CSE 190: Reinforcement Learning: An Introduction. Chapter 8: Generalization and Function Approximation. Pop Quiz: What Function Are We Approximating?
|
|
- Christopher Morrison
- 6 years ago
- Views:
Transcription
1 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 produce good behavior over a much larger part: Generalization How to accomplish generalization by using parameterized functions that approximate the Value or Q functions: Function Approximation Acknowledgment: A good number of these slides are cribbed from Rich Sutton Function Approximation Methods Many possible methods: artificial neural networks decision trees multivariate regression methods Kernel density methods But RL has some special requirements: Usually want to learn while interacting Want to be able to handle nonstationarity In this chapter, we focus on linear function approximators Simple models Simple learning rules Pop Quiz: What Function Are We Approximating? The Value function and/or the Q-value function The methods we have used so far are called tabular methods The V and Q functions were essentially a table: V(s is represented in an array. But these are still functions: V(s: a mapping from states to values Q(s,a: A mapping from states and actions to values Problem: An entry in an array doesn t tell you anything about the entry in the next cell: No generalization Goal: learning something about a state should generalize to nearby states. 3 4
2 Linear Function Approximators Gradient Descent Methods Assume V is a (sufficiently smooth differentiable function Represent states as vectors of features (note: I am using different notation than the book: F(s = ( f 1 (s, f 2 (s,...f n (s T Then represent the Value as a linear combination of the features: V (s = T F(s = i f i (s n " I.e., a simple weighted sum of the features. Often, one of the features (e.g., f 0 (s is a constant. i=1 of, for all s "S. Assume, for now, training examples of this form: {(s 1, V (s 1,(s 2, V (s 2,...(s T, V (s T } where our goal: by modifying: s i = ( f 1 (s i, f 2 (s i,..., f n (s i V (s i "V # (s i # = (# 1,# 2,,# n T 5 6 This is our performance measure a common and simple one is the sum-squared error (SSE over a probability distribution P : SSE( = P(s $ % V " (s # V (s ' s(s Why P? Why minimize SSE? Let us assume that P is always the distribution of states at which backups are done. The on-policy distribution: the distribution created while following the policy being evaluated. Stronger results are available for this distribution. 2 7 Gradient Descent Main idea: Change in order to go downhill in the Sum Squared Error Which way is downhill? The negative of the slope of the SSE with respect to When the slope is a vector, it s called the gradient. Current parameters: = 1, 2 Gradient (downhill in the parameters: - " SSE SSE ( T 2 Iteratively move t +1 = down the gradient: t " #$ SSE( t 1 8
3 Gradient Descent What is - SSE "? % - SSE = # $SSE, $SSE,, $SSE ( " ' $" 1 $" 2 $" n * Looking at one component of this vector: - SSE 1 = # 2 (V $ (s # V(s 2 " i " i = #(V $ (s # V(s(# V(s " i = (V $ (s # V(s V(s " i T 9 So this is what - SSE " Now, what for V(s Gradient Descent is: % - SSE = # $SSE " ' V(s " i, $SSE,, $SSE ( $" 1 $" 2 $" n * % = (V + (s # V(s $V(s, $V(s,, $V(s ( ' $" 1 $" 2 $" n * is depends on your function approximator T T 10 Linear Function Approximators Linear Function Approximators Representing the Value function as a linear combination of features makes the derivative very simple: V (s = T F(s = i f i (s V(s " i = i=1 So the learning rule becomes: i = i + "(V # (s $ V(s f i (s n # n " " j f j (s j =1 " i = " i f i (s " i = f i (s So the learning rule becomes: i = i + "(V # (s $ V(s f i (s Why does this make sense? 11 12
4 Linear Function Approximators i = i + "(V # (s $ V(s f i (s Targets Where does the teacher V (s come from? We don t actually have access to V (s However, if we have something whose expected value is V (s we re guaranteed to converge to the optimal solution. This is true of: Monte Carlo (R t,td( s return of R " (but only if =1. Not true of R " for <1, or of Dynamic Programming targets - but these methods work well anyway Using the TD error: t = r t + "V t +1 # V t Now, we update the elegibility trace using the gradient: e t = $" e t #1 + % t V t On-Line Gradient-Descent TD( Nice Properties of Linear FA Methods The gradient is very simple: V " t (s = F(s For MSE, the error surface is simple: quadratic surface with a single minimum. Linear gradient descent TD( converges: Step size decreases appropriately On-line sampling (states sampled from the on-policy distribution Converges to parameter vector with property: " MSE( " # 1 $ % 1 $ % MSE( ' 15 (Tsitsiklis Van Roy, 1997 best parameter vector 16
