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Intelligent Systems: More on Search

This presentation covers advanced search algorithms including depth-limited search, iterative deepening search, best-first search, and A* search. It also explores adversarial search in multiplayer games.

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Intelligent Systems: More on Search

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  1. Intelligent Systems: More on Search Stefan Schlobach With slides from Tom Lenaerts

  2. Part 1 MORE ON UNINFORMED SEARCH January 8, 2018 IS: More on search 2

  3. Remember January 8, 2018 IS: More on search 3

  4. Depth-limited search • Is DF-search with depth limit l. • i.e. nodes at depth l have no successors. • Problem knowledge can be used • Solves the infinite-path problem. • If l < d then incompleteness results. • If l > d then not optimal. • Time complexity: • Space complexity: January 8, 2018 IS: More on search 4

  5. Iterative deepening search • What? • A general strategy to find best depth limit l. • Goals is found at depth d, the depth of the shallowest goal-node. • Often used in combination with DF-search • Combines benefits of DF- en BF-search January 8, 2018 IS: More on search 5

  6. ID-search, example • Limit=0 January 8, 2018 IS: More on search 6

  7. ID-search, example • Limit=1 January 8, 2018 IS: More on search 7

  8. ID-search, example • Limit=2 January 8, 2018 IS: More on search 8

  9. ID-search, example • Limit=3 January 8, 2018 IS: More on search 9

  10. ID search, evaluation • Completeness: • YES (no infinite paths) January 8, 2018 IS: More on search 10

  11. ID search, evaluation • Completeness: • YES (no infinite paths) • Time complexity: • Space complexity: • Cfr. depth-first search January 8, 2018 IS: More on search 11

  12. Summary of algorithms January 8, 2018 IS: More on search 12

  13. Search direction 5 Maze, data-driven 4 3 e1 b4 2 1 a4 c4 a b c d e a2 b5 e5 d4 a1 c1 e2 d3 • Data-driven = Start with initial state • Goal-driven = Start with goal state c3 AI2 13 January 8, 2018 IS: More on search 13

  14. Search direction 5 4 3 d4 2 c4 e4 1 a b c d e b4 c5 e3 a4 b3 e2 c3 • Data-driven = Start with initial state • Goal-driven = Start with goal state Maze, goal-driven d3 January 8, 2018 IS: More on search 14

  15. Goal vs Data-driven Search 1. Is there a clear unique goal? 2. Which branching factor is bigger? Example: Is Matty Huntjes a descendent of Willem van Oranje? • Data-driven: • Check children of WvO, grandchildren, grandgrandchildren, .... • N generations, 3 children = 3N • Goal-driven: • Parents of MH, grand-parents, grand-grand parents • N generaties, 2 parents = 2N (310=59049) (210=1024) January 8, 2018 IS: More on search 15

  16. (25 Minutes break) Mondriaan evolver • GUI shows population of 9 pictures • User gives grades (thus defines fitness values) • Computer performs one evolutionary cycle, i.e. • selection, based on this fitness (thus creates mating pool) • crossover & mutation (thus creates new population) • Repeat 16

  17. Part 2 MORE ON INFORMED SEARCH January 8, 2018 IS: More on search 17

  18. Previously: tree-search function TREE-SEARCH(problem,fringe) return a solution or failure fringe INSERT(MAKE-NODE(INITIAL-STATE[problem]), fringe) loop do if EMPTY?(fringe) then return failure node REMOVE-FIRST(fringe) if GOAL-TEST[problem] applied to STATE[node] succeeds then return SOLUTION(node) fringe INSERT-ALL(EXPAND(node, problem), fringe) January 8, 2018 IS: More on search 18

  19. Best-first search • General approach of informed search: • Best-first search: node is selected for expansion based on an evaluation functionf(n) • Idea: evaluation function measures distance to the goal. • Choose node which appears best • Implementation: • fringe is queue sorted in decreasing order of desirability. • Special cases: Greedy search, Hill climbing, A, A* search January 8, 2018 IS: More on search 19

  20. A search • Best-known form of best-first search. • Idea: avoid expanding paths that are already expensive. • Evaluation function f(n)=g(n) + h(n) • g(n) the cost (so far) to reach the node. • h(n) estimated cost to get from the node to the goal. • f(n) estimated total cost of path through n to goal. January 8, 2018 IS: More on search 20 * IS: Problem Solving

  21. A* search • A*= A search, but with an admissible heuristic • A heuristic is admissible if it never overestimates the cost to reach the goal • Admissible heuristics are optimistic • Formally: • 1. h(n) <= h*(n) where h*(n) is the true cost from n • 2. h(n) >= 0 so h(G)=0 for any goal G. • e.g. hSLD(n) never overestimates the actual road distance January 8, 2018 IS: More on search 21 * IS: Problem Solving

  22. Romania example January 8, 2018 IS: More on search 22 * IS: Problem Solving

  23. 6-27 februari 6-27 februari A* search, evaluation • Completeness: YES • Time complexity: (exponential with path length) • Space complexity:(all nodes are stored) • Optimality: YES January 8, 2018 IS: More on search 23 * IS: Problem Solving

