Chapter 6: Temporal Difference Learning

Size: px
Start display at page:

Download "Chapter 6: Temporal Difference Learning"

Transcription

1 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. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 1

2 D Prediction Policy Evaluation (the prediction problem): for a given policy π, compute the state-value function V π Recall: Simple every - visit Monte Carlo method : V( s ) V( s ) + R V( s ) α [ ] t t t t target: the actual return after time t he simplest D method, D(0) : [ ] V( s ) V( s ) + α r + γ V( s ) V( s ) t t t + 1 t + 1 t target: an estimate of the return R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 2

3 Simple Monte Carlo V( s ) V( s ) + R V( s ) t t t t where R is the actual return following state s. t α [ ] s t t R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 3

4 Simplest D Method [ ] V( s ) V( s ) + α r + γ V( s ) V( s ) t t t + 1 t + 1 t s t s t +1 r t +1 R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 4

5 cf. Dynamic Programming { } V( s ) E r + γ V( s ) t π t + 1 t s t r t +1 s t +1 R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 5

6 D Bootstraps and Samples Bootstrapping: update involves an estimate MC does not bootstrap DP bootstraps D bootstraps Sampling: update does not involve an expected value MC samples DP does not sample D samples R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 6

7 Example: Driving Home State Elapsed ime Predicted Predicted (minutes) ime to Go otal ime leaving office reach car, raining exit highway behind truck home street arrive home R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 7

8 Driving Home Changes recommended by Monte Carlo methods (α=1) Changes recommended by D methods (α=1) Predicted total travel time actual outcome Predicted total travel time actual outcome leaving office reach exiting 2ndary home arrive car highway road street home Situation leaving office reach exiting 2ndary home arrive car highway road street home Situation R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 8

9 Advantages of D Learning D methods do not require a model of the environment, only experience D, but not MC, methods can be fully incremental You can learn before knowing the final outcome Less memory Less peak computation You can learn without the final outcome From incomplete sequences Both MC and D converge (under certain assumptions to be detailed later), but which is faster? R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 9

10 Random Walk Example A B C D E start 1 Estimated value Values learned by D(0) after various numbers of episodes A B C D E State true values R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 10

11 D and MC on the Random Walk α=.01 RMS error, averaged over states α=.15 D α=.02 MC α= Walks / Episodes Data averaged over 100 sequences of episodes α=.1 α=.04 α=.03 R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 11

12 Optimality of D(0) Batch Updating: train completely on a finite amount of data, e.g., train repeatedly on 10 episodes until convergence. Compute updates according to D(0), but only update estimates after each complete pass through the data. For any finite Markov prediction task, under batch updating, D(0) converges for sufficiently small α. Constant-α MC also converges under these conditions, but to a difference answer! R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 12

13 Random Walk under Batch Updating BACH RAINING RMS error, averaged over states D MC Walks / Episodes After each new episode, all previous episodes were treated as a batch, and algorithm was trained until convergence. All repeated 100 times. R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 13

14 You are the Predictor Suppose you observe the following 8 episodes: A, 0, B, 0 B, 1 B, 1 B, 1 B, 1 B, 1 B, 1 B, 0 V( A )? V( B)? R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 14

15 You are the Predictor A r = 0 100% B r = 1 75% r = 0 25% V( A )? R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 15

16 You are the Predictor he prediction that best matches the training data is V(A)=0 his minimizes the mean-square-error on the training set his is what a batch Monte Carlo method gets If we consider the sequentiality of the problem, then we would set V(A)=.75 his is correct for the maximum likelihood estimate of a Markov model generating the data i.e, if we do a best fit Markov model, and assume it is exactly correct, and then compute what it predicts (how?) his is called the certainty-equivalence estimate his is what D(0) gets R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 16

17 Learning An Action-Value Function Estimate Q π for the current behavior policy π. r t+1 st s t+1 r t+2 s t+1,a t+1 s t,a t s t+2 s t+2,a t+2 After every transition from a nonterminal state s, do this : Q s, a Q s, a α r γ Q s, a Q s, a If ( ) ( ) + + ( ) ( ) t t t t t + 1 t + 1 t + 1 t t s is terminal, then Q( s, a ) =. t + 1 t + 1 t [ ] t R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 17

