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Admin

Lecturer: Subramanian (Ram) Ramamoorthy

IPAB, School of Informatics

[email protected] (preferred method of contact)

Informatics Forum 1.41, x505119

Main Tutor: Majd Hawasly, [email protected], IF 1.43

Class representative?

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

Reinforcement Learning

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

Reinforcement Learning

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

Reinforcement Learning

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?

Reinforcement Learning

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

- 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.

- 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?

- 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

Reinforcement Learning

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

- 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

- 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

Reinforcement Learning

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

- Objective: Minimize total inventory cost
- Decisions:
- How much to order?
- When to order?

Reinforcement Learning

Components of Total Cost

- 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?

- 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

Reinforcement Learning

EOQ Model Total Cost

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

Demand

Costs

Reinforcement Learning

Realistically, How Much to Order –If 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

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?

Reinforcement Learning

The Dialogue Management Loop

Reinforcement Learning

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

Reinforcement Learning

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