cambridge University Psychology Department, 1989.

### T ai Temp Air In Duct Temp Set Point f a Mass Flow Air T wo Temp H 2O Out PI Controller T ao Temp Air Out T wi Temp H 2O In f w Mass Flow Rate H 2O Fi

Neural Networks and PI Control using Steady State Prediction Applied to a Heating Coil CHRIS C. DELNERO, Department of Mechanical Engineering, Colorado State University DOUGLAS C. HITTLE, Department of

### CS599 Lecture 1 Introduction To RL

CS599 Lecture 1 Introduction To RL Reinforcement Learning Introduction Learning from rewards Policies Value Functions Rewards Models of the Environment Exploitation vs. Exploration Dynamic Programming

### Q-Learning in Continuous State Action Spaces

Q-Learning in Continuous State Action Spaces Alex Irpan alexirpan@berkeley.edu December 5, 2015 Contents 1 Introduction 1 2 Background 1 3 Q-Learning 2 4 Q-Learning In Continuous Spaces 4 5 Experimental

### In Advances in Neural Information Processing Systems 6. J. D. Cowan, G. Tesauro and. Convergence of Indirect Adaptive. Andrew G.

In Advances in Neural Information Processing Systems 6. J. D. Cowan, G. Tesauro and J. Alspector, (Eds.). Morgan Kaufmann Publishers, San Fancisco, CA. 1994. Convergence of Indirect Adaptive Asynchronous

### An application of the temporal difference algorithm to the truck backer-upper problem

ESANN 214 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Bruges (Belgium), 23-25 April 214, i6doc.com publ., ISBN 978-28741995-7. Available

### Reinforcement Learning: the basics

Reinforcement Learning: the basics Olivier Sigaud Université Pierre et Marie Curie, PARIS 6 http://people.isir.upmc.fr/sigaud August 6, 2012 1 / 46 Introduction Action selection/planning Learning by trial-and-error

### Q-learning. Tambet Matiisen

Q-learning Tambet Matiisen (based on chapter 11.3 of online book Artificial Intelligence, foundations of computational agents by David Poole and Alan Mackworth) Stochastic gradient descent Experience

### Approximate Optimal-Value Functions. Satinder P. Singh Richard C. Yee. University of Massachusetts.

An Upper Bound on the oss from Approximate Optimal-Value Functions Satinder P. Singh Richard C. Yee Department of Computer Science University of Massachusetts Amherst, MA 01003 singh@cs.umass.edu, yee@cs.umass.edu

### Temporal difference learning

Temporal difference learning AI & Agents for IET Lecturer: S Luz http://www.scss.tcd.ie/~luzs/t/cs7032/ February 4, 2014 Recall background & assumptions Environment is a finite MDP (i.e. A and S are finite).

### Chapter 7: Eligibility Traces. R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 1

Chapter 7: Eligibility Traces R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 1 Midterm Mean = 77.33 Median = 82 R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction

### 6 Reinforcement Learning

6 Reinforcement Learning As discussed above, a basic form of supervised learning is function approximation, relating input vectors to output vectors, or, more generally, finding density functions p(y,

### Chapter 6: Temporal Difference Learning

Chapter 6: emporal Difference Learning Objectives of this chapter: Introduce emporal Difference (D) learning Focus first on policy evaluation, or prediction, methods hen extend to control methods R. S.

In: Proc. BENELEARN-98, 8th Belgian-Dutch Conference on Machine Learning, pp 9-46, 998 Linear Quadratic Regulation using Reinforcement Learning Stephan ten Hagen? and Ben Krose Department of Mathematics,

### ( t) Identification and Control of a Nonlinear Bioreactor Plant Using Classical and Dynamical Neural Networks

Identification and Control of a Nonlinear Bioreactor Plant Using Classical and Dynamical Neural Networks Mehmet Önder Efe Electrical and Electronics Engineering Boðaziçi University, Bebek 80815, Istanbul,

