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Reinforcement Learning Introduction. Subramanian Ramamoorthy School of Informatics 17 January 2012. Admin. Lecturer : Subramanian (Ram) Ramamoorthy IPAB, School of Informatics s.ramamoorthy@ed ( preferred method of contact) Informatics Forum 1.41, x505119

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Reinforcement learning introduction

Reinforcement LearningIntroduction

Subramanian Ramamoorthy

School of Informatics

17 January 2012


Lecturer: Subramanian (Ram) Ramamoorthy

IPAB, School of Informatics

s.ramamoorthy@ed (preferred method of contact)

Informatics Forum 1.41, x505119

Main Tutor: Majd Hawasly, M.Hawasly@sms.ed, IF 1.43

Class representative?

Mailing list: Are you on it – I will use it for announcements!

Reinforcement Learning



  • Tuesday and Friday 12:10 - 13:00 (FH 3.D02 and AT 2.14)

    Assessment: Homework/Exam 10+10% / 80%

  • HW1: Out 7 Feb, Due 23 Feb

    • Use MDP based methods in a robot navigation problem

  • HW2: Out 6 Mar, Due 29 Mar

    • POMDP version of the previous exercise

Reinforcement Learning


Tutorials (M. Hawasly, K. Etessami, M. von Rossum), tentatively:

T1 [Warm-up: Formulation, bandits] - week of 30th Jan T2 [Dyn. Prog.] - week of 6th Feb T3 [MC methods] - week of 13th Feb T4 [TD methods] - week of 27th Feb T5 [POMDP] - week of 12th Mar

  • We’ll assign questions (combination of pen & paper and computational exercises) – you attempt them before sessions.

  • Tutor will discuss and clarify concepts underlying exercises

  • Tutorials are not assessed; gain feedback from participation

Reinforcement Learning



  • Lecture slides will be uploaded as they become available


  • R. Sutton and A. Barto, Reinforcement Learning, MIT Press, 1998

  • S. Thrun, W. Burgard, D. Fox, Probabilistic Robotics, MIT Press, 2006

  • Other readings: uploaded to web page as needed

    Background: Mathematics, Matlab, Exposure to machine learning?

Reinforcement Learning

Problem of learning from interaction
Problem of Learning from Interaction

  • with environment

  • to achieve some goal

  • Baby playing. No teacher. Sensorimotor connection to environment.

    – Cause – effect

    – Action – consequences

    – How to achieve goals

  • Learning to drive car, hold conversation, etc.

  • Environment’s response affects our subsequent actions

  • We find out the effects of our actions later

  • Reinforcement Learning

    Rough history of rl ideas
    Rough History of RL Ideas

    • Psychology – learning by trial and error

      … actions followed by good or bad outcomes have their tendency to be reselected altered accordingly

      • Selectional: try alternatives and pick good ones

      • Associative: associate alternatives with particular situations

    • Computational studies (e.g., credit assignment problem)

      • Minsky’s SNARC, 1950

      • Michie’s MENACE, BOXES, etc. 1960s

    • Temporal Difference learning (Minsky, Samuel, Shannon, …)

      • Driven by differences between successive estimates over time

    Reinforcement Learning

    Rough history of rl contd
    Rough History of RL, contd.

    • In 1970-80, many researchers, e.g., Klopf, Sutton & Barto,…, looked seriously at issues of “getting results from the environment” as opposed to supervised learning (distinction is subtle!)

      • Although supervised learning methods such as backpropagation were sometimes used, emphasis was different

    • Stochastic optimal control (mathematics, operations research)

      • Deep roots: Hamilton-Jacobi → Bellman/Howard

      • By the 1980s, people began to realize the connection between MDPs and the RL problem as above…

    Reinforcement Learning

    What is the nature of the problem
    What is the Nature of the Problem?

    • As you can tell from the history, many ways to understand the problem – you will see this as we proceed through course

    • One unifying perspective: Stochastic optimization over time

    • Given (a) Environment to interact with, (b) Goal

    • Formulate cost (or reward)

    • Objective: Maximize rewards over time

    • The catch: Reward may not be rich enough as optimization is over time – selecting entire paths

    • Let us unpack this through a few application examples…

    Reinforcement Learning

    Motivating rl problem 1 control
    Motivating RL Problem 1: Control

    Reinforcement Learning

    The notion of feedback control
    The Notion of Feedback Control

    Compute corrective actions so as

    to minimise a measured error

    Design involves the following:

    • What is a good policy for

      determining the corrections?

