Reinforcement Learning

Introduction

Subramanian RamamoorthySchool of Informatics

17 January 2012

Admin

Lecturer: Subramanian (Ram) RamamoorthyIPAB, School of Informaticss.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!

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Admin

Lectures: • 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

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Admin

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

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Admin

Webpage: www.informatics.ed.ac.uk/teaching/courses/rl• Lecture slides will be uploaded as they become available

Readings:• 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?

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Problem of Learning from Interaction

with environmentto 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

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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

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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…17/01/2012 Reinforcement Learning 8

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…

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Motivating RL Problem 1: Control

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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 specificationsare achievable by such systems?

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Feedback Control

• The Proportional-Integral-Derivative Controller Architecture

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

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• 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 K to place the eigenvalues and eigenvectors of the closed-loop system

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

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The Linear Quadratic Regulator

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Idea in Pictures

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Main point to takeaway: notion of value surface

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

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Example Application 2: Inventory Control

Objective: Minimize total inventory cost

Decisions:How much to order?When to order?

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Components of Total Cost

1. Cost of items2. Cost of ordering3. Cost of carrying or holding inventory4. Cost of stockouts5. Cost of safety stock (extra inventory held to help avoid

stockouts)

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The Economic Order Quantity Model- How Much to Order?

1. Demand is known and constant2. Lead time is known and constant3. Receipt of inventory is instantaneous4. Quantity discounts are not available5. Variable costs are limited to: ordering cost and carrying (or

holding) cost6. If orders are placed at the right time, stockouts can be

avoided

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Inventory Level Over Time Based on EOQ Assumptions

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EOQ Model Total Cost

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

)/2( hCDCo

Demand Costs

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Realistically, How Much to Order –If these Assumptions Didn’t Hold?

1. Demand is known and constant2. Lead time is known and constant3. Receipt of inventory is instantaneous4. Quantity discounts are not available5. Variable costs are limited to: ordering cost and carrying (or

holding) cost6. If orders are placed at right time, stockouts can be avoided

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

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Example Application 3: Dialogue Mgmt.

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[S. Singh et al., JAIR 2002]

Dialogue Management: What is Going On?

• 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?

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The Dialogue Management Loop

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Common Themes in these Examples

• 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

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