### Lecture 1: March 7, 2018

Reinforcement Learning Spring Semester, 2017/8 Lecture 1: March 7, 2018 Lecturer: Yishay Mansour Scribe: ym DISCLAIMER: Based on Learning and Planning in Dynamical Systems by Shie Mannor c, all rights

### A STATE-SPACE NEURAL NETWORK FOR MODELING DYNAMICAL NONLINEAR SYSTEMS

A STATE-SPACE NEURAL NETWORK FOR MODELING DYNAMICAL NONLINEAR SYSTEMS Karima Amoura Patrice Wira and Said Djennoune Laboratoire CCSP Université Mouloud Mammeri Tizi Ouzou Algeria Laboratoire MIPS Université

### 1 Introduction 2. 4 Q-Learning The Q-value The Temporal Difference The whole Q-Learning process... 5

Table of contents 1 Introduction 2 2 Markov Decision Processes 2 3 Future Cumulative Reward 3 4 Q-Learning 4 4.1 The Q-value.............................................. 4 4.2 The Temporal Difference.......................................

### Weight Initialization Methods for Multilayer Feedforward. 1

Weight Initialization Methods for Multilayer Feedforward. 1 Mercedes Fernández-Redondo - Carlos Hernández-Espinosa. Universidad Jaume I, Campus de Riu Sec, Edificio TI, Departamento de Informática, 12080

### Using Gaussian Processes for Variance Reduction in Policy Gradient Algorithms *

Proceedings of the 8 th International Conference on Applied Informatics Eger, Hungary, January 27 30, 2010. Vol. 1. pp. 87 94. Using Gaussian Processes for Variance Reduction in Policy Gradient Algorithms

### DISSERTATION A SYNTHESIS OF REINFORCEMENT LEARNING AND ROBUST CONTROL THEORY. Submitted by R. Matthew Kretchmar Department of Computer Science

DISSERTATION A SYNTHESIS OF REINFORCEMENT LEARNING AND ROBUST CONTROL THEORY Submitted by R. Matthew Kretchmar Department of Computer Science In partial fulfillment of the requirements for the Degree of

### Reinforcement Learning

Reinforcement Learning Temporal Difference Learning Temporal difference learning, TD prediction, Q-learning, elibigility traces. (many slides from Marc Toussaint) Vien Ngo Marc Toussaint University of

POMDPs and Policy Gradients MLSS 2006, Canberra Douglas Aberdeen Canberra Node, RSISE Building Australian National University 15th February 2006 Outline 1 Introduction What is Reinforcement Learning? Types

### EEE 550 ADVANCED CONTROL SYSTEMS

UNIVERSITI SAINS MALAYSIA Semester I Examination Academic Session 2007/2008 October/November 2007 EEE 550 ADVANCED CONTROL SYSTEMS Time : 3 hours INSTRUCTION TO CANDIDATE: Please ensure that this examination

### CM 3310 Process Control, Spring Lecture 21

CM 331 Process Control, Spring 217 Instructor: Dr. om Co Lecture 21 (Back to Process Control opics ) General Control Configurations and Schemes. a) Basic Single-Input/Single-Output (SISO) Feedback Figure

### Elements of Reinforcement Learning

Elements of Reinforcement Learning Policy: way learning algorithm behaves (mapping from state to action) Reward function: Mapping of state action pair to reward or cost Value function: long term reward,

### Reinforcement Learning II

Reinforcement Learning II Andrea Bonarini Artificial Intelligence and Robotics Lab Department of Electronics and Information Politecnico di Milano E-mail: bonarini@elet.polimi.it URL:http://www.dei.polimi.it/people/bonarini

### IMC based automatic tuning method for PID controllers in a Smith predictor configuration

Computers and Chemical Engineering 28 (2004) 281 290 IMC based automatic tuning method for PID controllers in a Smith predictor configuration Ibrahim Kaya Department of Electrical and Electronics Engineering,

### Intelligent Modular Neural Network for Dynamic System Parameter Estimation

Intelligent Modular Neural Network for Dynamic System Parameter Estimation Andrzej Materka Technical University of Lodz, Institute of Electronics Stefanowskiego 18, 9-537 Lodz, Poland Abstract: A technique

