1. COMP SCI 5400 – Introduction to Artificial Intelligence Dr. Daniel Tauritz (Dr. T) Department of Computer Science tauritzd@mst.edu http://web.mst.edu/~tauritzd/ general course website: http://web.mst.edu/~tauritzd/courses/intro_AI.html http://web.mst.edu/~tauritzd/courses/intro_AI.html

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

3. Computer Agent Perceives environment Operates autonomously Persists over prolonged periods

4. Rational Agents Environment Sensors (percepts) Actuators (actions)

6. Rational Agents Environment Sensors (percepts) Actuators (actions) Agent Function Agent Program

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

9. 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.”

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

11. Agent Types Simple Reflex Agents Model-Based Reflex Agents Goal-Based Agents Utility-Based Agents Learning Agents

12. 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.

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

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

15. 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

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

17. 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!

18. 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

19. Redundant paths Loopy paths Repeated states Redundant paths

20. 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

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

22. function CHILD-NODE(problem,parent,action) returns a node return a node with: STATE = problem.RESULT(parent.STATE,action) PARENT = parent ACTION = action PATH-COST = parent.PATH-COST + problem.STEP-COST(parent.STATE,action)

23. 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

24. Explored Set Explored Set = Set of expanded nodes Implemented typically as a hash table for constant time insertion & lookup

25. Problem-solving performance Completeness Optimality Time complexity Space complexity

26. 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

27. 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)

28. Example state space #1

29. 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)

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

31. Depth First Tree Search (DFTS) Frontier: LIFO queue (a.k.a. stack) Complete: no (DGFS is complete for finite state spaces) Optimal: no Time complexity: O(b m ) Space complexity: O(bm) Backtracking version of DFTS: –space complexity: O(m) –modifies rather than copies state description

32. 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

33. Diameter example 1

34. Diameter example 2

35. Iterative-Deepening Depth-First Tree Search (ID-DFTS) function ID-DFS(problem) returns solution/fail for depth = 0 to ∞ do result ← DLS(problem,depth) if result ≠ 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)

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

37. Example state space #2

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

39. 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]

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

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

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

43. 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

44. Example state space # 3

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

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

47. 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

48. 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

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

50. Sample relaxed problem n-puzzle legal actions: Move from A to B if horizontally or vertically adjacent and B is blank Relaxed problems: (a)Move from A to B if adjacent (b)Move from A to B if B is blank (c)Move from A to B

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

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

53. Search problem formulation S 0 : 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

54. Minimax

55. Example game tree 1

56. Depth-Limited Minimax State Evaluation Heuristic estimates Minimax value of a node Note that the Minimax value of a node is always calculated for the Max player, even when the Min player is at move in that node!

57. Heuristic Depth-Limited Minimax

58. State Eval Heuristic Qualities A good State Eval Heuristic should: (1)order the terminal states in the same way as the utility function (2)be relatively quick to compute (3)strongly correlate nonterminal states with chance of winning

59. Weighted Linear State Eval Heuristic

60. Heuristic Iterative-Deepening Minimax IDM(s,d) calls DLM(s,1), DLM(s,2), …, DLM(s,d) Advantages: –Solution availability when time is critical –Guiding information for deeper searches

61. Redundant info example

62. Alpha-Beta Pruning α: worst value that Max will accept at this point of the search tree β: worst value that Min will accept at this point of the search tree Fail-low: encountered value <= α Fail-high: encountered value >= β Prune if fail-low for Min-player Prune if fail-high for Max-player

63. DLM w/ Alpha-Beta Pruning Time Complexity Worst-case: O(b d ) Best-case: O(b d/2 ) [Knuth & Moore, 1975] Average-case: O(b 3d/4 )

64. Example game tree 2

65. Move Ordering Heuristics Knowledge based (e.g., try captures first in chess) Principal Variant (PV) based Killer Move: the last move at a given depth that caused αβ-pruning or had best minimax value History Table: track how often a particular move at any depth caused αβ- pruning or had best minimax value

66. History Table (HT) Option 1: generate set of legal moves and use HT value as f-value Option 2: keep moves with HT values in a sorted array and for a given state traverse the array to find the legal move with the highest HT value

67. Example game tree 3

68. Search Depth Heuristics Time based / State based Horizon Effect: the phenomenon of deciding on a non-optimal principal variant because an ultimately unavoidable damaging move seems to be avoided by blocking it till passed the search depth Singular Extensions / Quiescence Search

69. Time Per Move Constant Percentage of remaining time State dependent Hybrid

70. Quiescence Search When search depth reached, compute quiescence state evaluation heuristic If state quiescent, then proceed as usual; otherwise increase search depth if quiescence search depth not yet reached Call format: QSDLM(root,depth,QSdepth), QSABDLM(root,depth,QSdepth,α,β), etc.