5 Coarse Coding Shaping Generalization in Coarse Coding Learning and Coarse Coding Tile Coding Binary feature for each tile Number of features present at any one time is constant Binary features means weighted sum easy to compute Easy to compute indices of the features present 19 20
6 Tile Coding Cont. Radial Basis Functions (RBFs e.g., Gaussians Irregular tilings # f i (s = exp s c i % 2 $ 2" i 2 ( ' Hashing CMAC Cerebellar model arithmetic computer Albus Can you beat the curse of dimensionality? Can you keep the number of features from going up exponentially with the dimension? Function complexity, not dimensionality, is the problem. Kanerva coding: Select a bunch of binary prototypes Use hamming distance as distance measure Dimensionality is no longer a problem, only complexity Lazy learning schemes: Remember all the data To get new value, find nearest neighbors and interpolate e.g., locally-weighted regression Control with FA Learning state-action values The general gradient-descent rule: t +1 = t + " [ v t # Q t,a t ]$ Q(s t,a t Gradient-descent Sarsa( (backward view: t +1 = t + " # t et where # t = r t +1 + $ Q t +1,a t +1 % Q t,a t e t = $ e t %1 + ' Q t,a t 23 24
7 GPI Linear Gradient Descent Watkins Q( Linear Gradient Descent Sarsa( (with GPI Mountain-Car Task 27 28
8 Mountain Car with Radial Basis Functions Mountain-Car Results Baird s Counterexample Baird s Counterexample Cont
9 Should We Bootstrap? Summary Generalization Adapting supervised-learning function approximation methods Gradient-descent methods Linear gradient-descent methods Radial basis functions Tile coding Kanerva coding Nonlinear gradient-descent methods? Backpropagation? Subtleties involving function approximation, bootstrapping and the on-policy/off-policy distinction Value Prediction with FA As usual: Policy Evaluation (the prediction problem: for a given policy #, compute the state-value function V Adapt Supervised Learning Algorithms Training Info = desired (target outputs In earlier chapters, value functions were stored in lookup tables. Here, the value function estimate at time t, V t, depends on a parameter vector t, and only the parameter vector Inputs Supervised Learning System Outputs is updated. Training example = {input, target output} e.g., t could be the vector of connection weights of a neural network. Error = (target output actual output 35 36
10 Backups as Training Examples e.g., the TD(0 backup: [ ] V V + " r t +1 + # V +1 $ V As a training example: { description of s t, r t +1 + V +1 } Gradient Descent Cont. For the MSE given above and using the chain rule: t +1 = t " 1 2 #$ MSE( t = t " 1 2 #$ P(s V ' 2 (s " V ( t (s* + s%s = t + # P(s ( V ' (s " V t (s* + $ V t (s s%s input target output Gradient Descent Cont. But We Don t have these Targets Use just the sample gradient instead: t +1 = t " 1 2 #$ V % 2 (s ' t " V t ( Suppose we just have targets v t instead : t +1 = t + " [ v t # V t ]$ V (s t t = t + # ' V % " V t ( $ V (s, t t Since each sample gradient is an unbiased estimate of the true gradient, this converges to a local minimum of the MSE if " decreases appropriately with t. E #$ V " V t % ' V ( t = * P(s #$ V (s " V t (s% ' V ( t (s ss 39 If each v t is an unbiased estimate of V, { } = V, then gradient descent converges i.e., E v t to a local minimum (provided " decreases appropriately. e.g., the Monte Carlo target v t = R t : t +1 = t + " [ R t # V t ]$ V (s t t 40
11 What about TD( Targets? t +1 = t + " % R # t $ V t ' ( V t Not for # < 1 But we do it anyway, using the backwards view: t +1 = t + " # t et, where: # t = r t +1 + $ V t +1 % V t, as usual, and e t = $ e t %1 + ' V t END 41
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
More informationChapter 8: Generalization and Function Approximation
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 produce good behavior over a much larger part. Overview
More informationCS599 Lecture 2 Function Approximation in RL
CS599 Lecture 2 Function Approximation in RL Look at how experience with a limited part of the state set be used to produce good behavior over a much larger part. Overview of function approximation (FA)
More informationGeneralization and Function Approximation
Generalization and Function Approximation 0 Generalization and Function Approximation Suggested reading: Chapter 8 in R. S. Sutton, A. G. Barto: Reinforcement Learning: An Introduction MIT Press, 1998.