### On the Worst-case Analysis of Temporal-difference Learning Algorithms

Machine Learning, 22(1/2/3:95-121, 1996. On the Worst-case Analysis of Temporal-difference Learning Algorithms schapire@research.att.com ATT Bell Laboratories, 600 Mountain Avenue, Room 2A-424, Murray

### Reinforcement Learning. Machine Learning, Fall 2010

Reinforcement Learning Machine Learning, Fall 2010 1 Administrativia This week: finish RL, most likely start graphical models LA2: due on Thursday LA3: comes out on Thursday TA Office hours: Today 1:30-2:30

### Neural Network Identification of Non Linear Systems Using State Space Techniques.

Neural Network Identification of Non Linear Systems Using State Space Techniques. Joan Codina, J. Carlos Aguado, Josep M. Fuertes. Automatic Control and Computer Engineering Department Universitat Politècnica

Adaptive Inverse Control based on Linear and Nonlinear Adaptive Filtering Bernard Widrow and Gregory L. Plett Department of Electrical Engineering, Stanford University, Stanford, CA 94305-9510 Abstract

### Robust Reinforcement Learning Control with Static and Dynamic Stability a

Computer Science Technical Report Robust Reinforcement Learning Control with Static and Dynamic Stability a R. Matthew retchmar, Peter M. Young, Charles W. Anderson, Douglas C. Hittle, Michael L. Anderson,

### Design Artificial Nonlinear Controller Based on Computed Torque like Controller with Tunable Gain

World Applied Sciences Journal 14 (9): 1306-1312, 2011 ISSN 1818-4952 IDOSI Publications, 2011 Design Artificial Nonlinear Controller Based on Computed Torque like Controller with Tunable Gain Samira Soltani

### Equivalence of Backpropagation and Contrastive Hebbian Learning in a Layered Network

LETTER Communicated by Geoffrey Hinton Equivalence of Backpropagation and Contrastive Hebbian Learning in a Layered Network Xiaohui Xie xhx@ai.mit.edu Department of Brain and Cognitive Sciences, Massachusetts

### Decision Theory: Q-Learning

Decision Theory: Q-Learning CPSC 322 Decision Theory 5 Textbook 12.5 Decision Theory: Q-Learning CPSC 322 Decision Theory 5, Slide 1 Lecture Overview 1 Recap 2 Asynchronous Value Iteration 3 Q-Learning

### Reinforcement Learning

Reinforcement Learning Dipendra Misra Cornell University dkm@cs.cornell.edu https://dipendramisra.wordpress.com/ Task Grasp the green cup. Output: Sequence of controller actions Setup from Lenz et. al.

### Chapter 3: The Reinforcement Learning Problem

Chapter 3: The Reinforcement Learning Problem Objectives of this chapter: describe the RL problem we will be studying for the remainder of the course present idealized form of the RL problem for which

### Lecture 13: Introduction to Neural Networks

Lecture 13: Introduction to Neural Networks Instructor: Aditya Bhaskara Scribe: Dietrich Geisler CS 5966/6966: Theory of Machine Learning March 8 th, 2017 Abstract This is a short, two-line summary of

### Feedback Control of Linear SISO systems. Process Dynamics and Control

Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals

### Neural Network Based Response Surface Methods a Comparative Study

. LS-DYNA Anwenderforum, Ulm Robustheit / Optimierung II Neural Network Based Response Surface Methods a Comparative Study Wolfram Beyer, Martin Liebscher, Michael Beer, Wolfgang Graf TU Dresden, Germany

### CSE 190: Reinforcement Learning: An Introduction. Chapter 8: Generalization and Function Approximation. Pop Quiz: What Function Are We Approximating?

