CS325 Artificial Intelligence Chs. 10, 11 Planning

Transcription

1 CS325 Artificial Intelligence Chs. 10, 11 Planning Cengiz Günay, Emory Univ. Spring 2013 Günay () Chs. 10, 11 Planning Spring / 24

2 Planning Günay () Chs. 10, 11 Planning Spring / 24

3 Planning Planning is coming up with a solution for an agent: it s at the heart of AI Günay () Chs. 10, 11 Planning Spring / 24

4 Entry/Exit Surveys Exit survey: Knowledge Representation and Inference What knowledge representation do you think our brains have? What knowledge base topic/domain would you wish you had? Entry survey: Planning (0.25 points of final grade) What previous class topic would count as a planning algorithm? Where do you think you used an automated planning system? Günay () Chs. 10, 11 Planning Spring / 24

5 Graph Search Is a Form of Planning 71 Oradea Neamt Zerind 75 Arad Timisoara Drobeta 151 Sibiu 99 Fagaras 80 Rimnicu Vilcea Lugoj Mehadia 120 Pitesti Bucharest 90 Craiova Giurgiu 87 Iasi Urziceni Vaslui Hirsova 86 Eforie Search algorithm like A is a planning method Günay () Chs. 10, 11 Planning Spring / 24

6 Graph Search Is a Form of Planning 71 Oradea Neamt Zerind 75 Arad Timisoara Drobeta 151 Sibiu 99 Fagaras 80 Rimnicu Vilcea Lugoj Mehadia 120 Pitesti Bucharest 90 Craiova Giurgiu 87 Iasi Urziceni Vaslui Hirsova 86 Eforie Search algorithm like A is a planning method Only works for observable and deterministic environment What if you cannot plan all the way? Günay () Chs. 10, 11 Planning Spring / 24

7 Blind Walking Günay () Chs. 10, 11 Planning Spring / 24

8 Blind Walking Need to alternate plan & execution Günay () Chs. 10, 11 Planning Spring / 24

9 How Does the Brain Do It? Günay () Chs. 10, 11 Planning Spring / 24

10 How Does the Brain Do It? Frontal lobes are biggest in humans, dedicated to planning, reasoning and other high-order skills Günay () Chs. 10, 11 Planning Spring / 24

11 So When Do You Need Planning? Stochastic environment Multi-agent situation Partial observable Unknown Hierarchical Günay () Chs. 10, 11 Planning Spring / 24

12 So When Do You Need Planning? Stochastic environment Multi-agent situation Partial observable Unknown Hierarchical In these cases, may need to plan in belief states Günay () Chs. 10, 11 Planning Spring / 24

13 Sensorless World L R R S L S L R R L R R S L S S L S L R R L S S Günay () Chs. 10, 11 Planning Spring / 24

14 Sensorless World L Günay () Chs. 10, 11 Planning Spring / 24

15 Sensorless World L Start: clean place Go: left wall, clean Günay () Chs. 10, 11 Planning Spring / 24

16 Partially Observable Environment Deterministic, but sense only local dirt & location Günay () Chs. 10, 11 Planning Spring / 24

17 Partially Observable Environment Deterministic, but sense only local dirt & location Belief states get smaller with actions Günay () Chs. 10, 11 Planning Spring / 24

18 Stochastic (Random) Environment Still local sensing Robot has slippery wheels, may not move Günay () Chs. 10, 11 Planning Spring / 24

19 Stochastic (Random) Environment Still local sensing Robot has slippery wheels, may not move Belief states get larger with actions Günay () Chs. 10, 11 Planning Spring / 24

20 Stochastic (Random) Environment Can reach clean world? Still local sensing Robot has slippery wheels, may not move Belief states get larger with actions Günay () Chs. 10, 11 Planning Spring / 24

21 Stochastic (Random) Environment Can reach clean world? No finite solution! Still local sensing Robot has slippery wheels, may not move Belief states get larger with actions Günay () Chs. 10, 11 Planning Spring / 24

22 Infinite Sequences? Finite sequences don t work: [R, S, R, S] Günay () Chs. 10, 11 Planning Spring / 24

23 Infinite Sequences? Finite sequences don t work: [R, S, R, S] Make a finite plan with branches Günay () Chs. 10, 11 Planning Spring / 24

24 Infinite Sequences? Finite sequences don t work: [R, S, R, S] Make a finite plan with branches Gives an infinite sequence! Günay () Chs. 10, 11 Planning Spring / 24

25 Infinite Sequences? Finite sequences don t work: [R, S, R, S] Make a finite plan with branches Gives an infinite sequence! Can write it like: [S, While A : R, S] Günay () Chs. 10, 11 Planning Spring / 24

26 Searching For a Plan Like searching for paths, find a plan that reaches the goal. Günay () Chs. 10, 11 Planning Spring / 24

27 Searching For a Plan Unbounded solution: Some leaf goal Every leaf goal No Bounded solution: No branch No loops No Like searching for paths, find a plan that reaches the goal. Günay () Chs. 10, 11 Planning Spring / 24

28 Searching For a Plan Unbounded solution: Some leaf goal Every leaf goal No Bounded solution: No branch No loops No Like searching for paths, find a plan that reaches the goal. Günay () Chs. 10, 11 Planning Spring / 24

29 Mathematical Notation [A, S, F ] Result(Result(A, A S), S F ) Goals Deterministic: s = Result(a, s) where s is state and a is action. Günay () Chs. 10, 11 Planning Spring / 24