18 Sarsa: On-Policy D Control urn this into a control method by always updating the policy to be greedy with respect to the current estimate: R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 18

19 Windy Gridworld S G standard moves king's moves undiscounted, episodic, reward = 1 until goal R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 19

20 Results of Sarsa on the Windy Gridworld S G Episodes ime steps R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 20

21 Q-Learning: Off-Ploicy D Control One - step Q - learning : [ ] ( ) ( ) + + ( ) ( ) Q s, a Q s, a α r γ max Q s, a Q s, a t t t t t + 1 t + 1 t t a R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 21

22 Cliffwalking r = 1 safe path S h e C l i f f G optimal path r = 100 ε greedy, ε = Sarsa Reward per epsiode Q-learning Episodes R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 22

23 Actor-Critic Methods state Critic Actor Value Function Policy D error action Explicit representation of policy as well as value function Minimal computation to select actions Can learn an explicit stochastic policy Can put constraints on policies reward Appealing as psychological and neural models Environment R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 23

24 Actor-Critic Details D - error is used to evaluate actions : δ = r + γ V( s ) V( s ) t t + 1 t + 1 t If actions are determined by preferences, p( s, a), as follows : { } = π ( s, a) = Pr a = a s = s t t t e e then you can update the preferences like this : p( s, a ) p( s, a ) + β δ t t t t t b p( s, a) p( s, b), R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 24

25 Dopamine Neurons and D Error W. Schultz et al. Universite de Fribourg R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 25

26 Average Reward Per ime Step Average expected reward per time step under policy π : ρ π 1 n = lim E { r } n n t = 1 π t the same for each state if ergodic Value of a state relative to ρ π { t + k t } π π V s E r ρ s s ( ) = = k = 1 π Value of a state - action pair relative to ρ : π { t + k t t } π π Q s, a E r ρ s s, a a ( ) = = = k = 1 π : R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 26

27 R-Learning R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 27

28 Access-Control Queuing ask n servers Customers have four different priorities, which pay reward of 1, 2, 3, or 4, if served At each time step, customer at head of queue is accepted (assigned to a server) or removed from the queue Proportion of randomly distributed high priority customers in queue is h Busy server becomes free with probability p on each time step Statistics of arrivals and departures are unknown Value of best action Apply R-learning n=10, h=.5, p= Priority 0 1 REJEC POLICY ACCEP Number of free servers priority 8 priority 4 priority 2 priority Number of free servers VALUE FUNCION R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 28

29 Afterstates Usually, a state-value function evaluates states in which the agent can take an action. But sometimes it is useful to evaluate states after agent has acted, as in tic-tac-toe. Why is this useful? X O + X O X + X X O X What is this in general? R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 29

30 Summary D prediction Introduced one-step tabular model-free D methods Extend prediction to control by employing some form of GPI On-policy control: Sarsa Off-policy control: Q-learning and R-learning hese methods bootstrap and sample, combining aspects of DP and MC methods R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 30

Monte 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: 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 information

Introduction to Reinforcement Learning. Part 5: Temporal-Difference Learning

Introduction 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 information

Chapter 6: Temporal Difference Learning

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 Compare efficiency of D learning with

More information

Temporal Difference. Learning KENNETH TRAN. Principal Research Engineer, MSR AI

Temporal Difference. Learning KENNETH TRAN. Principal Research Engineer, MSR AI Temporal Difference Learning KENNETH TRAN Principal Research Engineer, MSR AI Temporal Difference Learning Policy Evaluation Intro to model-free learning Monte Carlo Learning Temporal Difference Learning

More information

Reinforcement Learning

Reinforcement 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 information

Temporal difference learning

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).

