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COMP 8620 Advanced Topics in AI

COMP 8620 Advanced Topics in AI. Lecturers: Philip Kilby & Jinbo Huang. Part 1: Search Lecturer: Dr Philip Kilby Philip.Kilby@nicta.com.au Weeks 1-7 (Week 7 is assignment seminars) Part 2: Probabilistic Reasoning with Bayesian networks Lecturer: Dr Jinbo Huang

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COMP 8620 Advanced Topics in AI

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  1. COMP 8620Advanced Topics in AI Lecturers: Philip Kilby & Jinbo Huang

  2. Part 1: Search Lecturer: Dr Philip Kilby Philip.Kilby@nicta.com.au Weeks 1-7(Week 7 is assignment seminars) Part 2: Probabilistic Reasoning with Bayesian networks Lecturer: Dr Jinbo Huang Jinbo.Huang@nicta.com.au Weeks 8-13

  3. 1-2 Introduction Systematic Search 3-4 Linear Programming / Integer Programming / Branch and Bound 5-6 Neighbourhood-based methods:  Simulated Annealing Tabu Search  Genetic Algorithms 7-8 Constraint Programming (Guest lecturer: Jason Li) 7-8 Constraint Programming (Guest lecturer: Jason Li) 9-10 Case Studies:  TSP Planning (Jussi Rintanen) 11 Dynamic Programming 12 Qualitative Reasoning (Guest lecturer: Jason Li) 13-14 Seminars (Guest Lecturers: You lot!) Course Outline – Part 1 Search – Lecture 1-2

  4. Assessment • 40% Exam • 60% Assignment • Search • 1 x Assignment (next week) 15% • 1 x Seminar 15% • Reasoning • 3 x Assignment (10% each) (tentative) Search – Lecture 1-2

  5. What is Search? • Search finds a solution to a problem • Landscape of solutions • Some are “good” • Lots (and lots and lots) are “bad” How do we find the good ones? Search – Lecture 1-2

  6. What is Search? • Landscape can continuous or discrete • (We will only deal with discrete) • Landscape can be (approximated by?) a tree • Landscape can be (approximated by?) a graph Search – Lecture 1-2

  7. What is Search? X + 2 * Y < 3, X  [0,5] Y  [1,5] Search – Lecture 1-2

  8. X=2Y=4 X=0Y=4 X=1Y=1 X=1Y=2 X=1Y=3 X=1Y=4 X=1Y=5 X=0Y=2 X=0Y=3 X=2Y=1 X=0Y=5 X=0Y=1 X=0Y=0 X=2Y=5 X=5Y=2 X=5Y=1 X=5Y=3 X=2Y=2 X=3Y=5 X=3Y=4 X=3Y=3 X=3Y=2 X=4Y=5 X=2Y=3 X=3Y=1 X=4Y=4 X=4Y=3 X=4Y=2 X=4Y=1 X=5Y=4 X=5Y=5 X=0Y=1 What is Search? X + 2 * Y < 3, X  [0,5] Y  [1,5] Search – Lecture 1-2

  9. X=0 X=1 X=2 X=3 X=4 X=5 What is Search? X + 2 * Y < 3, X  [0,5] Y  [1,5] Y=1 Y=2 Y=3 Y=4 Y=5 Search – Lecture 1-2

  10. Y=1 Y=2 Y=3 Y=4 Y=5 X=0 X=1 X=2 X=3 X=4 What is Search? X + 2 * Y < 3, X  [0,5] Y  [1,5] X=5 Search – Lecture 1-2

  11. What is Search? X + 2 * Y < 3, X  [0,5] Y  [1,5] X>0 X=0 Y>1 Y=1 Search – Lecture 1-2

  12. What is Search? • Different flavours • Find a solution (Satisfaction/Decision) • Find the best solution (Combinatorial Optimisation) • Decision problems: • Search variant: Find a solution (or show none exists) • Decision variant: Does a solution exist? Search – Lecture 1-2

  13. What is Search • Constructive Search – Find a solution by construction • Local Search – Given a solution, explore the “neighbourhood” of that solution to find other (possibly better) solutions Search – Lecture 1-2

  14. What is Search? Anytime algorithm (for optimisation prob): • After a (short) startup time, an answer is available • The longer the alg is run, the better the solution • Quality guarantee may be available (e.g. solution is within 5% of optimal) One-shot algorithm • Answer only available at completion Search – Lecture 1-2

  15. What is Search? A problem is defined by • Initial state • Successor function (an action leading from one state to another) • Goal test • Path cost • A solution is a sequence of actions leading from the start state to a goal state Search – Lecture 1-2

  16. Example: Romania Search – Lecture 1-2

  17. Problem formulation • A problem is defined by four items: • initial state • e.g., “at Arad” • successor function S(x) • set of action–state pairs • e.g., S(Arad) = {<Arad → Zerind, at Zerind>, . . .} • goal test e.g., x = “at Bucharest” • can be implicit, e.g., HasAirport(x) • path cost (additive) • e.g. sum of distances, number of actions executed, etc. • c(x, a, y) is the step cost, assumed to be ≥ 0 Search – Lecture 1-2

  18. Tree Search functionTree-Search (problem, fringe) returns a solution, or failure fringe ← Insert (Make-Node (Initial-State (problem)), fringe) loop do if Is-Empty(fringe)then return failure node ← Remove-Front (fringe) ifGoal-Test (problem, State[node]) then return node fringe ← InsertAll (Expand (node, problem), fringe) functionExpand (node, problem) returns a set of nodes successors ← the empty set foreach (action, result) inSuccessor-Fn (problem, State[node]) do s ← a new Node Parent-Node[s] ← node; Action[s] ← action; State[s] ← result Path-Cost[s] ← Path-Cost[node] + Step-Cost(State[node], action, result) Depth[s] ← Depth[node] + 1 successors ← Insert (s) return successors Search – Lecture 1-2

  19. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  20. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  21. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  22. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  23. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  24. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  25. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  26. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  27. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  28. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  29. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  30. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  31. Breadth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  32. Breadth-first Search A B C D E F G !! H I L M O Search – Lecture 1-2

  33. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  34. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  35. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  36. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  37. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  38. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  39. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  40. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  41. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  42. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  43. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  44. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  45. Depth-first Search A B C D E F G H I L M O Search – Lecture 1-2

  46. Breadth-first Search A B C D E F G !! H I L M O Search – Lecture 1-2

  47. Iterative Deepening DFS Search A B C D E F G H I L M O Search – Lecture 1-2

  48. Iterative Deepening DFS Search A B C D E F G H I L M O Search – Lecture 1-2

  49. Iterative Deepening DFS Search A B C D E F G H I L M O Search – Lecture 1-2

  50. Iterative Deepening DFS Search A B C D E F G H I L M O Search – Lecture 1-2

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