Problem Solving Agents

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1 Problem Solving Agents CSL 302 ARTIFICIAL INTELLIGENCE SPRING 2014

2 Goal Based Agents Representation Mechanisms (propositional/first order/probabilistic logic) Learning Models Search (blind and informed) Planning Inference 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 2

3 Example 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 3

4 Problem Solving Agents Goal Formulation oorganize behavior of the agent ogoal set of states in the world where the goal is satisfied 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 4

5 Example Initial Goal 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 5

6 Problem Solving Agents Goal Formulation oorganize behavior of the agent ogoal set of states in the world where the goal is satisfied Problem Formulation owhat are the actions? owhat are the states? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 6

7 Assumptions about the Task Environment Observable or partially observable? Discrete or Continuous? Deterministic or Stochastic? Static or Dynamic? Episodic or Sequential? Multiple or Single Agent? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 7

8 Assumptions about the Task Environment Observable or partially observable? Discrete or Continuous? Deterministic or Stochastic? Static or Dynamic? Episodic or Sequential? Multiple or Single Agent? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 8

9 Assumptions about the Task Environment Observable or partially observable? Discrete or Continuous? Deterministic or Stochastic? Static or Dynamic? Episodic or Sequential? Multiple or Single Agent? Finding a sequence of actions Search! 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 9

10 Problem Solving Agents Goal Formulation oorganize behavior of the agent ogoal set of states in the world where the goal is satisfied Problem Formulation owhat are the actions? owhat are the states? Search ofinding the sequence of actions 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 10

11 Example What is the solution? Initial States Operator/Action Goal 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 11

12 Problem Types Deterministic and Fully Observable: Single state problem osolution is sequence Non-observable: Conformant problem osolution (if any) is a sequence Stochastic and/or Partially Observable: Contingency problem osolution is a contingency plan or a policy Unknown state space: Exploration problem 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 12

13 Problem Solving Atomic Agents Atomic Agents ostates are indivisible osearching through the states to reach the goal. 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 13

14 Single State Problem Formulation Problem can be defined by 5 components 1. Initial State: the state the agent starts 2. Actions: the set of operators that can be executed at a state 3. Transition model: returns the state that results from doing an action in a state 4. Goal test: determines whether a given state is a goal state 5. Path Cost: function that assigns a numeric cost to a path Step cost: cost of taking a single action State Space Graph Path 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 14

15 Example Initial State: Arad Actions: Drive(Sibiu),Drive(Timisora) Goal Test: In(Bucharest) Path Cost:? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 15

16 Example: Toy Vacuum Problem State: Robot and Dirt Locations Initial State: Any State Actions: Left, Right Suck Goal Test: No Dirt Path Cost: cost 1 per action? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 16

17 Example: Eight Puzzle Problem State: Tile Locations Initial State: A specific tile configuration Actions: move the blank tile left, right, up or down Goal Test: tiles are in the required configuration Path Cost: cost 1 per move? Note: Optimal solution for an n-puzzle family is NP hard. 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 17

18 Example: 8 Queens Problem State: Configuration of the Queens Initial State: Empty board Actions: Add a queen to the board Goal Test: configuration with 8 queens on the board with none attacking another Path Cost: time taken to solve? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 18

19 Example: Missionaries and Cannibals State: number of missionaries and cannibals on the boat and each bank Initial State: all objects one bank Actions: move boat with x missionaries and y cannibals, no more cannibals than missionaries on the boat or the shore, a boat with a maximum capacity. Goal Test: All objects on the opposite bank Path Cost: 1 per river crossing 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 19

20 Example: Rubik s Cube State: List of colors on each face Initial State: A specific color pattern Actions: rotate a row or column or a face Goal Test: configuration has the same color on all tiles on every face Path Cost: cost 1 per move? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 20

21 Example: Rubik s Cube 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 21

22 Example: Real World Travelling Salesman Problem (TSP) Robot Navigation Protein folding Graph Coloring 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 22

23 Uninformed Search 21/1 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 23

24 Search - Trees Basic Principle: ooffline simulated exploration of search space ogenerate successors of already explored states 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 24

25 Search Space as a Tree Actions Parent Root Initial State State Node Node Solution Children Children Goal State 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 25

26 Example 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 26

27 Search Strategies Strategies vary in the order in which nodes are picked for expansion Evaluating search strategies ocompleteness Does it always find a solution if one exists? ooptimality Does it always find a least cost solution? ospace complexity How much memory is needed to perform search? otime complexity How long does it take to find a solution? Time and Space complexities are measured ob maximum branching factor of the search tree od shallowest depth of the least cost solution om- maximum depth of the search space 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 27

28 Uninformed search strategies Use only the information available in the problem definition Breadth-first search Uniform-cost search Depth-first search Depth-limited search Iterative deepening search 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 28

29 Breadth-first search (BFS) Expand shallowest unexpanded node Implementation: FIFO Queue; successors at the end of the queue 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 29

30 BFS Analysis Completeness: Yes (if b is finite) Optimality: Not optimal; Yes- Uniform cost edges Time Complexity: exponential in d 1 + b + b 2 + b b d + b b d 1 = O(b d+1 ) Space Complexity: O(b d+1 ) b = nodes sec 10 3 bytes node 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 30

31 Uniform cost search (UCS) Expand least-cost (g(n))unexpanded node Implementation: Priority queue sort the nodes in the queue based on cost. 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 31

32 UCS - Analysis Completeness: Yes; if step cost ε Optimality: Yes; nodes are expanded in increasing order of g(n) Time Complexity: # of nodes with g cost of optimal solution(c ) - O(b C ε ) Space Complexity: # of nodes with g cost of optimal solution - O(b C ε ) Large subtrees with inexpensive steps may be explored before useful paths with costly steps 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 32

33 Depth-first search (DFS) Expand deepest unexpanded node Implementation: LIFO queue; successors at the front of the queue 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 33

34 DFS - Analysis Completeness: complete only in finite spaces; incomplete when there are loops and infinite spaces Optimality: No Time Complexity: O(b m ); terrible when m d; might be faster than BFS, when solutions are dense. Space Complexity: 1 + b + b + + (m th level)b = O(bm); Linear space!! Depth # nodes Memory BFS Memory DFS Eb 156Kb 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 34

35 Depth-limited search (DLS) Depth-first search with depth limit l Implementation: nodes at depth l have no successors. Only finite space to be explored. Completeness: Yes/No??? Optimality: Yes/No??? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 35

36 Iterative deepening search(ids) depth = 0 depth = 1 depth =2 depth =3 depth =4 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 36

37 IDS- Analysis Completeness: Yes! Optimality: Yes for uniform cost edges; can be modified to explore uniform cost tree Time Complexity: db + d 1 b b d = O(b d ) Space Complexity: O(bd) Asymptotic ratio of # nodes expanded by IDS vs DFS: (b + 1) b 1 1for large values of b 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 37

38 Summary 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 38

39 Graph Search BFS-? DFS-? IDDFS-? 1/21/2014 CSL 302 ARTIFICIAL INTELLIGENCE, INDIAN INSTITUTE OF TECHNOLOGY ROPAR 39

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