More information

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 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 information

Introduction 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 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 information

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 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 information

The Book: Where we are and where we re going. CSE 190: Reinforcement Learning: An Introduction. Chapter 7: Eligibility Traces. Simple Monte Carlo

The 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 information

Lecture 23: Reinforcement Learning

Lecture 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 information

Introduction. Reinforcement Learning

Introduction. 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 information

CS599 Lecture 1 Introduction To RL

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

More information

Introduction to Reinforcement Learning. CMPT 882 Mar. 18

Introduction 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 information

What we learned last time

What 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

Temporal-Difference Learning

Temporal-Difference Learning R L & A I Temporal-Difference Learning Rich Sutton Reinforcement Learning & Artificial Intelligence Laboratory Alberta Machine Intelligence Institute Dept. of Computing Science, University of Alberta Canada

More information

Machine Learning. Reinforcement learning. Hamid Beigy. Sharif University of Technology. Fall 1396

Machine 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 information

arxiv: v1 [cs.ai] 5 Nov 2017

arxiv: v1 [cs.ai] 5 Nov 2017 arxiv:1711.01569v1 [cs.ai] 5 Nov 2017 Markus Dumke Department of Statistics Ludwig-Maximilians-Universität München markus.dumke@campus.lmu.de Abstract Temporal-difference (TD) learning is an important

More information

Reinforcement Learning. Value Function Updates

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

More information

Review: 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. 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 information

This 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. 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 information

Chapter 4: Dynamic Programming

Chapter 4: Dynamic Programming Chapter 4: Dynamic Programming Objectives of this chapter: Overview of a collection of classical solution methods for MDPs known as dynamic programming (DP) Show how DP can be used to compute value functions,

More information

Reinforcement Learning

Reinforcement 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 information

Open Theoretical Questions in Reinforcement Learning

Open 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 information

Prof. Dr. Ann Nowé. Artificial Intelligence Lab ai.vub.ac.be

Prof. 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 information

Basics of reinforcement learning

Basics of reinforcement learning Basics of reinforcement learning Lucian Buşoniu TMLSS, 20 July 2018 Main idea of reinforcement learning (RL) Learn a sequential decision policy to optimize the cumulative performance of an unknown system

More information

Reinforcement learning an introduction

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,

More information

CMU Lecture 12: Reinforcement Learning. Teacher: Gianni A. Di Caro

CMU 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 information

Reinforcement Learning

Reinforcement Learning Reinforcement Learning 1 Reinforcement Learning Mainly based on Reinforcement Learning An Introduction by Richard Sutton and Andrew Barto Slides are mainly based on the course material provided by the

More information

Planning in Markov Decision Processes

Planning in Markov Decision Processes Carnegie Mellon School of Computer Science Deep Reinforcement Learning and Control Planning in Markov Decision Processes Lecture 3, CMU 10703 Katerina Fragkiadaki Markov Decision Process (MDP) A Markov

More information

Reinforcement Learning. Machine Learning, Fall 2010

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

More information

Reinforcement Learning. Spring 2018 Defining MDPs, Planning

Reinforcement 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 information

Reinforcement Learning II

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

More information

Reinforcement Learning. Introduction

Reinforcement Learning. Introduction Reinforcement Learning Introduction Reinforcement Learning Agent interacts and learns from a stochastic environment Science of sequential decision making Many faces of reinforcement learning Optimal control

More information

ECE276B: Planning & Learning in Robotics Lecture 16: Model-free Control

ECE276B: Planning & Learning in Robotics Lecture 16: Model-free Control ECE276B: Planning & Learning in Robotics Lecture 16: Model-free Control Lecturer: Nikolay Atanasov: natanasov@ucsd.edu Teaching Assistants: Tianyu Wang: tiw161@eng.ucsd.edu Yongxi Lu: yol070@eng.ucsd.edu

More information

Reinforcement 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.

More information

Grundlagen der Künstlichen Intelligenz

Grundlagen 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 information

Lecture 3: The Reinforcement Learning Problem

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

More information

Reinforcement Learning. George Konidaris

Reinforcement 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 information

Lecture 7: Value Function Approximation

Lecture 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 information

6 Reinforcement Learning

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,

More information

Reinforcement Learning

Reinforcement 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 information

Reinforcement Learning with Function Approximation. Joseph Christian G. Noel

Reinforcement 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 information

Balancing 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 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 information

Chapter 3: The Reinforcement Learning Problem

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

More information

Lecture 25: Learning 4. Victor R. Lesser. CMPSCI 683 Fall 2010

Lecture 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 information

PART A and ONE question from PART B; or ONE question from PART A and TWO questions from PART B.

