W09

1. SEARCHING WITH NO TRANSITION MODEL –
ONLINE SEARCH

2. Offline vs. online search
Offline search: With the transition
model, we can
1. Initial state
2. Possible actions: ACTIONS
3. Transition model: RESULT
4. Goal test: GOAL-TEST
5. Cost: STEP-COST, PATH-COST
Online search: Without the transition model,
we need to

3. Online search is useful in
 There is a penalty for
 Nondeterministic environments:
 No environment model:
Examples of online search:

4. Competitive ratio
There are 2 types of path costs in online search:
 Actual path cost:
 Shortest path cost:
Competitive ratio = Actual path cost / Shortest path cost

5. Dead-end state
Some actions are irreversible, they lead to a dead-end state:

For example,
Safely explorable state space:
For example,

6. Online depth-first search agent
Source:
(Russell,
2016)

7. Why depth-first?
In online search: the agent actually walks in the environment.

In depth-first search: the agent only moves to its next position (with 1 or a few
actions)
However,


8. Online A* search: LRTA* (Learning Real-Time A*) algorithm
Ideas:
 At each step, from state s, agent moves to the successor s’
which has the best estimated cost:
 H(s):

9. Learning Real-Time A* agent
Source:
(Russell,
2016)

10. Demo
Source:
(Russell,
2016)

11. NOTE:

12. CONSTRAINT SATISFACTOIN
PROBLEMS
Main reference:
Chapters 6 of Russell, S., & Norvig, P. (2016). Artificial intelligence: a modern approach.

13. Previous algorithms use atomic state representation:
Now, we move to factored representation:
Constraint satisfaction problems:
Constraint satisfaction problems (CSP)

14. Defining a CSP
Three components:
 X:
 D:
 C:
A solution of a CSP:

15. Example: Map coloring problem
Problem: color each region
Problem components:
Image: pngwave

16. Example 2: Car assembly scheduling
Factories have the problem of job scheduling, subject to various constraints.
For example,

17. Example 2: Car assembly scheduling
Problem components:
Variables:
Domains:
Constraints:

18. Other examples
Discrete, finite domains:
Discrete, infinite domains:
Continuous domains:

19. Solve CSPs using
Constraint Propagation

20. Can CSPs be solved using searching on state space?
Yes, but
CSP solvers (e.g., constraint propagation methods) can be faster than state-space
searchers because
For example, once we have chosen {HaNoi = blue}

21. Constraint propagation
Using the constraints to reduce the domain (legal values) for a variable,
which in turn


22. Local consistency: the key idea of constraint propagation
Enforcing local consistency in each part of the graph causes inconsistent values to be
eliminated throughout the graph.
Types of local consistency:

23. Constraint graph
Nodes:
Arcs:

24. Node consistency
Enforcing domains to satisfy unary constraints.
For example,

25. Arc consistency
Enforcing domains to satisfy binary constraints.
Xi is arc-consistent with respect to Xj if
For example, consider the constraint 𝐘 = 𝐗𝟐
 To make the problem arc-consistent:
Example 2: Map coloring problem:

26. AC-3 algorithm
Source:
(Russell,
2016)

27. Sodoku problem
No digit appears twice in any row, column, or 3 ×
3 box.
Image:
(Russell,
2016)