30 Mathematical Notation Deterministic: [A, S, F ] Result(Result(A, A S), S F ) Goals s = Result(a, s) where s is state and a is action. Non-deterministic: Predict-update beliefs (b) cycle: b = Update(Predict(b, a), o) where o is observation. Günay () Chs. 10, 11 Planning Spring / 24

31 Predict-Update Cycle Babies randomly dirtying floors Günay () Chs. 10, 11 Planning Spring / 24

32 Predict-Update Cycle Babies randomly dirtying floors Problems: Large solution, simpler to list world state as variables Günay () Chs. 10, 11 Planning Spring / 24

33 Classical Planning State space: k boolean variables; size: Günay () Chs. 10, 11 Planning Spring / 24

34 Classical Planning State space: k boolean variables; size: 2 k Günay () Chs. 10, 11 Planning Spring / 24

35 Classical Planning State space: k boolean variables; size: 2 k World state: Complete assignment Belief state: Complete/partial/arbitrary formula Called an action schema Günay () Chs. 10, 11 Planning Spring / 24

36 Action Schemas 1 Action 2 Precondition 3 Effect Günay () Chs. 10, 11 Planning Spring / 24

37 Action Schemas 1 Action 2 Precondition 3 Effect Example: Action(Fly(p, from, to), Pre: At(p, from) Plane(p) Airport(from) Airport(to) Eff: At(p, from) At(p, to)) Günay () Chs. 10, 11 Planning Spring / 24

38 Action Schemas 1 Action 2 Precondition 3 Effect Example: Action(Fly(p, from, to), Pre: At(p, from) Plane(p) Airport(from) Airport(to) Eff: At(p, from) At(p, to)) Is it FOL? Günay () Chs. 10, 11 Planning Spring / 24

39 Air Cargo Example Günay () Chs. 10, 11 Planning Spring / 24

40 Progression/Forward Search Like regular search. Günay () Chs. 10, 11 Planning Spring / 24

41 Regression/Backward Search Start with goal, have many unknowns. Günay () Chs. 10, 11 Planning Spring / 24

42 When to Choose Forward vs. Backward? Remember when to choose breadth-first vs. depth first. Fewer options when starting from the goal. Can think of other examples? Günay () Chs. 10, 11 Planning Spring / 24

43 Searching the Plan Space Günay () Chs. 10, 11 Planning Spring / 24

44 Searching the Plan Space How would one use genetic algorithms? Günay () Chs. 10, 11 Planning Spring / 24

45 Current Trend: Forward Search with Heuristics Tiles example: Action(Slide(t, a, b), Pre: On(t, a) Tile(t) Blank(b) Adj(a, b) Eff: On(t, b) Blank(a) On(t, a) Blank(b)) Günay () Chs. 10, 11 Planning Spring / 24

46 Current Trend: Forward Search with Heuristics Tiles example: Action(Slide(t, a, b), Pre: On(t, a) Tile(t) Blank(b) Adj(a, b) Eff: On(t, b) Blank(a) On(t, a) Blank(b)) How to use heuristics? Remember Romania routes. Günay () Chs. 10, 11 Planning Spring / 24

47 Current Trend: Forward Search with Heuristics Tiles example: Action(Slide(t, a, b), Pre: On(t, a) Tile(t) Blank(b) Adj(a, b) Eff: On(t, b) Blank(a) On(t, a) Blank(b)) How to use heuristics? Remember Romania routes. Choose approximate solutions and use during search Delete terms from schema Günay () Chs. 10, 11 Planning Spring / 24

48 Current Trend: Forward Search with Heuristics Tiles example: Action(Slide(t, a, b), Pre: On(t, a) Tile(t) Blank(b) Adj(a, b) Eff: On(t, b) Blank(a) On(t, a) Blank(b)) How to use heuristics? Remember Romania routes. Choose approximate solutions and use during search Delete terms from schema Can also do this programmatically Günay () Chs. 10, 11 Planning Spring / 24

49 One Last Bit: Situation Calculus Uses First Order Logic (FOL) for planning: Actions: are objects; e.g., Fly(p, x, y) Situations: objects; e.g., s = Result(s, a) Fluents: change at each situation: e.g., At(p, x, s) Possible actions: objects; Poss(a, s) Written as in: Pre(s) Poss(a, s) Günay () Chs. 10, 11 Planning Spring / 24

50 One Last Bit: Situation Calculus Uses First Order Logic (FOL) for planning: Actions: are objects; e.g., Fly(p, x, y) Situations: objects; e.g., s = Result(s, a) Fluents: change at each situation: e.g., At(p, x, s) Possible actions: objects; Poss(a, s) Written as in: Pre(s) Poss(a, s) Plane example: Plane(p, s) Airport(x, s) Airport(y, s) At(p, x, s) Poss(Fly(p, x, y), s) Günay () Chs. 10, 11 Planning Spring / 24

51 Situation Calculus: Effects Effects: Successor state axioms: a, s Poss(a, s) (fluent caused it didn t undo it) Günay () Chs. 10, 11 Planning Spring / 24

52 Situation Calculus: Effects Effects: Successor state axioms: a, s Poss(a, s) (fluent caused it didn t undo it) Cargo example: Poss(a, s) In(c, p, Result(s, a)) (a = Load(c, p, x) (In(c, p, s) a Unload(c, p, x))) Günay () Chs. 10, 11 Planning Spring / 24

53 Situation Calculus: Effects Effects: Successor state axioms: a, s Poss(a, s) (fluent caused it didn t undo it) Cargo example: Poss(a, s) In(c, p, Result(s, a)) (a = Load(c, p, x) (In(c, p, s) a Unload(c, p, x))) Can use power of FOL Can use existing theorem provers Problem: slow Günay () Chs. 10, 11 Planning Spring / 24