  24. Part 3 MORE ON ADVERSARIAL SEARCH January 8, 2018 IS: More on search 24

  25. Multi-player games January 8, 2018 IS: More on search 25

  26. Multiplayer games • Games allow more than two players • Single minimax values become vectors January 8, 2018 IS: More on search 26

  27. Games with Chance January 8, 2018 IS: More on search 27

  28. Games that include chance • Possible moves (5-10,5-11), (5-11,19-24),(5-10,10-16) and (5-11,11-16) January 8, 2018 IS: More on search 28

  29. Games that include chance chance nodes • Possible moves (5-10,5-11), (5-11,19-24),(5-10,10-16) and (5-11,11-16) • [1,1], [6,6] chance 1/36, all other chance 1/18 January 8, 2018 IS: More on search 29

  30. Games that include chance • [1,1], [6,6] chance 1/36, all other chance 1/18 • Can not calculate definite minimax value, only expected value January 8, 2018 IS: More on search 30

  31. Expected minimax value EXPECTED-MINIMAX-VALUE(n)= UTILITY(n) If n is a terminal maxs  successors(n) MINIMAX-VALUE(s) If n is a max node mins  successors(n) MINIMAX-VALUE(s) If n is a max node s  successors(n) P(s) . EXPECTEDMINIMAX(s) If n is a chance node These equations can be backed-up recursively all the way to the root of the game tree. January 8, 2018 IS: More on search 31

  32. Part 4 (or what should have been the beginning) RATIONAL AGENTS January 8, 2018 IS: More on search 32

  33. Intelligent Systems Building intelligent artificial agents Subfield of Artificial Intelligence • A rational agentchooses whichever action maximizes the expected value of the performance measure given the percept sequence to date and prior environment knowledge. January 8, 2018 IS: More on search 33

  34. Outline: Rational Agents • Agents • Rationality • Task Environments. • Agent types. January 8, 2018 IS: More on search 34

  35. Agents • The agent function maps percept sequence to actions • The agent function will internally be represented by the agent program. • The agent program runs on the physical architecture to produce f. January 8, 2018 IS: More on search 35

  36. Rationality • A rational agent chooses whichever action maximizes the expected value of the performance measure given the percept sequence to date and prior environment knowledge • What is rational at a given time depends on four things: • Expected value of performance measure (heuristics) • Actions and choices (Search) • Percept sequence to date (Learning) • Prior environment knowledge, (KR) • Rationality  omniscience • Rationality  perfection January 8, 2018 IS: More on search 36

  37. Task Environments • To design a rational agent we must specify its task environment: • Performance (what it does) • Environment (where it does it) • Actuators (how it does it) • Sensors (what it perceives) Remember PEAS acronym for task environment January 8, 2018 IS: More on search 37

  38. Task Environments • E.g. Fully automated taxi: • PEAS description of the environment: • Performance • Safety, destination, profits, legality, comfort • Environment • Streets/freeways, other traffic, pedestrians, weather,, … • Actuators • Steering, accelerating, brake, horn, speaker/display,… • Sensors • Video, sonar, speedometer, engine sensors, keyboard, GPS, … January 8, 2018 IS: More on search 38

  39. Environment types January 8, 2018 IS: More on search 39

  40. Environment types Fully vs. partially observable: an environment is full observable when the sensors can detect all aspects that are relevant to the choice of action. January 8, 2018 IS: More on search 40

  41. Environment types Fully vs. partially observable: an environment is fully observable when the sensors can detect all aspects that are relevant to the choice of action. January 8, 2018 IS: More on search 41

  42. Environment types Deterministic vs. stochastic: if the next environment state is completely determined by the current state & the executed action then the environment is deterministic. January 8, 2018 IS: More on search 42

  43. Environment types Deterministic vs. stochastic: if the next environment state is completely determined by the current state & the executed action then the environment is deterministic. January 8, 2018 IS: More on search 43

  44. Environment types Static vs. dynamic: If the environment can change while the agent is choosing an action, the environment is dynamic. Semi-dynamic if the agent’s performance changes even when the environment remains the same. January 8, 2018 IS: More on search 44

  45. Environment types Static vs. dynamic: If the environment can change while the agent is choosing an action, the environment is dynamic. Semi-dynamic if the agent’s performance changes even when the environment remains the same. January 8, 2018 IS: More on search 45

  46. Environment types Single vs. multi-agent: Does the environment contain other agents who are also maximizing some performance measure that depends on the current agent’s actions? January 8, 2018 IS: More on search 46

  47. Environment types Single vs. multi-agent: Does the environment contain other agents who are also maximizing some performance measure that depends on the current agent’s actions? January 8, 2018 IS: More on search 47

  48. Environment type for Schnapsen • Observable: Not fully • Deterministic: Yes • Static: Yes • Discrete: Yes • Single-agent: no January 8, 2018 IS: More on search 48

  49. Environment types • The simplest environment is • Fully observable, deterministic, episodic, static, discrete and single-agent. • Most real situations are: • Partially observable, stochastic, sequential, dynamic, continuous and multi-agent. January 8, 2018 IS: More on search 49

  50. Agent types • Four basic kind of agent programs will be discussed: • Simple reflex agents • Model-based reflex agents • Goal-based agents • Utility-based agents • All these can be turned into learning agents. January 8, 2018 IS: More on search 50

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