1. Search

2. Many AI Systems use Search!
Define a representation for the problem
Use search and a criteria to solve the problem
Rules systems do search!
Search is a weak method
Search does not depend on domain knowledge

3. History Shannon proposed chess by search in 1950
Samuel does checkers by search in late 50’s
Logic Theorist of Newell and Simon in 63
Geometry Theorem Prover by Gelernter in 63

4. Problem Types Path finding Two player Games Constraint Satisfaction
Puzzles e.g. Rubic’s Cube
Two player Games
Constraint Satisfaction
Eight Queens

5. Problem Spaces Hypothesis: [Newell and Simon] A problem space is:
All goal-oriented problem symbolic activity occurs in a problem space
A problem space is:
Set of states
Set of operations mapping state to new state
A problem instance is:
A goal and stating state.

6. Choosing a Problem Space
There may be several choices!
Looking at a problem different way!
Space may allow sub-goals or macro-operations
If one level of abstraction is good, is multiple levels better?
Search direction? Forward or backward.

7. General Questions: Is search the best way to solve the problem?
Which search methods can solve the problem?
Efficiency?

8. Blind Search Methods that don’t use any domain knowledge!
Example – given a highway map find a path from A to B.
Costs:
Computation cost of finding a path
Travel cost of executing the path

9. Net Search Start a A Add to paths one link at a time
Iterate until you reach B
Loop removal!
This is really a tree search!

10. Tree Search Cost Basically Exponential! Depth First Breadth First
Choice based on branching factor
Non deterministic (random)

11. Heuristically Informed Search
Order search choices by a quality function
Effect is often increased efficiency
DFS -> hill climbing
For the map problem: straight line distance
Sort paths by straight line distance from end point to goal!

12. Hill Climbing Problems
Foothills
Local vs. Global optima
Plateau
Which way to go?
Ridge
More Subtle
Ridge running at an angle to our paths means all steps go down!

13. Simulated Annealing Example: Ping Pong Ball Annealing Neural Nets
means slowly lowering temperature
Temperature is related to randomness
Neural Nets

14. Some General Principles
More knowledge leads to reduced search!
Use another search space!

15. Beam Search Use a quality function to sort paths Purge paths by “Beam”
Keep best N
Keep paths within a tolerance from the quality

16. Branch and Bound Use lower bound estimate for remaining path
Good when estimate is good.
Dynamic Programming Principle:
Best path thorough an intermediate node is the best path to the node and the best path from the node to the goal
In B&B delete multiple paths to a node keeping the lowest code path.
Good when multiple paths converge

17. B & B (cont.)
A* Search
Lower bound combined with Dynamic Programming Principle

18. Adversarial Search Game Tree Exhaustive search: impossible!
Nodes represent Game State (e.g. board position)
Levels represent choices by alternating players
Exhaustive search: impossible!
Some Game Theory Ideas
Games represent more than “games”
Zero Sum games

19. Minmax Search Need Static Evaluator Use look ahead
Rates game state’s value for a player
One player needs to minimize, the other needs to maximize
Use look ahead

20. Alpha-Beta If an idea is clearly bad – don’t waste time on it!
Keep two params –
alpha for maximer
Beta for minimizer
Use terms to limit search

21. Heuristic Additions Progressive deepening Horizon Effect
Use breadth first
Limit by amount of time available
Horizon Effect
Some paths need to analyzed to deeper levels
Singular-extension
Expand paths with values that standout from the rest

22. Heuristic Additions (cont.)
Heuristic Pruning to reduce search space

23. Games of Chance Chance can become a “player”
Tree has three types of layers
Max
Min
Chance

24. Partial Information in Games
Many card games have partial information!
Strategy based on belief states
Given information revealed so far
What does my opponent believe
What do I believe

25. Genetic Algorithms A topic we look a more later
Search in a genetic space
Problem solution encoded in genes
Crossover and Mutation
Evaluation function (Fitness)

26. “Online” Search Interleave computation and action Cost for inaction
Impossible to compute the search tree
Ex: Maze problems!
Search Types
DFS not BFS (Why?)
Hill Climbing (uses local information)
Random Walk
LRTA*

27. LRTA* Learning in Real Time A*
Requires
Deterministic, Finite, Safe
Results Table – [state X action]
Cost table (H)
Results and Cost are empty at start

28. Search Considered Search has solved some problems at an expert level:
Chess
Mathematical manipulation
Search has failed at:
Common sense reasoning
Language and Vision

29. Open Problems
Parallel Search
Learning Heuristic Evaluation Functions