CSE 190: Reinforcement Learning: An Introduction Chapter 8: Generalization and Function Approximation Objectives of this chapter: Look at how experience with a limited part of the state set be used to

### Solution of Stiff Differential Equations & Dynamical Systems Using Neural Network Methods

Advances in Dynamical Systems and Applications. ISSN 0973-5321, Volume 12, Number 1, (2017) pp. 21-28 Research India Publications http://www.ripublication.com Solution of Stiff Differential Equations &

### Does the Wake-sleep Algorithm Produce Good Density Estimators?

Does the Wake-sleep Algorithm Produce Good Density Estimators? Brendan J. Frey, Geoffrey E. Hinton Peter Dayan Department of Computer Science Department of Brain and Cognitive Sciences University of Toronto

### Artificial Neural Networks Examination, June 2005

Artificial Neural Networks Examination, June 2005 Instructions There are SIXTY questions. (The pass mark is 30 out of 60). For each question, please select a maximum of ONE of the given answers (either

### Effect of number of hidden neurons on learning in large-scale layered neural networks

ICROS-SICE International Joint Conference 009 August 18-1, 009, Fukuoka International Congress Center, Japan Effect of on learning in large-scale layered neural networks Katsunari Shibata (Oita Univ.;

### MODELING OF A HOT AIR DRYING PROCESS BY USING ARTIFICIAL NEURAL NETWORK METHOD

MODELING OF A HOT AIR DRYING PROCESS BY USING ARTIFICIAL NEURAL NETWORK METHOD Ahmet DURAK +, Ugur AKYOL ++ + NAMIK KEMAL UNIVERSITY, Hayrabolu, Tekirdag, Turkey. + NAMIK KEMAL UNIVERSITY, Çorlu, Tekirdag,

### Reinforcement Learning (1)

Reinforcement Learning 1 Reinforcement Learning (1) Machine Learning 64-360, Part II Norman Hendrich University of Hamburg, Dept. of Informatics Vogt-Kölln-Str. 30, D-22527 Hamburg hendrich@informatik.uni-hamburg.de

### Neural Networks with Applications to Vision and Language. Feedforward Networks. Marco Kuhlmann

Neural Networks with Applications to Vision and Language Feedforward Networks Marco Kuhlmann Feedforward networks Linear separability x 2 x 2 0 1 0 1 0 0 x 1 1 0 x 1 linearly separable not linearly separable

### What Do Neural Networks Do? MLP Lecture 3 Multi-layer networks 1

What Do Neural Networks Do? MLP Lecture 3 Multi-layer networks 1 Multi-layer networks Steve Renals Machine Learning Practical MLP Lecture 3 7 October 2015 MLP Lecture 3 Multi-layer networks 2 What Do Single

### ARTIFICIAL NEURAL NETWORK PART I HANIEH BORHANAZAD

ARTIFICIAL NEURAL NETWORK PART I HANIEH BORHANAZAD WHAT IS A NEURAL NETWORK? The simplest definition of a neural network, more properly referred to as an 'artificial' neural network (ANN), is provided

### Lecture 16: Introduction to Neural Networks

Lecture 16: Introduction to Neural Networs Instructor: Aditya Bhasara Scribe: Philippe David CS 5966/6966: Theory of Machine Learning March 20 th, 2017 Abstract In this lecture, we consider Bacpropagation,

### Keywords- Source coding, Huffman encoding, Artificial neural network, Multilayer perceptron, Backpropagation algorithm

Volume 4, Issue 5, May 2014 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com Huffman Encoding

### NONLINEAR CLASSIFICATION AND REGRESSION. J. Elder CSE 4404/5327 Introduction to Machine Learning and Pattern Recognition

NONLINEAR CLASSIFICATION AND REGRESSION Nonlinear Classification and Regression: Outline 2 Multi-Layer Perceptrons The Back-Propagation Learning Algorithm Generalized Linear Models Radial Basis Function

### Negatively Correlated Echo State Networks

Negatively Correlated Echo State Networks Ali Rodan and Peter Tiňo School of Computer Science, The University of Birmingham Birmingham B15 2TT, United Kingdom E-mail: {a.a.rodan, P.Tino}@cs.bham.ac.uk

### Course 16:198:520: Introduction To Artificial Intelligence Lecture 13. Decision Making. Abdeslam Boularias. Wednesday, December 7, 2016