More informationValue Prediction with FA. Chapter 8: Generalization and Function Approximation. Adapt Supervised Learning Algorithms. Backups as Training Examples [ ]
Chapte 8: Genealization and Function Appoximation Objectives of this chapte:! Look at how expeience with a limited pat of the state set be used to poduce good behavio ove a much lage pat.! Oveview of function
More informationChapter 8: Generalization and Function Approximation
Chapte 8: Genealization and Function Appoximation Objectives of this chapte: Look at how expeience with a limited pat of the state set be used to poduce good behavio ove a much lage pat. Oveview of function
More informationReinforcement Learning
Reinforcement Learning RL in continuous MDPs March April, 2015 Large/Continuous MDPs Large/Continuous state space Tabular representation cannot be used Large/Continuous action space Maximization over action
More informationReinforcement Learning: An Introduction. ****Draft****
i Reinforcement Learning: An Introduction Second edition, in progress ****Draft**** Richard S. Sutton and Andrew G. Barto c 2014, 2015 A Bradford Book The MIT Press Cambridge, Massachusetts London, England
More informationReinforcement Learning
Reinforcement Learning Function approximation Mario Martin CS-UPC May 18, 2018 Mario Martin (CS-UPC) Reinforcement Learning May 18, 2018 / 65 Recap Algorithms: MonteCarlo methods for Policy Evaluation
More informationLecture 7: Value Function Approximation
Lecture 7: Value Function Approximation Joseph Modayil Outline 1 Introduction 2 3 Batch Methods Introduction Large-Scale Reinforcement Learning Reinforcement learning can be used to solve large problems,
More informationReinforcement 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
More informationReinforcement Learning
Reinforcement Learning Function approximation Daniel Hennes 19.06.2017 University Stuttgart - IPVS - Machine Learning & Robotics 1 Today Eligibility traces n-step TD returns Forward and backward view Function
More informationCS 287: Advanced Robotics Fall Lecture 14: Reinforcement Learning with Function Approximation and TD Gammon case study
CS 287: Advanced Robotics Fall 2009 Lecture 14: Reinforcement Learning with Function Approximation and TD Gammon case study Pieter Abbeel UC Berkeley EECS Assignment #1 Roll-out: nice example paper: X.
More informationApproximation Methods in Reinforcement Learning
2018 CS420, Machine Learning, Lecture 12 Approximation Methods in Reinforcement Learning Weinan Zhang Shanghai Jiao Tong University http://wnzhang.net http://wnzhang.net/teaching/cs420/index.html Reinforcement
More informationReinforcement Learning with Function Approximation. Joseph Christian G. Noel
Reinforcement Learning with Function Approximation Joseph Christian G. Noel November 2011 Abstract Reinforcement learning (RL) is a key problem in the field of Artificial Intelligence. The main goal is
More informationThis question has three parts, each of which can be answered concisely, but be prepared to explain and justify your concise answer.
