Uninformed Search

1. Uninformed Search Reading: Chapter 3 by today, Chapter 4.1-4.3 by Wednesday, 9/12 Homework #2 will be given out on Wednesday DID YOU TURN IN YOUR SURVEY? USE COURSEWORKS AND TAKE THE TEST

2. Pending Questions • Class web page: • http://www.cs.columbia.edu/~kathy/cs4701 • Reminder: Don’t forget assignment 0 (survey). See courseworks

3. When solving problems, dig at the roots instead of just hacking at the leaves. • Anthony J. D'Angelo, The College Blue Book

4. Agenda • Introduction of search as a problem-solving paradigm • Uninformed search algorithms • Example using the 8-puzzle • Formulation of another example: sodoku • Transition to greedy search, one method for informed search

5. Goal-based Agents • Agents that work towards a goal • Select the action that more likely achieve the goal • Sometimes an action directly achieves a goal; sometimes a series of actions are required

6. Problem solving as search • Goal formulation • Problem formulation • Actions • States

7. Uninformed • Search through the space of possible solutions • Use no knowledge about which path is likely to be best

8. Characteristics • Before actually doing something to solve a puzzle, an intelligent agent explores possibilities “in its head” • Search = “mental exploration of possibilities” • Making a good decision requires exploring several possibilities • Execute the solution once it’s found

9. Formulating Problems as Search Given an initial state and a goal, find the sequence of actions leading through a sequence of states to the final goal state. Terms: • Successor function: given action and state, returns {action, successors} • State space: the set of all states reachable from the initial state • Path: a sequence of states connected by actions • Goal test: is a given state the goal state? • Path cost: function assigning a numeric cost to each path • Solution: a path from initial state to goal state

10. Example: the 8-puzzle • How would you use AI techniques to solve the 8-puzzle problem?

11. 8-puzzle URLS • http://www.permadi.com/java/puzzle8 • http://www.cs.rmit.edu.au/AI-Search/Product

12. 8 Puzzle • States: integer locations of tiles • (0 1 2 3 4 5 6 7 B) • (0 1 2)(3 4 5) (6 7 B) • Action: left, right, up, down • Goal test: is current state = (0 1 2 3 4 5 6 7 B)? • Path cost: same for all paths • Successor function: given {up, (5 2 3 B 1 8 4 7 6)} -> ? • What would the state space be for this problem?

13. What are we searching? • State space vs. search space • State represents a physicalconfiguration • Search space represents a tree/graph of possible solutions… an abstract configuration • Nodes • Abstract data structure in search space • Parent, children, depth, path cost, associated state • Expand • A function that given a node, creates all children nodes, using successsor function

15. Data structures: Searching data AI: Searching solutions

16. Uninformed Search Strategies The strategy gives the order in which the search space is searched • Breadth first • Depth first • Depth limited search • Iterative deepening • Uniform cost

17. Breadth first Algorithm

22. Depth-first Algorithm

31. Complexity Analysis • Completeness: is the algorithm guaranteed to find a solution when there is one? • Optimality: Does the strategy find the optimal solution? • Time: How long does it take to find a solution? • Space: How much memory is needed to perform the search?

32. Cost variables • Time: number of nodes generated • Space: maximum number of nodes stored in memory • Branching factor: b • Maximum number of successors of any node • Depth: d • Depth of shallowest goal node • Path length: m • Maximum length of any path in the state space

33. Can we combine benefits of both? • Depth limited • Select some limit in depth to explore the problem using DFS • How do we select the limit? • Iterative deepening • DFS with depth 1 • DFS with depth 2 up to depth d

37. Fully observable Deterministic Episodic Static Discrete Single agent Partially observable Stochastic Sequential Dynamic Continuous Multiagent Properties of the task environment?

38. Three types of incompleteness • Sensorless problems • Contingency problems • Adversarial problems • Exploration problems

39. End of Class Questions?

40. Sodoku

41. Informed Search

42. Heuristics • Suppose 8-puzzle off by one • Is there a way to choose the best move next? • Good news: Yes! • We can use domain knowledge or heuristic to choose the best move

44. Nature of heuristics • Domain knowledge: some knowledge about the game, the problem to choose • Heuristic: a guess about which is best, not exact • Heuristic function, h(n): estimate the distance from current node to goal

45. Heuristic for the 8-puzzle • # tiles out of place (h1) • Manhattan distance (h2) • Sum of the distance of each tile from its goal position • Tiles can only move up or down  city blocks

46. Goal State h1=1 h2=1 h1=5 h2=1+1+1+2+2=7

47. Best first searches • A class of search functions • Choose the “best” node to expand next • Use an evaluation function for each node • Estimate of desirability • Implementation: sort fringe, open in order of desirability • Today: greedy search, A* search

48. Greedy search • Evaluation function = heuristic function • Expand the node that appears to be closest to the goal

49. Greedy Search • OPEN = start node; CLOSED = empty • While OPEN is not empty do • Remove leftmost state from OPEN, call it X • If X = goal state, return success • Put X on CLOSED • SUCCESSORS = Successor function (X) • Remove any successors on OPEN or CLOSED • Compute heuristic function for each node • Put remaining successors on either end of OPEN • Sort nodes on OPEN by value of heuristic function • End while

50. End of Class Questions?