    • What performance specifications

      are achievable by such systems?

    Reinforcement Learning

    Feedback control
    Feedback Control

    • The Proportional-Integral-Derivative Controller Architecture

    • ‘Model-free’ technique, works reasonably in simple (typically first & second order) systems

    • More general: consider feedback architecture, u= - Kx

    • When applied to a linear system, closed-loop dynamics:

    • Using basic linear algebra, you can study dynamic properties

    • e.g., choose Kto place the eigenvalues and eigenvectors of the closed-loop system

    Reinforcement Learning

    The optimal feedback controller
    The Optimal Feedback Controller

    • Begin with the following:

      • Dynamics: “Velocity” = f(State, Control)

      • Cost: Integral involving State/Control squared (e.g., x’Qx)

    • Basic idea: Optimal control actions correspond to a cost or value surface in an augmented state space

    • Computation: What is the path equivalent of f’(x) = 0?

    • In the special case of linear dynamics and quadratic cost, we can explicitly solve the resulting Ricatti equation

    Reinforcement Learning

    The linear quadratic regulator
    The Linear Quadratic Regulator

    Reinforcement Learning

    Idea in pictures
    Idea in Pictures

    Main point to takeaway: notion of value surface

    Reinforcement Learning

    Connection between reinforcement learning and control problems
    Connection between Reinforcement Learning and Control Problems

    • RL has close connection to stochastic control (and OR)

    • Main differences seem to arise from what is ‘given’

    • Also, motivations such as adaptation

    • In RL, we emphasize sample-based computation, stochastic approximation

    Reinforcement Learning

    Example application 2 inventory control
    Example Application 2: Inventory Control Problems

    • Objective: Minimize total inventory cost

    • Decisions:

      • How much to order?

      • When to order?

    Reinforcement Learning

    Components of total cost
    Components of Total Cost Problems

    • Cost of items

    • Cost of ordering

    • Cost of carrying or holding inventory

    • Cost of stockouts

    • Cost of safety stock (extra inventory held to help avoid stockouts)

    Reinforcement Learning

    The economic order quantity model how much to order
    The Economic Order Quantity Model Problems- How Much to Order?

    • Demand is known and constant

    • Lead time is known and constant

    • Receipt of inventory is instantaneous

    • Quantity discounts are not available

    • Variable costs are limited to: ordering cost and carrying (or holding) cost

    • If orders are placed at the right time, stockouts can be avoided

    Reinforcement Learning

    Inventory level over time based on eoq assumptions
    Inventory Level Over Time Problems Based on EOQ Assumptions

    Reinforcement Learning

    Eoq model total cost
    EOQ Model Total Cost Problems

    At optimal order quantity (Q*): Carrying cost = Ordering cost



    Reinforcement Learning

    Realistically how much to order if these assumptions didn t hold
    Realistically, How Much to Order – ProblemsIf these Assumptions Didn’t Hold?

    • Demand is known and constant

    • Lead time is known and constant

    • Receipt of inventory is instantaneous

    • Quantity discounts are not available

    • Variable costs are limited to: ordering cost and carrying (or holding) cost

    • If orders are placed at right time, stockouts can be avoided

    The result may be need for a more detailed stochastic optimization.

    Reinforcement Learning

    Example application 3 dialogue mgmt
    Example Application 3: Dialogue Mgmt. Problems

    [S. Singh et al., JAIR 2002]

    Reinforcement Learning

    Dialogue management what is going on
    Dialogue Management: What is Going On? Problems

    • System is interacting with the user by choosing things to say

    • Possible policies for things to say is huge, e.g., 242 in NJFun

      Some questions:

    • What is the model of dynamics?

    • What is being optimized?

    • How much experimentation is possible?

    Reinforcement Learning

    The dialogue management loop
    The Dialogue Management Loop Problems

    Reinforcement Learning

    Common themes in these examples
    Common Themes in these Examples Problems

    • Stochastic Optimization – make decisions!

      Over time; may not be immediately obvious how we’re doing

    • Some notion of cost/reward is implicit in problem – defining this, and constraints to defining this, are key!

    • Often, we may need to work with models that can only generate sample traces from experiments

    Reinforcement Learning