This question has three parts, each of which can be answered concisely, but be prepared to explain and justify your concise answer. 1. Suppose you have a policy and its action-value function, q, then you
More informationReinforcement Learning
Reinforcement Learning Function Approximation Continuous state/action space, mean-square error, gradient temporal difference learning, least-square temporal difference, least squares policy iteration Vien
More informationReplacing eligibility trace for action-value learning with function approximation
Replacing eligibility trace for action-value learning with function approximation Kary FRÄMLING Helsinki University of Technology PL 5500, FI-02015 TKK - Finland Abstract. The eligibility trace is one
More informationReinforcement Learning. George Konidaris
Reinforcement Learning George Konidaris gdk@cs.brown.edu Fall 2017 Machine Learning Subfield of AI concerned with learning from data. Broadly, using: Experience To Improve Performance On Some Task (Tom
More informationProf. Dr. Ann Nowé. Artificial Intelligence Lab ai.vub.ac.be
REINFORCEMENT LEARNING AN INTRODUCTION Prof. Dr. Ann Nowé Artificial Intelligence Lab ai.vub.ac.be REINFORCEMENT LEARNING WHAT IS IT? What is it? Learning from interaction Learning about, from, and while
More informationCSE446: non-parametric methods Spring 2017
CSE446: non-parametric methods Spring 2017 Ali Farhadi Slides adapted from Carlos Guestrin and Luke Zettlemoyer Linear Regression: What can go wrong? What do we do if the bias is too strong? Might want
More informationReinforcement 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,
More informationWeek 6, Lecture 1. Reinforcement Learning (part 3) Announcements: HW 3 due on 11/5 at NOON Midterm Exam 11/8 Project draft due 11/15
ME 537: Learning Based Control Week 6, Lecture 1 Reinforcement Learning (part 3 Announcements: HW 3 due on 11/5 at NOON Midterm Exam 11/8 Project draft due 11/15 Suggested reading : Chapters 7-8 in Reinforcement
More informationGrundlagen der Künstlichen Intelligenz
Grundlagen der Künstlichen Intelligenz Reinforcement learning II Daniel Hennes 11.12.2017 (WS 2017/18) University Stuttgart - IPVS - Machine Learning & Robotics 1 Today Eligibility traces n-step TD returns
More informationROB 537: Learning-Based Control. Announcements: Project background due Today. HW 3 Due on 10/30 Midterm Exam on 11/6.
ROB 537: Learning-Based Control Week 5, Lecture 1 Policy Gradient, Eligibility Traces, Transfer Learning (MaC Taylor Announcements: Project background due Today HW 3 Due on 10/30 Midterm Exam on 11/6 Reading:
More informationFast Gradient-Descent Methods for Temporal-Difference Learning with Linear Function Approximation
Fast Gradient-Descent Methods for Temporal-Difference Learning with Linear Function Approximation Rich Sutton, University of Alberta Hamid Maei, University of Alberta Doina Precup, McGill University Shalabh
More informationIntroduction. Reinforcement Learning
Introduction Reinforcement Learning Learn Act Sense Scott Sanner NICTA / ANU First.Last@nicta.com.au Lecture Goals 1) To understand formal models for decisionmaking under uncertainty and their properties
More informationMachine Learning. Nonparametric Methods. Space of ML Problems. Todo. Histograms. Instance-Based Learning (aka non-parametric methods)
Machine Learning InstanceBased Learning (aka nonparametric methods) Supervised Learning Unsupervised Learning Reinforcement Learning Parametric Non parametric CSE 446 Machine Learning Daniel Weld March
More informationValue Function Methods. CS : Deep Reinforcement Learning Sergey Levine
Value Function Methods CS 294-112: Deep Reinforcement Learning Sergey Levine Class Notes 1. Homework 2 is due in one week 2. Remember to start forming final project groups and writing your proposal! Proposal
More informationMachine Learning I Continuous Reinforcement Learning
Machine Learning I Continuous Reinforcement Learning Thomas Rückstieß Technische Universität München January 7/8, 2010 RL Problem Statement (reminder) state s t+1 ENVIRONMENT reward r t+1 new step r t
More informationOpen Theoretical Questions in Reinforcement Learning
Open Theoretical Questions in Reinforcement Learning Richard S. Sutton AT&T Labs, Florham Park, NJ 07932, USA, sutton@research.att.com, www.cs.umass.edu/~rich Reinforcement learning (RL) concerns the problem
More informationAN INTRODUCTION TO NEURAL NETWORKS. Scott Kuindersma November 12, 2009
AN INTRODUCTION TO NEURAL NETWORKS Scott Kuindersma November 12, 2009 SUPERVISED LEARNING We are given some training data: We must learn a function If y is discrete, we call it classification If it is
More informationThe Book: Where we are and where we re going. CSE 190: Reinforcement Learning: An Introduction. Chapter 7: Eligibility Traces. Simple Monte Carlo
CSE 190: Reinforcement Learning: An Introduction Chapter 7: Eligibility races Acknowledgment: A good number of these slides are cribbed from Rich Sutton he Book: Where we are and where we re going Part
More informationChapter 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
More informationReinforcement 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
More information6 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,
More informationTemporal 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).