71. QS game tree Ex. 1

72. QS game tree Ex. 2

74. Transposition Tables (1) Hash table of previously calculated state evaluation heuristic values Speedup is particularly huge for iterative deepening search algorithms! Good for chess because often repeated states in same search

75. Transposition Tables (2) Datastructure: Hash table indexed by position Element: –State evaluation heuristic value –Search depth of stored value –Hash key of position (to eliminate collisions) –(optional) Best move from position

76. Transposition Tables (3) Zobrist hash key –Generate 3d-array of random 64-bit numbers (piece type, location and color) –Start with a 64-bit hash key initialized to 0 –Loop through current position, XOR’ing hash key with Zobrist value of each piece found (note: once a key has been found, use an incremental approach that XOR’s the “from” location and the “to” location to move a piece)

77. Search versus lookup Balancing time versus memory Opening table –Human expert knowledge –Monte Carlo analysis End game database

78. Forward pruning Beam Search (n best moves) ProbCut (forward pruning version of alpha-beta pruning)

79. Null Move Forward Pruning Before regular search, perform shallower depth search (typically two ply less) with the opponent at move; if beta exceeded, then prune without performing regular search Sacrifices optimality for great speed increase

80. Futility Pruning If the current side to move is not in check, the current move about to be searched is not a capture and not a checking move, and the current positional score plus a certain margin (generally the score of a minor piece) would not improve alpha, then the current node is poor, and the last ply of searching can be aborted. Extended Futility Pruning Razoring

81. MTD(f) MTDf(root,guess,depth) { lower = -∞; upper = ∞; do { beta=guess+(guess==lower); guess = ABMaxV(root,depth,beta-1,beta); if (guess<beta) upper=guess; else lower=guess; } while (lower < upper); return guess; } // also needs to return best move

82. IDMTD(f) IDMTDf(root,first_guess,depth_limit) { guess = first_guess; for (depth=1; depth ≤ depth_limit; depth++) guess = MTDf(root,guess,depth); return guess; } // actually needs to return best move

84. Adversarial Search in Stochastic Environments Worst Case Time Complexity: O(b m n m ) with b the average branching factor, m the deepest search depth, and n the average chance branching factor

85. Example “chance” game tree

86. Expectiminimax & Pruning Interval arithmetic Monte Carlo simulations (for dice called a rollout)

87. State-Space Search Complete-state formulation Objective function Global optima Local optima (don’t use textbook’s definition!) Ridges, plateaus, and shoulders Random search and local search

88. Steepest-Ascent Hill-Climbing Greedy Algorithm - makes locally optimal choices Example 8 queens problem has 8 8 ≈17M states SAHC finds global optimum for 14% of instances in on average 4 steps (3 steps when stuck) SAHC w/ up to 100 consecutive sideways moves, finds global optimum for 94% of instances in on average 21 steps (64 steps when stuck)

89. Stochastic Hill-Climbing Chooses at random from among uphill moves Probability of selection can vary with the steepness of the uphill move On average slower convergence, but also less chance of premature convergence

90. More Local Search Algorithms First-choice hill-climbing Random-restart hill-climbing Simulated Annealing

91. Population Based Local Search Deterministic local beam search Stochastic local beam search Evolutionary Algorithms Particle Swarm Optimization Ant Colony Optimization

92. Particle Swarm Optimization PSO is a stochastic population-based optimization technique which assigns velocities to population members encoding trial solutions PSO update rules: PSO demo: http://www.borgelt.net//psopt.htmlhttp://www.borgelt.net//psopt.html

93. Ant Colony Optimization Population based Pheromone trail and stigmergetic communication Shortest path searching Stochastic moves

94. Online Search Offline search vs. online search Interleaving computation & action Dynamic, nondeterministic, unknown domains Exploration problems, safely explorable Agents have access to: –ACTIONS(s) –c(s,a,s’)  cannot be used until RESULT(s,a) –GOAL-TEST(s)

95. Online Search Optimality CR – Competitive Ratio TAPC – Total Actual Path Cost C* - Optimal Path Cost Best case: CR = 1 Worst case: CR = ∞

96. Online Search Algorithms Online-DFS-Agent Random Walk Learning Real-Time A* (LRTA*)

97. Online Search Example Graph 1

98. Online Search Example Graph 2

99. Online Search Example Graph 3

100. Descartes Mind-Body Connection René Descartes (1596-1650) Rationalism Dualism Materialism Star Trek & Souls

101. Key historical events for AI 4 th century BC Aristotle propositional logic 1600’s Descartes mind-body connection 1805 First programmable machine Mid 1800’s Charles Babbage’s “difference engine” & “analytical engine” Lady Lovelace’s Objection 1847 George Boole propositional logic 1879 Gottlob Frege predicate logic

102. Key historical events for AI 1931 Kurt Godel: Incompleteness Theorem In any language expressive enough to describe natural number properties, there are undecidable (incomputable) true statements 1943 McCulloch & Pitts: Neural Computation 1956 Term “AI” coined 1976 Newell & Simon’s “Physical Symbol System Hypothesis” A physical symbol system has the necessary and sufficient means for general intelligent action.

103. AI courses at S&T CS301 Intro to Data Mining (FS2014) CS345 Intro to Robotics (FS2014) CS346 Intro to Computer Vision (FS2014) CS347 Introduction to Artificial Intelligence CS348 Evolutionary Computing (FS2015) CS444 Data Mining & Knowledge Discovery (SP2015) CS447 Advanced Topics in AI (SP2015) CS448 Advanced Evolutionary Computing (SP2016) CpE358 Computational Intelligence (FS2014) SysEng378 Intro to Neural Networks & Applications

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