PART A and ONE question from PART B; or ONE question from PART A and TWO questions from PART B. Advanced Topics in Machine Learning, GI13, 2010/11 Advanced Topics in Machine Learning, GI13, 2010/11 Answer any THREE questions. Each question is worth 20 marks. Use separate answer books Answer any THREE

More information

Reinforcement Learning. Summer 2017 Defining MDPs, Planning

Reinforcement 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 information

Reinforcement Learning

Reinforcement 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 information

Computational Reinforcement Learning: An Introduction

Computational Reinforcement Learning: An Introduction Computational Reinforcement Learning: An Introduction Andrew Barto Autonomous Learning Laboratory School of Computer Science University of Massachusetts Amherst barto@cs.umass.edu 1 Artificial Intelligence

More information

Lecture 3: Markov Decision Processes

Lecture 3: Markov Decision Processes Lecture 3: Markov Decision Processes Joseph Modayil 1 Markov Processes 2 Markov Reward Processes 3 Markov Decision Processes 4 Extensions to MDPs Markov Processes Introduction Introduction to MDPs Markov

More information

Reinforcement Learning Part 2

Reinforcement 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 information

The Reinforcement Learning Problem

The Reinforcement Learning Problem The Reinforcement Learning Problem Slides based on the book Reinforcement Learning by Sutton and Barto Formalizing Reinforcement Learning Formally, the agent and environment interact at each of a sequence

More information

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

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 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 information

QUEUING MODELS AND MARKOV PROCESSES

QUEUING MODELS AND MARKOV PROCESSES QUEUING MODELS AND MARKOV ROCESSES Queues form when customer demand for a service cannot be met immediately. They occur because of fluctuations in demand levels so that models of queuing are intrinsically

More information

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. 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 information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.262 Discrete Stochastic Processes Midterm Quiz April 6, 2010 There are 5 questions, each with several parts.

More information

Elements of Reinforcement Learning

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,

More information

15-889e Policy Search: Gradient Methods Emma Brunskill. All slides from David Silver (with EB adding minor modificafons), unless otherwise noted

15-889e Policy Search: Gradient Methods Emma Brunskill. All slides from David Silver (with EB adding minor modificafons), unless otherwise noted 15-889e Policy Search: Gradient Methods Emma Brunskill All slides from David Silver (with EB adding minor modificafons), unless otherwise noted Outline 1 Introduction 2 Finite Difference Policy Gradient

More information

Reading Response: Due Wednesday. R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 1

Reading Response: Due Wednesday. R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 1 Reading Response: Due Wednesday R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 1 Another Example Get to the top of the hill as quickly as possible. reward = 1 for each step where

More information

Notes on Reinforcement Learning

Notes 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 information

Grundlagen der Künstlichen Intelligenz

Grundlagen der Künstlichen Intelligenz Grundlagen der Künstlichen Intelligenz Reinforcement learning Daniel Hennes 4.12.2017 (WS 2017/18) University Stuttgart - IPVS - Machine Learning & Robotics 1 Today Reinforcement learning Model based and

More information

https://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 information

Payments System Design Using Reinforcement Learning: A Progress Report

Payments System Design Using Reinforcement Learning: A Progress Report Payments System Design Using Reinforcement Learning: A Progress Report A. Desai 1 H. Du 1 R. Garratt 2 F. Rivadeneyra 1 1 Bank of Canada 2 University of California Santa Barbara 16th Payment and Settlement

More information

, and rewards and transition matrices as shown below:

, 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

More information

Course basics. CSE 190: Reinforcement Learning: An Introduction. Last Time. Course goals. The website for the class is linked off my homepage.

Course basics. CSE 190: Reinforcement Learning: An Introduction. Last Time. Course goals. The website for the class is linked off my homepage. Course basics CSE 190: Reinforcement Learning: An Introduction The website for the class is linked off my homepage. Grades will be based on programming assignments, homeworks, and class participation.