Course 16:198:520: Introduction To Artificial Intelligence Lecture 13 Decision Making Abdeslam Boularias Wednesday, December 7, 2016 1 / 45 Overview We consider probabilistic temporal models where the

### Reinforcement Learning

Reinforcement Learning Model-Based Reinforcement Learning Model-based, PAC-MDP, sample complexity, exploration/exploitation, RMAX, E3, Bayes-optimal, Bayesian RL, model learning Vien Ngo MLR, University

### Back-propagation as reinforcement in prediction tasks

Back-propagation as reinforcement in prediction tasks André Grüning Cognitive Neuroscience Sector S.I.S.S.A. via Beirut 4 34014 Trieste Italy gruening@sissa.it Abstract. The back-propagation (BP) training

### (Feed-Forward) Neural Networks Dr. Hajira Jabeen, Prof. Jens Lehmann

(Feed-Forward) Neural Networks 2016-12-06 Dr. Hajira Jabeen, Prof. Jens Lehmann Outline In the previous lectures we have learned about tensors and factorization methods. RESCAL is a bilinear model for

### CSE 352 (AI) LECTURE NOTES Professor Anita Wasilewska. NEURAL NETWORKS Learning

CSE 352 (AI) LECTURE NOTES Professor Anita Wasilewska NEURAL NETWORKS Learning Neural Networks Classifier Short Presentation INPUT: classification data, i.e. it contains an classification (class) attribute.

### (Artificial) Neural Networks in TensorFlow

(Artificial) Neural Networks in TensorFlow By Prof. Seungchul Lee Industrial AI Lab http://isystems.unist.ac.kr/ POSTECH Table of Contents I. 1. Recall Supervised Learning Setup II. 2. Artificial Neural

### CSC321 Lecture 5: Multilayer Perceptrons

CSC321 Lecture 5: Multilayer Perceptrons Roger Grosse Roger Grosse CSC321 Lecture 5: Multilayer Perceptrons 1 / 21 Overview Recall the simple neuron-like unit: y output output bias i'th weight w 1 w2 w3

### Sections 18.6 and 18.7 Artificial Neural Networks

Sections 18.6 and 18.7 Artificial Neural Networks CS4811 - Artificial Intelligence Nilufer Onder Department of Computer Science Michigan Technological University Outline The brain vs. artifical neural

### Source localization in an ocean waveguide using supervised machine learning

Source localization in an ocean waveguide using supervised machine learning Haiqiang Niu, Emma Reeves, and Peter Gerstoft Scripps Institution of Oceanography, UC San Diego Part I Localization on Noise09

### Lecture 10 - Planning under Uncertainty (III)

Lecture 10 - Planning under Uncertainty (III) Jesse Hoey School of Computer Science University of Waterloo March 27, 2018 Readings: Poole & Mackworth (2nd ed.)chapter 12.1,12.3-12.9 1/ 34 Reinforcement

### Reinforcement Learning based on On-line EM Algorithm

Reinforcement Learning based on On-line EM Algorithm Masa-aki Sato t t ATR Human Information Processing Research Laboratories Seika, Kyoto 619-0288, Japan masaaki@hip.atr.co.jp Shin Ishii +t tnara Institute

### Reinforcement Learning. Value Function Updates

Reinforcement Learning Value Function Updates Manfred Huber 2014 1 Value Function Updates Different methods for updating the value function Dynamic programming Simple Monte Carlo Temporal differencing

### CSE 190: Reinforcement Learning: An Introduction. Chapter 8: Generalization and Function Approximation. Pop Quiz: What Function Are We Approximating?

