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Agents and Uninformed Search ECE457 Applied Artificial Intelligence Spring 2007 Lecture #2.5 Rational Agents Sensors Actions Environment Percepts Simple reflex agent Model-based agent Goal-based agent Utility-based agent Learning agent Actuators Agent Program ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 2 Simple Reflex Agent Environment Percepts Actions Actuators Sensors Current State Selected Action If-then Rules ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 3 Simple Reflex Agent Dune II (1992) units were simple reflex agents Harvester rules: ECE457 Applied Artificial Intelligence IF at refinery AND not empty THEN empty IF at refinery AND empty THEN go harvest IF harvesting AND not full THEN continue harvesting IF harvesting AND full THEN go to refinery IF under attack by infantry THEN squash them R. Khoury (2007) Page 4 Model-Based Agent Environment Percepts Actions Actuators Sensors Current State Previous perceptions Selected Action World changes Impact of actions ECE457 Applied Artificial Intelligence R. Khoury (2007) If-then Rules Page 5 Goal-Based Agent Environment Percepts Actions Actuators Sensors Current State Previous perceptions State if I do action X Selected Action World changes Goal Impact of actions ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 6 Utility-Based Agent Environment Percepts Actions Actuators Sensors Current State Previous perceptions State if I do action X Happiness in that state World changes Selected Action Utility Impact of actions ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 7 Learning Agent Environment Percepts Actions Actuators Sensors Performance Element Critic Feedback Knowledge Changes Learning Problem Element Learning Goals Generator ECE457 Applied Artificial Intelligence Performance standard R. Khoury (2007) Page 8 Properties of the Environment Fully observable vs. partially observable Deterministic vs. stochastic vs. strategic Waits for agent vs. goes on without agent vs. timer Discrete vs. continuous Independent episodes vs. series of events Static vs. dynamic vs. semi-dynamic Controlled by agent vs. randomness vs. multiagents Episodic vs. sequential See everything vs. hidden information Finite distinct states vs. uninterrupted sequence Single agent vs. cooperative vs. competitive Alone vs. team-mates vs. opponents ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 9 Properties of the Environment Crossword Puzzle Monopoly Fully observable, stochastic, sequential, static, discrete, competitive multi-agent Driving a car Fully observable, deterministic, sequential, static, discrete, single-agent Partially observable, stochastic, sequential, dynamic, continuous, cooperative multi-agent Assembly-line inspection robot Fully observable, deterministic, episodic, dynamic, continuous, single-agent ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 10 Well-Defined Problems Initial state Set of actions Goal test Move blank left, right, up or down, provided it does not get out of the game Are the tiles in the “goal state” order? Concept of cost Each action costs 1 Path cost is the sum of actions ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 11 Well-Defined Problems Travelling salesman problem Initial state Am I in the initial city after having visited every city? Concept of cost ECE457 Applied Artificial Intelligence Move to an unvisited city Goal test Any city Set of actions Find the shortest round trip to visit each city exactly once Action cost: distance between cities Path cost: total distance travelled R. Khoury (2007) Page 12 Properties of Search Algos. Completeness Optimality Is the algorithm guaranteed to find the best goal node, i.e. the one with the cheapest path cost? Time complexity Is the algorithm guaranteed to find a goal node, if one exists? How many nodes are generated? Space complexity What’s the maximum number of nodes stored in memory? ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 13 Breath-First Search Explores each node of each level in order Complete if b finite & optimal if cost constant ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 14 Breath-First Search Worst case: goal is last node of depth d Number of generated nodes: b+b²+b³+…+bd+(bd+1-b) = O(bd+1) Space & time complexity: all generated nodes ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 15 Uniform-Cost Search Explore the node with the cheapest path cost first Condition: No zero-cost or negative-cost edges. Minimum cost of an action is є Complete and optimal ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 16 Uniform-Cost Search Worst case: goal has path cost C*, all other actions have minimum cost of є Depth explored before taking action C*: C*/є Number of generated nodes: O(bC*/є) Space & time complexity: all generated nodes є C* є є є ECE457 Applied Artificial Intelligence є є є є є є R. Khoury (2007) є є є є Page 17 є Depth-First Search Explores an entire branch first Removes branch from memory after exploration Complete if m finite & not optimal ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 18 Depth-First Search Worst case for space: goal is last node of first branch After that, we start deleting nodes Number of generated nodes: b nodes at each of m levels Space complexity: all generated nodes = O(bm) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 19 Depth-First Search Worst case for time: goal is last node of last branch Number of nodes generated: b nodes for each node of m levels (entire tree) Time complexity: all generated nodes O(bm) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 20 Depth-Limited Search Depth-First Search with depth limit l Avoids problems of Depth-First Search when trees are unbounded Depth-First Search is Depth-Limited Search with l = Complete, if l > d Not optimal ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 21 Depth-Limited Search Worst case for space: goal is last node of first branch After that, we start deleting nodes Number of generated nodes: b nodes at each of l levels Space complexity: all generated nodes = O(bl) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 22 Depth-Limited Search Worst case for time: goal is last node of last branch Number of nodes generated: b nodes for each node of l levels (entire tree to depth l) Time complexity: all generated nodes O(bl) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 23 Iterative Deepening Search Depth-First Search with increasing depth limit l Repeat depth-limited search over and over, with l=l+1 Avoids problems of Depth-First Search when trees are unbounded Avoids problem of Depth-Limited Search when goal depth d > l Complete , if b is finite Optimal, if path cost is equal to depth Guaranteed to return the shallowest goal ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 24 Depth-Limited Search Worst case for space: goal is last node of first branch After that, we start deleting nodes Number of generated nodes: b nodes at each of d levels Space complexity: all generated nodes = O(bd) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 25 Depth-Limited Search Worst case for time: goal is last node of last branch Number of nodes generated: b nodes for each node of d levels (entire tree to depth d) Time complexity: all generated nodes O(bd) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 26 Depth Searches Depth-first Depth-limited Iterative search search deepening search Depth limit m l d Time complexity O(bm) O(bl) O(bd) Space complexity O(bm) O(bl) O(bd) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 27 Summary of Searches Breath- Uniform Depth Depth- Iterative first Cost -first limited deepening Complete Yes1 Yes1 No4 No5 Yes1 Optimal Yes2 Yes3 No No Yes2 Time O(bd+1) O(bC*/є) O(bm) O(bl) O(bd) Space O(bd+1) O(bC*/є) O(bm) O(bl) O(bd) 1: Assuming b finite (common in trees) 2: Assuming equal action costs 3: Assuming all costs є ECE457 Applied Artificial Intelligence 4: Unless m finite (uncommon in trees) 5: Unless l precisely selected R. Khoury (2007) Page 28 Summary / Example Going from Arad to Bucharest ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 29 Summary / Example Initial state Action Move to a neighbouring city, if a road exists. Goal test Being in Arad Are we in Bucharest? Cost Move cost = distance between cities Path cost = distance travelled since Arad ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 30 Summary / Example Breath-First Search ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 31 Summary / Example Uniform-Cost Search ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 32 Summary / Example Depth-First Search ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 33 Summary / Example Depth-Limited Search, l = 4 ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 34 Summary / Example Iterative Deepening Search ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 35 Repeated States Example: 8-puzzle left left right down ECE457 Applied Artificial Intelligence down left R. Khoury (2007) up down Page 36 Repeated States Unavoidable in problems where Actions are reversible Multiple paths to the same state are possible Can greatly increase the number of nodes in a tree Or even make a finite tree infinite! ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 37 Repeated States A A B B B C C C C C D E D D D D D D D D EEEEEEEE EEEEEEEE ECE457 Applied Artificial Intelligence Each state generates a single child twice 26 different states 225 leaves (i.e. state Z) Over 67M nodes in the tree R. Khoury (2007) Page 38 Repeated States Maintain a closed list of visited states Closed list (for expanded nodes) vs. open list (for fringe nodes) Detect and discard repeated states upon generation Increases space complexity ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 39