More information

Generalization and Function Approximation

Generalization 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 information

Chapter 3: The Reinforcement Learning Problem

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

More information

Reinforcement Learning: the basics

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

More information

ARTIFICIAL INTELLIGENCE. Reinforcement learning

ARTIFICIAL INTELLIGENCE. Reinforcement learning INFOB2KI 2018-2019 Utrecht University The Netherlands ARTIFICIAL INTELLIGENCE Reinforcement learning Lecturer: Silja Renooij These slides are part of the INFOB2KI Course Notes available from www.cs.uu.nl/docs/vakken/b2ki/schema.html

More information

Reinforcement Learning. Up until now we have been

Reinforcement Learning. Up until now we have been Reinforcement Learning Slides by Rich Sutton Mods by Dan Lizotte Refer to Reinforcement Learning: An Introduction by Sutton and Barto Alpaydin Chapter 16 Up until now we have been Supervised Learning Classifying,

More information

Key concepts: Reward: external «cons umable» s5mulus Value: internal representa5on of u5lity of a state, ac5on, s5mulus W the learned weight associate

Key concepts: Reward: external «cons umable» s5mulus Value: internal representa5on of u5lity of a state, ac5on, s5mulus W the learned weight associate Key concepts: Reward: external «cons umable» s5mulus Value: internal representa5on of u5lity of a state, ac5on, s5mulus W the learned weight associated to the value Teaching signal : difference between

More information

CS Machine Learning Qualifying Exam

CS Machine Learning Qualifying Exam CS Machine Learning Qualifying Exam Georgia Institute of Technology March 30, 2017 The exam is divided into four areas: Core, Statistical Methods and Models, Learning Theory, and Decision Processes. There

More information

Lecture 8: Policy Gradient

Lecture 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 information

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. 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

More information

ROB 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. 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 information

Probabilistic Planning. George Konidaris

Probabilistic Planning. George Konidaris Probabilistic Planning George Konidaris gdk@cs.brown.edu Fall 2017 The Planning Problem Finding a sequence of actions to achieve some goal. Plans It s great when a plan just works but the world doesn t

More information

Chapter 8: Generalization and Function Approximation

Chapter 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 information

Emphatic Temporal-Difference Learning

Emphatic Temporal-Difference Learning Emphatic Temporal-Difference Learning A Rupam Mahmood Huizhen Yu Martha White Richard S Sutton Reinforcement Learning and Artificial Intelligence Laboratory Department of Computing Science, University

More information

Marks. bonus points. } Assignment 1: Should be out this weekend. } Mid-term: Before the last lecture. } Mid-term deferred exam:

Marks. bonus points. } Assignment 1: Should be out this weekend. } Mid-term: Before the last lecture. } Mid-term deferred exam: Marks } Assignment 1: Should be out this weekend } All are marked, I m trying to tally them and perhaps add bonus points } Mid-term: Before the last lecture } Mid-term deferred exam: } This Saturday, 9am-10.30am,

More information

Introduction to Reinforcement Learning

Introduction to Reinforcement Learning CSCI-699: Advanced Topics in Deep Learning 01/16/2019 Nitin Kamra Spring 2019 Introduction to Reinforcement Learning 1 What is Reinforcement Learning? So far we have seen unsupervised and supervised learning.

More information

PART A and ONE question from PART B; or ONE question from PART A and TWO questions from PART B.

PART A and ONE question from PART B; or ONE question from PART A and TWO questions from PART B. Advanced Topics in Machine Learning, GI13, 2010/11 Advanced Topics in Machine Learning, GI13, 2010/11 Answer any THREE questions. Each question is worth 20 marks. Use separate answer books Answer any THREE

More information

Introduction to Reinforcement Learning

Introduction to Reinforcement Learning Introduction to Reinforcement Learning Rémi Munos SequeL project: Sequential Learning http://researchers.lille.inria.fr/ munos/ INRIA Lille - Nord Europe Machine Learning Summer School, September 2011,

