CS347 – Introduction to Artificial Intelligence

1. CS347 – Introduction toArtificial Intelligence CS347 course website: http://web.mst.edu/~tauritzd/courses/cs347/ Dr. Daniel Tauritz (Dr. T) Department of Computer Science tauritzd@mst.edu http://web.mst.edu/~tauritzd/

2. What is AI? Systems that… • act like humans (Turing Test) • think like humans • think rationally • act rationally Play Ultimatum Game

3. How difficult is it to achieve AI? • Three Sisters Puzzle

4. Rational Agents • Environment • Sensors (percepts) • Actuators (actions) • Agent Function • Agent Program • Performance Measures

5. Rational Behavior Depends on: • Agent’s performance measure • Agent’s prior knowledge • Possible percepts and actions • Agent’s percept sequence

6. Rational Agent Definition “For each possible percept sequence, a rational agent selects an action that is expected to maximize its performance measure, given the evidence provided by the percept sequence and any prior knowledge the agent has.”

7. PEAS description & properties: • Fully/Partially Observable • Deterministic, Stochastic, Strategic • Episodic, Sequential • Static, Dynamic, Semi-dynamic • Discrete, Continuous • Single agent, Multiagent • Competitive, Cooperative • Known, Unknown

8. Problem-solving agents A definition: Problem-solving agents are goal based agents that decide what to do based on an action sequence leading to a goal state.

9. Environment Assumptions • Fully Observable • Single Agent • Discrete • Sequential • Known & Deterministic

10. Open-loop problem-solving steps • Problem-formulation (actions & states) • Goal-formulation (states) • Search (action sequences) • Execute solution

11. Well-defined problems • Initial state • Action set: ACTIONS(s) • Transition model: RESULT(s,a) • Goal test • Step cost: c(s,a,s’) • Path cost • Solution / optimal solution

12. Example problems • Vacuum world • Tic-tac-toe • 8-puzzle • 8-queens problem

13. Search trees • Root corresponds with initial state • Vacuum state space vs. search tree • Search algorithms iterate through goal testing and expanding a state until goal found • Order of state expansion is critical!

14. function TREE-SEARCH(problem) returns solution/fail initialize frontier using initial problem state loop do if empty(frontier) then return fail choose leaf node and remove it from frontier if chosen node contains goal state then return corresponding solution expand chosen node and add resulting nodes to frontier

15. Redundant paths • Loopy paths • Repeated states • Redundant paths

16. function GRAPH-SEARCH(problem) returns solution/fail initialize frontier using initial problem state initialize explored set to be empty loop do if empty(frontier) then return fail choose leaf node and remove it from frontier if chosen node contains goal state then return corresponding solution add chosen node to explored set expand chosen node and add resulting nodes to frontier only if not yet in frontier or explored set

17. Search node datastructure • n.STATE • n.PARENT-NODE • n.ACTION • n.PATH-COST States are NOT search nodes!

18. Frontier • Frontier = Set of leaf nodes • Implemented as a queue with ops: • EMPTY?(queue) • POP(queue) • INSERT(element,queue) • Queue types: FIFO, LIFO (stack), and priority queue

19. Problem-solving performance • Completeness • Optimality • Time complexity • Space complexity

20. Complexity in AI • b – branching factor • d – depth of shallowest goal node • m – max path length in state space • Time complexity: # generated nodes • Space complexity: max # nodes stored • Search cost: time + space complexity • Total cost: search + path cost

21. Tree Search • Breadth First Tree Search (BFTS) • Uniform Cost Tree Search (UCTS) • Depth-First Tree Search (DFTS) • Depth-Limited Tree Search (DLTS) • Iterative-Deepening Depth-First Tree Search (ID-DFTS)

22. Example state space #1

23. Breadth First Tree Search (BFTS) • Frontier: FIFO queue • Complete: if b and d are finite • Optimal: if path-cost is non-decreasing function of depth • Time complexity: O(b^d) • Space complexity: O(b^d)