More informationCS599 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
More informationLecture 25: Learning 4. Victor R. Lesser. CMPSCI 683 Fall 2010
Lecture 25: Learning 4 Victor R. Lesser CMPSCI 683 Fall 2010 Final Exam Information Final EXAM on Th 12/16 at 4:00pm in Lederle Grad Res Ctr Rm A301 2 Hours but obviously you can leave early! Open Book
More informationMonte Carlo is important in practice. CSE 190: Reinforcement Learning: An Introduction. Chapter 6: Temporal Difference Learning.
Monte Carlo is important in practice CSE 190: Reinforcement Learning: An Introduction Chapter 6: emporal Difference Learning When there are just a few possibilitieo value, out of a large state space, Monte
More informationIntroduction to Natural Computation. Lecture 9. Multilayer Perceptrons and Backpropagation. Peter Lewis
Introduction to Natural Computation Lecture 9 Multilayer Perceptrons and Backpropagation Peter Lewis 1 / 25 Overview of the Lecture Why multilayer perceptrons? Some applications of multilayer perceptrons.
More informationLecture 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
More informationhttps://www.youtube.com/watch?v=ymvi1l746us Eligibility traces Chapter 12, plus some extra stuff! Like n-step methods, but better! Eligibility traces A mechanism that allow TD, Sarsa and Q-learning to
More informationCSE 417T: Introduction to Machine Learning. Final Review. Henry Chai 12/4/18
CSE 417T: Introduction to Machine Learning Final Review Henry Chai 12/4/18 Overfitting Overfitting is fitting the training data more than is warranted Fitting noise rather than signal 2 Estimating! "#$
More informationMachine Learning I Reinforcement Learning
Machine Learning I Reinforcement Learning Thomas Rückstieß Technische Universität München December 17/18, 2009 Literature Book: Reinforcement Learning: An Introduction Sutton & Barto (free online version:
More informationReinforcement Learning
Reinforcement Learning Ron Parr CompSci 7 Department of Computer Science Duke University With thanks to Kris Hauser for some content RL Highlights Everybody likes to learn from experience Use ML techniques
More informationReinforcement Learning
Reinforcement Learning Temporal Difference Learning Temporal difference learning, TD prediction, Q-learning, elibigility traces. (many slides from Marc Toussaint) Vien Ngo MLR, University of Stuttgart
More informationReinforcement Learning Part 2
Reinforcement Learning Part 2 Dipendra Misra Cornell University dkm@cs.cornell.edu https://dipendramisra.wordpress.com/ From previous tutorial Reinforcement Learning Exploration No supervision Agent-Reward-Environment
More informationIntroduction to Reinforcement Learning. CMPT 882 Mar. 18
Introduction to Reinforcement Learning CMPT 882 Mar. 18 Outline for the week Basic ideas in RL Value functions and value iteration Policy evaluation and policy improvement Model-free RL Monte-Carlo and
More informationReinforcement Learning
Reinforcement Learning Value Function Approximation Continuous state/action space, mean-square error, gradient temporal difference learning, least-square temporal difference, least squares policy iteration
More informationReinforcement Learning. Spring 2018 Defining MDPs, Planning
Reinforcement Learning Spring 2018 Defining MDPs, Planning understandability 0 Slide 10 time You are here Markov Process Where you will go depends only on where you are Markov Process: Information state
More informationLecture 23: Reinforcement Learning
Lecture 23: Reinforcement Learning MDPs revisited Model-based learning Monte Carlo value function estimation Temporal-difference (TD) learning Exploration November 23, 2006 1 COMP-424 Lecture 23 Recall:
More informationOverview Example (TD-Gammon) Admission Why approximate RL is hard TD() Fitted value iteration (collocation) Example (k-nn for hill-car)
Function Approximation in Reinforcement Learning Gordon Geo ggordon@cs.cmu.edu November 5, 999 Overview Example (TD-Gammon) Admission Why approximate RL is hard TD() Fitted value iteration (collocation)
More informationCS 6375 Machine Learning
CS 6375 Machine Learning Nicholas Ruozzi University of Texas at Dallas Slides adapted from David Sontag and Vibhav Gogate Course Info. Instructor: Nicholas Ruozzi Office: ECSS 3.409 Office hours: Tues.