CSE 190: Reinforcement Learning: An Introduction Chapter 8: Generalization and Function Approximation Objectives of this chapter: Look at how experience with a limited part of the state set be used to

### CS 188: Artificial Intelligence

CS 188: Artificial Intelligence Reinforcement Learning Instructor: Fabrice Popineau [These slides adapted from Stuart Russell, Dan Klein and Pieter Abbeel @ai.berkeley.edu] Reinforcement Learning Double

Radial-Basis Function etworks A function is radial basis () if its output depends on (is a non-increasing function of) the distance of the input from a given stored vector. s represent local receptors,

### , and rewards and transition matrices as shown below:

CSE 50a. Assignment 7 Out: Tue Nov Due: Thu Dec Reading: Sutton & Barto, Chapters -. 7. Policy improvement Consider the Markov decision process (MDP) with two states s {0, }, two actions a {0, }, discount

### AN INTRODUCTION TO THE CONTROL THEORY

Open-Loop controller An Open-Loop (OL) controller is characterized by no direct connection between the output of the system and its input; therefore external disturbance, non-linear dynamics and parameter

### CS 4700: Foundations of Artificial Intelligence

CS 4700: Foundations of Artificial Intelligence Prof. Bart Selman selman@cs.cornell.edu Machine Learning: Neural Networks R&N 18.7 Intro & perceptron learning 1 2 Neuron: How the brain works # neurons

### Reinforcement learning an introduction

Reinforcement learning an introduction Prof. Dr. Ann Nowé Computational Modeling Group AIlab ai.vub.ac.be November 2013 Reinforcement Learning What is it? Learning from interaction Learning about, from,

### Abstract. In this paper we propose recurrent neural networks with feedback into the input

Recurrent Neural Networks for Missing or Asynchronous Data Yoshua Bengio Dept. Informatique et Recherche Operationnelle Universite de Montreal Montreal, Qc H3C-3J7 bengioy@iro.umontreal.ca Francois Gingras

### Lecture 3: The Reinforcement Learning Problem

Lecture 3: The Reinforcement Learning Problem Objectives of this lecture: describe the RL problem we will be studying for the remainder of the course present idealized form of the RL problem for which

### A FUZZY NEURAL NETWORK MODEL FOR FORECASTING STOCK PRICE

A FUZZY NEURAL NETWORK MODEL FOR FORECASTING STOCK PRICE Li Sheng Institute of intelligent information engineering Zheiang University Hangzhou, 3007, P. R. China ABSTRACT In this paper, a neural network-driven

### Probabilistic inference for computing optimal policies in MDPs

Probabilistic inference for computing optimal policies in MDPs Marc Toussaint Amos Storkey School of Informatics, University of Edinburgh Edinburgh EH1 2QL, Scotland, UK mtoussai@inf.ed.ac.uk, amos@storkey.org

### Lecture 3: Policy Evaluation Without Knowing How the World Works / Model Free Policy Evaluation

Lecture 3: Policy Evaluation Without Knowing How the World Works / Model Free Policy Evaluation CS234: RL Emma Brunskill Winter 2018 Material builds on structure from David SIlver s Lecture 4: Model-Free

### Modeling and Control Overview

Modeling and Control Overview D R. T A R E K A. T U T U N J I A D V A N C E D C O N T R O L S Y S T E M S M E C H A T R O N I C S E N G I N E E R I N G D E P A R T M E N T P H I L A D E L P H I A U N I

### Connecting the Demons

Connecting the Demons How connection choices of a Horde implementation affect Demon prediction capabilities. Author: Jasper van der Waa jaspervanderwaa@gmail.com Supervisors: Dr. ir. Martijn van Otterlo

### Introduction to Neural Networks

Introduction to Neural Networks Steve Renals Automatic Speech Recognition ASR Lecture 10 24 February 2014 ASR Lecture 10 Introduction to Neural Networks 1 Neural networks for speech recognition Introduction

### On Average Versus Discounted Reward Temporal-Difference Learning

Machine Learning, 49, 179 191, 2002 c 2002 Kluwer Academic Publishers. Manufactured in The Netherlands. On Average Versus Discounted Reward Temporal-Difference Learning JOHN N. TSITSIKLIS Laboratory for

### Dynamics and Control of Double-Pipe Heat Exchanger

Nahrain University, College of Engineering Journal (NUCEJ) Vol.13 No.2, 21 pp.129-14 Dynamics and Control of Double-Pipe Heat Exchanger Dr.Khalid.M.Mousa Chemical engineering Department Nahrain University

