1
Foundations of Artificial Intelligence
Reinforcement Learning
CS472 – Fall 2007
Thorsten Joachims
Reinforcement Learning
•
Problem
–
Make sequence of decisions (policy) to get to goal / maximize utility
•
Search Problems so far
–
Known environment
•
State space
•
Consequences of actions
•
Probability distribution of nondeterministic elements
–
Known utility / cost function
–
First compute the sequence of decisions, then execute (potentially re
compute)
•
RealWorld Problems
–
Environment is unknown a priori and needs to be explored
–
Utility function unknown – only examples are available for some states
•
No feedback on individual actions
•
Learn to act and to assign blame/credit to individual actions
–
Need to quickly react to unforeseen events (have learned what to do)
Reinforcement Learning
•
Issues
–
Agent knows the full environment a priori vs. unknown
environment
–
Agent can be passive (watch) or active (explore)
–
Feedback (i.e. rewards) in terminal states only; or a bit of
feedback in any state
–
How to measure and estimate the utility of each action
–
Environment fully observable, or partially observable
–
Have model of environment and effects of action…or not
Æ
Reinforcement Learning will address these issues!
Markov Decision Process
•
Representation of Environment:
–
finite set of states S
–
set of actions A for each state s
∈
S
•
Process
–
At each discrete time step, the agent
•
observes state s
t
∈
S and then
•
chooses action a
t
∈
A.
–
After that, the environment
•
gives agent an immediate reward r
t
•
changes state to s
t+1
(can be probabilistic)
Markov Decision Process
•
Model:
–
Initial state: S
0
–
Transition function: T(s,a,s’)
Æ
T(s,a,s’) is the probability of moving from state s to s’
when executing action a.
–
Reward function: R(s)
Æ
Real valued reward that the agent receives for entering
state s.
•
Assumptions
–
Markov property: T(s,a,s’) and R(s) only depend on current
state s, but not on any states visited earlier.
–
Extension: Function R may be nondeterministic as well
Example
Reward:
•
In terminal states reward of +1 / 1 and agent gets “stuck”
•
Each other state has a reward of 0.04.
1
2
3
1
2
3
 1
+ 1
4
START
0.8
0.1
0.1
• move into desired
direction with prob 80%
• move 90 degrees to left
with prob 10%
• move 90 degrees to right
with prob 10%
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2
Policy
•
Definition:
–
A policy
π
describes which
action an agent selects in
each state
– a=
π
(s)
•
Utility
–
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 JOACHIMS
 Artificial Intelligence, Machine Learning, Bellman equation, Markov decision process, Uπ

Click to edit the document details