More informationSample questions for Fundamentals of Machine Learning 2018
Sample questions for Fundamentals of Machine Learning 2018 Teacher: Mohammad Emtiyaz Khan A few important informations: In the final exam, no electronic devices are allowed except a calculator. Make sure
More informationIntroduction to Reinforcement Learning. Part 6: Core Theory II: Bellman Equations and Dynamic Programming
Introduction to Reinforcement Learning Part 6: Core Theory II: Bellman Equations and Dynamic Programming Bellman Equations Recursive relationships among values that can be used to compute values The tree
More informationApproximate Q-Learning. Dan Weld / University of Washington
Approximate Q-Learning Dan Weld / University of Washington [Many slides taken from Dan Klein and Pieter Abbeel / CS188 Intro to AI at UC Berkeley materials available at http://ai.berkeley.edu.] Q Learning
More informationLecture 4: Approximate dynamic programming
IEOR 800: Reinforcement learning By Shipra Agrawal Lecture 4: Approximate dynamic programming Deep Q Networks discussed in the last lecture are an instance of approximate dynamic programming. These are
More informationReinforcement 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
More informationReinforcement Learning using Continuous Actions. Hado van Hasselt
Reinforcement Learning using Continuous Actions Hado van Hasselt 2005 Concluding thesis for Cognitive Artificial Intelligence University of Utrecht First supervisor: Dr. Marco A. Wiering, University of
More informationMidterm Review CS 6375: Machine Learning. Vibhav Gogate The University of Texas at Dallas
Midterm Review CS 6375: Machine Learning Vibhav Gogate The University of Texas at Dallas Machine Learning Supervised Learning Unsupervised Learning Reinforcement Learning Parametric Y Continuous Non-parametric
More informationReview: TD-Learning. TD (SARSA) Learning for Q-values. Bellman Equations for Q-values. P (s, a, s )[R(s, a, s )+ Q (s, (s ))]
Review: TD-Learning function TD-Learning(mdp) returns a policy Class #: Reinforcement Learning, II 8s S, U(s) =0 set start-state s s 0 choose action a, using -greedy policy based on U(s) U(s) U(s)+ [r
More informationOn and Off-Policy Relational Reinforcement Learning
On and Off-Policy Relational Reinforcement Learning Christophe Rodrigues, Pierre Gérard, and Céline Rouveirol LIPN, UMR CNRS 73, Institut Galilée - Université Paris-Nord first.last@lipn.univ-paris13.fr
More informationLecture 8: Policy Gradient
Lecture 8: Policy Gradient Hado van Hasselt Outline 1 Introduction 2 Finite Difference Policy Gradient 3 Monte-Carlo Policy Gradient 4 Actor-Critic Policy Gradient Introduction Vapnik s rule Never solve
More informationNonlinear Classification
Nonlinear Classification INFO-4604, Applied Machine Learning University of Colorado Boulder October 5-10, 2017 Prof. Michael Paul Linear Classification Most classifiers we ve seen use linear functions
More informationReinforcement Learning. Summer 2017 Defining MDPs, Planning
Reinforcement Learning Summer 2017 Defining MDPs, Planning understandability 0 Slide 10 time You are here Markov Process Where you will go depends only on where you are Markov Process: Information state
More informationCPSC 340: Machine Learning and Data Mining. Gradient Descent Fall 2016
CPSC 340: Machine Learning and Data Mining Gradient Descent Fall 2016 Admin Assignment 1: Marks up this weekend on UBC Connect. Assignment 2: 3 late days to hand it in Monday. Assignment 3: Due Wednesday
More informationIntroduction to Reinforcement Learning. Part 5: Temporal-Difference Learning
Introduction to Reinforcement Learning Part 5: emporal-difference Learning What everybody should know about emporal-difference (D) learning Used to learn value functions without human input Learns a guess
More information15-780: Graduate Artificial Intelligence. Reinforcement learning (RL)
15-780: Graduate Artificial Intelligence Reinforcement learning (RL) From MDPs to RL We still use the same Markov model with rewards and actions But there are a few differences: 1. We do not assume we
More informationPattern Recognition and Machine Learning
Christopher M. Bishop Pattern Recognition and Machine Learning ÖSpri inger Contents Preface Mathematical notation Contents vii xi xiii 1 Introduction 1 1.1 Example: Polynomial Curve Fitting 4 1.2 Probability
More informationArtificial Neural Networks" and Nonparametric Methods" CMPSCI 383 Nov 17, 2011!
