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Berkeley COMPSCI 188 - Lecture 2: Queue-Based Search

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1CS 188: Artificial IntelligenceFall 2009Lecture 2: Queue-Based Search9/1/2009Dan Klein – UC BerkeleyMultiple slides from Stuart Russell, Andrew Moore Announcements Project 0: Python Tutorial Due tomorrow! There is a lab tomorrow from 1pm-3pm in Soda 275 The lab time is optional, but P0 itself is not On submit, you should get email from the autograder Project 1: Search On the web today Start early and ask questions. It’s longer than most! Other Section 107 was opened up, Fridays 1-2pm My OHs Monday were in the lab, Thursday back in 711 Soda GSI OHs on web site2Today Agents that Plan Ahead Search Problems Uninformed Search Methods (part review for some) Depth-First Search Breadth-First Search Uniform-Cost Search Heuristic Search Methods (new for all) Greedy SearchReflex Agents Reflex agents: Choose action based on current percept (and maybe memory) May have memory or a model of the world’s current state Do not consider the future consequences of their actions Act on how the world IS Can a reflex agent be rational?[demo: reflex optimal / loop ]3Goal Based Agents Goal-based agents: Plan ahead Ask “what if” Decisions based on (hypothesized) consequences of actions Must have a model of how the world evolves in response to actions Act on how the world WOULD BE[demo: plan fast / slow ]Search Problems A search problem consists of: A state space A successor function A start state and a goal test A solution is a sequence of actions (a plan) which transforms the start state to a goal state“N”, 1.0“E”, 1.04Example: Romania State space: Cities Successor function: Go to adj city with cost = dist Start state: Arad Goal test: Is state == Bucharest? Solution?State Space Graphs State space graph: A mathematical representation of a search problem For every search problem, there’s a corresponding state space graph The successor function is represented by arcs We can rarely build this graph in memory (so we don’t)SGdbpqcehafrRidiculously tiny search graph for a tiny search problem5State Space Sizes? Search Problem:Eat all of the food Pacman positions:10 x 12 = 120 Food count: 30 Ghost positions: 12 Pacman facing:up, down, left, rightSearch Trees A search tree: This is a “what if” tree of plans and outcomes Start state at the root node Children correspond to successors Nodes contain states, correspond to PLANS to those states For most problems, we can never actually build the whole tree“E”, 1.0“N”, 1.06Another Search Tree Search: Expand out possible plans Maintain a fringe of unexpanded plans Try to expand as few tree nodes as possibleGeneral Tree Search Important ideas: Fringe Expansion Exploration strategy Main question: which fringe nodes to explore?Detailed pseudocode is in the book!7Example: Tree SearchSGdbpqcehafrState Graphs vs. Search TreesSabdpacephfrqq cGaqephfrqq cGaSGdbpqcehafrWe construct both on demand – and we construct as little as possible.Each NODE in in the search tree is an entire PATH in the problem graph.8States vs. Nodes Nodes in state space graphs are problem states Represent an abstracted state of the world Have successors, can be goal / non-goal, have multiple predecessors Nodes in search trees are plans Represent a plan (sequence of actions) which results in the node’s state Have a problem state and one parent, a path length, a depth & a cost The same problem state may be achieved by multiple search tree nodesDepth 5Depth 6ParentNodeSearch NodesProblem StatesActionReview: Depth First SearchSabdpacephfrqq cGaqephfrqq cGaSGdbpqcehafrqphfdbacerStrategy: expand deepest node firstImplementation: Fringe is a LIFO stack9Review: Breadth First SearchSabdpacephfrqq cGaqephfrqq cGaSGdbpqcehafrSearchTiersStrategy: expand shallowest node firstImplementation: Fringe is a FIFO queueSearch Algorithm Properties Complete? Guaranteed to find a solution if one exists? Optimal? Guaranteed to find the least cost path? Time complexity? Space complexity?Variables:n Number of states in the problemb The average branching factor B(the average number of successors)C* Cost of least cost solutions Depth of the shallowest solutionm Max depth of the search tree10DFS Infinite paths make DFS incomplete… How can we fix this?Algorithm Complete Optimal Time SpaceDFSDepth First SearchN NO(BLMAX) O(LMAX)STARTGOALabN N Infinite InfiniteDFS With cycle checking, DFS is complete.*  When is DFS optimal?Algorithm Complete Optimal Time SpaceDFSw/ Path CheckingY NO(bm+1) O(bm)…b1 nodeb nodesb2nodesbmnodesm tiers* Or graph search – next lecture.11BFS When is BFS optimal?Algorithm Complete Optimal Time SpaceDFSw/ Path CheckingBFSY NO(bm+1) O(bm)…b1 nodeb nodesb2nodesbmnodess tiersY N*O(bs+1) O(bs)bsnodesComparisons When will BFS outperform DFS? When will DFS outperform BFS?12Iterative DeepeningIterative deepening uses DFS as a subroutine:1. Do a DFS which only searches for paths of length 1 or less. 2. If “1” failed, do a DFS which only searches paths of length 2 or less.3. If “2” failed, do a DFS which only searches paths of length 3 or less.….and so on.Algorithm Complete Optimal Time SpaceDFSw/ Path CheckingBFSIDY NO(bm+1) O(bm)Y N*O(bs+1) O(bs)Y N*O(bs+1) O(bs)…bCosts on ActionsNotice that BFS finds the shortest path in terms of number of transitions. It does not find the least-cost path.We will quickly cover an algorithm which does find the least-cost path. STARTGOALdbpqcehafr2928182314415132213Uniform Cost SearchSabdpacephfrqq cGaqephfrqq cGaExpand cheapest node first:Fringe is a priority queueSGdbpqcehafr39116411571381011171106391128811512Cost contours2Priority Queue Refresherpq.push(key, value) inserts (key, value) into the queue.pq.pop()returns the key with the lowest value, and removes it from the queue. You can decrease a key’s priority by pushing it again Unlike a regular queue, insertions aren’t constant time, usually O(log n) We’ll need priority queues for cost-sensitive search methods A priority queue is a data structure in which you can insert and retrieve (key, value) pairs with the following operations:14Uniform Cost SearchAlgorithm Complete Optimal Time SpaceDFSw/ Path CheckingBFSUCSY NO(bm+1) O(bm)…bC*/εtiersY NO(bs+1) O(bs)Y* YO(bC*/ε) O(bC*/ε)* UCS can fail


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Berkeley COMPSCI 188 - Lecture 2: Queue-Based Search

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