More information

An Introduction to Reinforcement Learning

An Introduction to Reinforcement Learning An Introduction to Reinforcement Learning Shivaram Kalyanakrishnan shivaram@cse.iitb.ac.in Department of Computer Science and Engineering Indian Institute of Technology Bombay April 2018 What is Reinforcement

More information

Sequential decision making under uncertainty. Department of Computer Science, Czech Technical University in Prague

Sequential decision making under uncertainty. Department of Computer Science, Czech Technical University in Prague Sequential decision making under uncertainty Jiří Kléma Department of Computer Science, Czech Technical University in Prague https://cw.fel.cvut.cz/wiki/courses/b4b36zui/prednasky pagenda Previous lecture:

More information

Actor-critic methods. Dialogue Systems Group, Cambridge University Engineering Department. February 21, 2017

Actor-critic methods. Dialogue Systems Group, Cambridge University Engineering Department. February 21, 2017 Actor-critic methods Milica Gašić Dialogue Systems Group, Cambridge University Engineering Department February 21, 2017 1 / 21 In this lecture... The actor-critic architecture Least-Squares Policy Iteration

More information

An Adaptive Clustering Method for Model-free Reinforcement Learning

An Adaptive Clustering Method for Model-free Reinforcement Learning An Adaptive Clustering Method for Model-free Reinforcement Learning Andreas Matt and Georg Regensburger Institute of Mathematics University of Innsbruck, Austria {andreas.matt, georg.regensburger}@uibk.ac.at

More information

Probability and Statistics Concepts

Probability and Statistics Concepts University of Central Florida Computer Science Division COT 5611 - Operating Systems. Spring 014 - dcm Probability and Statistics Concepts Random Variable: a rule that assigns a numerical value to each

More information

Reinforcement Learning

Reinforcement 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 information

Machine Learning I Continuous Reinforcement Learning

Machine 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 information

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. 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 information

Rewards and Value Systems: Conditioning and Reinforcement Learning

Rewards and Value Systems: Conditioning and Reinforcement Learning Rewards and Value Systems: Conditioning and Reinforcement Learning Acknowledgements: Many thanks to P. Dayan and L. Abbott for making the figures of their book available online. Also thanks to R. Sutton

More information

Reinforcement learning

Reinforcement learning Reinforcement learning Based on [Kaelbling et al., 1996, Bertsekas, 2000] Bert Kappen Reinforcement learning Reinforcement learning is the problem faced by an agent that must learn behavior through trial-and-error

More information

CS599 Lecture 2 Function Approximation in RL

CS599 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 information

Short Course: Multiagent Systems. Multiagent Systems. Lecture 1: Basics Agents Environments. Reinforcement Learning. This course is about:

Short Course: Multiagent Systems. Multiagent Systems. Lecture 1: Basics Agents Environments. Reinforcement Learning. This course is about: Short Course: Multiagent Systems Lecture 1: Basics Agents Environments Reinforcement Learning Multiagent Systems This course is about: Agents: Sensing, reasoning, acting Multiagent Systems: Distributed

More information

Reinforcement Learning and NLP

Reinforcement 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 information

CSC321 Lecture 22: Q-Learning

CSC321 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 information

INF 5860 Machine learning for image classification. Lecture 14: Reinforcement learning May 9, 2018

INF 5860 Machine learning for image classification. Lecture 14: Reinforcement learning May 9, 2018 Machine learning for image classification Lecture 14: Reinforcement learning May 9, 2018 Page 3 Outline Motivation Introduction to reinforcement learning (RL) Value function based methods (Q-learning)

More information

CS885 Reinforcement Learning Lecture 7a: May 23, 2018

CS885 Reinforcement Learning Lecture 7a: May 23, 2018 CS885 Reinforcement Learning Lecture 7a: May 23, 2018 Policy Gradient Methods [SutBar] Sec. 13.1-13.3, 13.7 [SigBuf] Sec. 5.1-5.2, [RusNor] Sec. 21.5 CS885 Spring 2018 Pascal Poupart 1 Outline Stochastic

More information

Machine Learning I Reinforcement Learning

Machine 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 information