Artificial Neural Networks" and Nonparametric Methods" CMPSCI 383 Nov 17, 2011! 1 Todayʼs lecture" How the brain works (!)! Artificial neural networks! Perceptrons! Multilayer feed-forward networks! Error
More informationCS325 Artificial Intelligence Chs. 18 & 4 Supervised Machine Learning (cont)
CS325 Artificial Intelligence Cengiz Spring 2013 Model Complexity in Learning f(x) x Model Complexity in Learning f(x) x Let s start with the linear case... Linear Regression Linear Regression price =
More informationUsing 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
More informationReinforcement Learning and NLP
1 Reinforcement Learning and NLP Kapil Thadani kapil@cs.columbia.edu RESEARCH Outline 2 Model-free RL Markov decision processes (MDPs) Derivative-free optimization Policy gradients Variance reduction Value
More informationAn online kernel-based clustering approach for value function approximation
An online kernel-based clustering approach for value function approximation N. Tziortziotis and K. Blekas Department of Computer Science, University of Ioannina P.O.Box 1186, Ioannina 45110 - Greece {ntziorzi,kblekas}@cs.uoi.gr
More informationMachine Learning. Reinforcement learning. Hamid Beigy. Sharif University of Technology. Fall 1396
Machine Learning Reinforcement learning Hamid Beigy Sharif University of Technology Fall 1396 Hamid Beigy (Sharif University of Technology) Machine Learning Fall 1396 1 / 32 Table of contents 1 Introduction
More informationilstd: Eligibility Traces and Convergence Analysis
ilstd: Eligibility Traces and Convergence Analysis Alborz Geramifard Michael Bowling Martin Zinkevich Richard S. Sutton Department of Computing Science University of Alberta Edmonton, Alberta {alborz,bowling,maz,sutton}@cs.ualberta.ca
More informationBalancing and Control of a Freely-Swinging Pendulum Using a Model-Free Reinforcement Learning Algorithm
Balancing and Control of a Freely-Swinging Pendulum Using a Model-Free Reinforcement Learning Algorithm Michail G. Lagoudakis Department of Computer Science Duke University Durham, NC 2778 mgl@cs.duke.edu
More informationCSC321 Lecture 22: Q-Learning
CSC321 Lecture 22: Q-Learning Roger Grosse Roger Grosse CSC321 Lecture 22: Q-Learning 1 / 21 Overview Second of 3 lectures on reinforcement learning Last time: policy gradient (e.g. REINFORCE) Optimize
More informationApproximate Dynamic Programming
Approximate Dynamic Programming A. LAZARIC (SequeL Team @INRIA-Lille) Ecole Centrale - Option DAD SequeL INRIA Lille EC-RL Course Value Iteration: the Idea 1. Let V 0 be any vector in R N A. LAZARIC Reinforcement
More informationDeep Reinforcement Learning SISL. Jeremy Morton (jmorton2) November 7, Stanford Intelligent Systems Laboratory
Deep Reinforcement Learning Jeremy Morton (jmorton2) November 7, 2016 SISL Stanford Intelligent Systems Laboratory Overview 2 1 Motivation 2 Neural Networks 3 Deep Reinforcement Learning 4 Deep Learning
More informationReinforcement 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.
More informationApproximate Dynamic Programming
Master MVA: Reinforcement Learning Lecture: 5 Approximate Dynamic Programming Lecturer: Alessandro Lazaric http://researchers.lille.inria.fr/ lazaric/webpage/teaching.html Objectives of the lecture 1.