### Autonomous Helicopter Flight via Reinforcement Learning

Autonomous Helicopter Flight via Reinforcement Learning Authors: Andrew Y. Ng, H. Jin Kim, Michael I. Jordan, Shankar Sastry Presenters: Shiv Ballianda, Jerrolyn Hebert, Shuiwang Ji, Kenley Malveaux, Huy

### Adaptive Boosting of Neural Networks for Character Recognition

Adaptive Boosting of Neural Networks for Character Recognition Holger Schwenk Yoshua Bengio Dept. Informatique et Recherche Opérationnelle Université de Montréal, Montreal, Qc H3C-3J7, Canada fschwenk,bengioyg@iro.umontreal.ca

### Methods for Supervised Learning of Tasks

Methods for Supervised Learning of Tasks Alper Denasi DCT 8.43 Traineeship report Coaching: Prof. dr. H. Nijmeijer Technische Universiteit Eindhoven Department Mechanical Engineering Dynamics and Control

### Open Loop Tuning Rules

Open Loop Tuning Rules Based on approximate process models Process Reaction Curve: The process reaction curve is an approximate model of the process, assuming the process behaves as a first order plus

### A predictive control system for concrete plants. Application of RBF neural networks for reduce dosing inaccuracies.

A predictive control system for concrete plants. Application of RBF neural networks for reduce dosing inaccuracies. Antonio Guerrero González, Juan Carlos Molina Molina, Pedro José Ayala Bernal and Francisco

### 16.410/413 Principles of Autonomy and Decision Making

16.410/413 Principles of Autonomy and Decision Making Lecture 23: Markov Decision Processes Policy Iteration Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology December

### Reinforcement learning

einforcement learning How to learn to make decisions in sequential problems (like: chess, a maze) Why is this difficult? Temporal credit assignment Prediction can help Further reading For modeling: Chapter

### MODULAR ECHO STATE NEURAL NETWORKS IN TIME SERIES PREDICTION

Computing and Informatics, Vol. 30, 2011, 321 334 MODULAR ECHO STATE NEURAL NETWORKS IN TIME SERIES PREDICTION Štefan Babinec, Jiří Pospíchal Department of Mathematics Faculty of Chemical and Food Technology

### Process Solutions. Process Dynamics. The Fundamental Principle of Process Control. APC Techniques Dynamics 2-1. Page 2-1

Process Dynamics The Fundamental Principle of Process Control APC Techniques Dynamics 2-1 Page 2-1 Process Dynamics (1) All Processes are dynamic i.e. they change with time. If a plant were totally static

### A multiple testing procedure for input variable selection in neural networks

A multiple testing procedure for input variable selection in neural networks MicheleLaRoccaandCiraPerna Department of Economics and Statistics - University of Salerno Via Ponte Don Melillo, 84084, Fisciano

### Iterative Learning Control Analysis and Design I

Iterative Learning Control Analysis and Design I Electronics and Computer Science University of Southampton Southampton, SO17 1BJ, UK etar@ecs.soton.ac.uk http://www.ecs.soton.ac.uk/ Contents Basics Representations

### Artificial neural networks

Artificial neural networks Chapter 8, Section 7 Artificial Intelligence, spring 203, Peter Ljunglöf; based on AIMA Slides c Stuart Russel and Peter Norvig, 2004 Chapter 8, Section 7 Outline Brains Neural

### A Black-Box Approach in Modeling Valve Stiction

Vol:4, No:8, A Black-Box Approach in Modeling Valve Stiction H. Zabiri, N. Mazuki International Science Index, Mechanical and Mechatronics Engineering Vol:4, No:8, waset.org/publication/46 Abstract Several

### SP-CNN: A Scalable and Programmable CNN-based Accelerator. Dilan Manatunga Dr. Hyesoon Kim Dr. Saibal Mukhopadhyay

SP-CNN: A Scalable and Programmable CNN-based Accelerator Dilan Manatunga Dr. Hyesoon Kim Dr. Saibal Mukhopadhyay Motivation Power is a first-order design constraint, especially for embedded devices. Certain