Slides for Introduction to Stochastic Search
and Optimization (ISSO) by J. C. Spall
CHAPTER 11
REINFORCEMENT LEARNING VIA
TEMPORAL DIFFERENCES
•Organization of chapter in ISSO
–Introduction
–Delayed reinforcement
–Basic temporal difference algorithm
–Batch and online implementations of TD
–Examples
–Connections to stochastic approximation
Reinforcement Learning
• Reinforcement learning is important class of methods in
computer science, AI, engineering, etc.
– Based on common-sense idea that good results are
reinforced while bad results provide negative reinforcement
• Delayed reinforcement only provides output after several
intermediate “actions”
• Want to create model for predicting state of system
– Model depends on 
– “Training” or “learning” (estimating ) not based on methods
such as stochastic gradient (supervised learning) because
of delay in response
– Need learning method to cope with delayed response
11-2
Schematic of Delayed
Reinforcement Process
• Suppose time moves left to right in diagram below
• Z represents some system output at a future time
• zˆ0, zˆ1,..., zˆn represent some intermediate predictions of Z
11-3
Temporal Difference (TD) Learning
• Focus is delayed reinforcement problem
• Prediction function has form ẑt  ht(, xt), where  are
parameters and xt is input
• Need to estimate  from sequence of inputs and outputs
{x0, x1, ..., xn ; Z}
• TD learning is method for using zˆt  zˆt in training
rather than only inputs and outputs
– Implies that some forms of TD allow for updating of  value
before observing Z
– TD exploits prior information embedded in predictions to
modify 
n
ˆ
ˆ
• Basic form of TD for updating  is new  0   t0 ()t ,
where ()t is increment to be determined
11-4
Exercise 11.4 in ISSO: Conceptual
Example of Benefits of TD. Circles
denote game states.
90%
Novel
Loss
Bad
10%
Game
outcome
Win
11-5
Batch Version of TD Learning
11-6
Random-Walk Model
(Example 11.3 in ISSO)
• All walks begin in state S3
• Each step involves 50–50 chance of moving left or right
until terminal state Tleft or Tright is reached
• Use TD to estimate probabilities of reaching Tright from
any of states S1 , S2 , S3 , S4 , or S5
Start
Tleft
S1
S2
S3
S4
S5
Tright
11-7