More informationChapter 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 Compare efficiency of D learning with
More informationCMU Lecture 12: Reinforcement Learning. Teacher: Gianni A. Di Caro
CMU 15-781 Lecture 12: Reinforcement Learning Teacher: Gianni A. Di Caro REINFORCEMENT LEARNING Transition Model? State Action Reward model? Agent Goal: Maximize expected sum of future rewards 2 MDP PLANNING
More informationReinforcement 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
More informationNotes on Reinforcement Learning
1 Introduction Notes on Reinforcement Learning Paulo Eduardo Rauber 2014 Reinforcement learning is the study of agents that act in an environment with the goal of maximizing cumulative reward signals.
More informationReinforcement Learning in Continuous Action Spaces
Reinforcement Learning in Continuous Action Spaces Hado van Hasselt and Marco A. Wiering Intelligent Systems Group, Department of Information and Computing Sciences, Utrecht University Padualaan 14, 3508
More informationArtificial Intelligence
Artificial Intelligence Jeff Clune Assistant Professor Evolving Artificial Intelligence Laboratory Announcements Be making progress on your projects! Three Types of Learning Unsupervised Supervised Reinforcement
More informationLeast-Squares Temporal Difference Learning based on Extreme Learning Machine
Least-Squares Temporal Difference Learning based on Extreme Learning Machine Pablo Escandell-Montero, José M. Martínez-Martínez, José D. Martín-Guerrero, Emilio Soria-Olivas, Juan Gómez-Sanchis IDAL, Intelligent
More information2015 Todd Neller. A.I.M.A. text figures 1995 Prentice Hall. Used by permission. Neural Networks. Todd W. Neller
2015 Todd Neller. A.I.M.A. text figures 1995 Prentice Hall. Used by permission. Neural Networks Todd W. Neller Machine Learning Learning is such an important part of what we consider "intelligence" that
More informationLecture 3 Feedforward Networks and Backpropagation
Lecture 3 Feedforward Networks and Backpropagation CMSC 35246: Deep Learning Shubhendu Trivedi & Risi Kondor University of Chicago April 3, 2017 Things we will look at today Recap of Logistic Regression
More informationLeast Mean Squares Regression
Least Mean Squares Regression Machine Learning Spring 2018 The slides are mainly from Vivek Srikumar 1 Lecture Overview Linear classifiers What functions do linear classifiers express? Least Squares Method
More informationCMU-Q Lecture 24:
CMU-Q 15-381 Lecture 24: Supervised Learning 2 Teacher: Gianni A. Di Caro SUPERVISED LEARNING Hypotheses space Hypothesis function Labeled Given Errors Performance criteria Given a collection of input
More informationQ-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
More informationFeedforward Neural Nets and Backpropagation
Feedforward Neural Nets and Backpropagation Julie Nutini University of British Columbia MLRG September 28 th, 2016 1 / 23 Supervised Learning Roadmap Supervised Learning: Assume that we are given the features
More informationCS 570: Machine Learning Seminar. Fall 2016
CS 570: Machine Learning Seminar Fall 2016 Class Information Class web page: http://web.cecs.pdx.edu/~mm/mlseminar2016-2017/fall2016/ Class mailing list: cs570@cs.pdx.edu My office hours: T,Th, 2-3pm or
More informationMARKOV DECISION PROCESSES (MDP) AND REINFORCEMENT LEARNING (RL) Versione originale delle slide fornita dal Prof. Francesco Lo Presti
1 MARKOV DECISION PROCESSES (MDP) AND REINFORCEMENT LEARNING (RL) Versione originale delle slide fornita dal Prof. Francesco Lo Presti Historical background 2 Original motivation: animal learning Early
More informationIntroduction to Machine Learning Prof. Sudeshna Sarkar Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur
Introduction to Machine Learning Prof. Sudeshna Sarkar Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Module 2 Lecture 05 Linear Regression Good morning, welcome
More informationWhat we learned last time
Wat we learned last time Value-function approximation by stocastic gradient descent enables RL to be applied to arbitrarily large state spaces Most algoritms just carry over Targets from tabular case Wit
More information