24. Uniform Cost Search (UCS) • g(n) = lowest path-cost from start node to node n • Frontier: priority queue ordered by g(n)

25. Depth First Tree Search (DFTS) • Frontier: LIFO queue (a.k.a. stack) • Complete: no • Optimal: no • Time complexity: O(bm) • Space complexity: O(bm) • Backtracking version of DFTS has a space complexity of: O(m)

26. Depth-Limited Tree Search (DLTS) • Frontier: LIFO queue (a.k.a. stack) • Complete: not when l < d • Optimal: no • Time complexity: O(b^l) • Space complexity: O(bl) • Diameter: min # steps to get from any state to any other state

27. Diameter example 1

28. Diameter example 2

29. Iterative-Deepening Depth-First Tree Search (ID-DFTS) function ID-DFS(problem) returns solution/fail for depth = 0 to ∞ do result ← DLS(problem,depth) ifresult ≠ cutoff then return result • Complete: Yes, if b is finite • Optimal: Yes, if path-cost is nondecreasing function of depth • Time complexity: O(b^d) • Space complexity: O(bd)

30. Bidirectional Search BiBFTS • Complete: Yes, if b is finite • Optimal: Not “out of the box” • Time & Space complexity: O(bd/2)

31. Example state space #2

32. Best First Search (BeFS) • Select node to expand based on evaluation function f(n) • Typically node with lowest f(n) selected because f(n) correlated with path-cost • Represent frontier with priority queue sorted in ascending order of f-values

33. Path-cost functions • g(n) = lowest path-cost from start node to node n • h(n) = estimated non-negative path-cost of cheapest path from node n to a goal node [with h(goal)=0]

34. Heuristics • h(n) is a heuristic function • Heuristics incorporate problem-specific knowledge • Heuristics need to be relatively efficient to compute

35. Important BeFS algorithms • UCS: f(n) = g(n) • GBeFS: f(n) = h(n) • A*S: f(n) = g(n)+h(n)

36. GBeFTS • Incomplete (so also not optimal) • Worst-case time and space complexity: O(bm) • Actual complexity depends on accuracy of h(n)

37. A*S • f(n) = g(n) + h(n) • f(n): estimated cost of optimal solution through node n • if h(n) satisfies certain conditions, A*S is complete & optimal

38. Example state space # 3

39. Admissible heuristics • h(n) admissible if: Example: straight line distance A*TS optimal if h(n) admissible

40. Consistent heuristics • h(n) consistent if: Consistency implies admissibility A*GS optimal if h(n) consistent

42. A* search notes • Optimally efficient for consistent heuristics • Run-time is a function of the heuristic error • Suboptimal variants • Not strictly admissible heuristics • A* Graph Search not scalable due to memory requirements

43. Memory-bounded heuristic search • Iterative Deepening A* (IDA*) • Recursive Best-First Search (RBFS) • IDA* and RBFS don’t use all avail. memory • Memory-bounded A* (MA*) • Simplified MA* (SMA*) • Meta-level learning aims to minimize total problem solving cost

44. Heuristic Functions • Effective branching factor • Domination • Composite heuristics • Generating admissible heuristics from relaxed problems

45. Sample relaxed problem • n-puzzle legal actions: Move from A to B if horizontally or vertically adjacent and B is blank Relaxed problems: • Move from A to B if adjacent • Move from A to B if B is blank • Move from A to B

46. Generating admissible heuristics The cost of an optimal solution to a relaxed problem is an admissible heuristic for the original problem.

47. Adversarial Search Environments characterized by: • Competitive multi-agent • Turn-taking Simplest type: Discrete, deterministic, two-player, zero-sum games of perfect information

48. Search problem formulation • S0: Initial state (initial board setup) • Player(s): which player has the move • Actions(s): set of legal moves • Result(s,a): defines transitional model • Terminal test: game over! • Utility function: associates player-dependent values with terminal states

49. Minimax

50. Example game tree 1