Uninformed Search

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Uninformed Search

• Reading Chapter 3 by today, Chapter 4.1-4.3 by
  Wednesday, 9/12
• Homework 2 will be given out on Wednesday
• DID YOU TURN IN YOUR SURVEY? USE COURSEWORKS AND
  TAKE THE TEST

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Pending Questions

• Class web page
• http//www.cs.columbia.edu/kathy/cs4701
• Reminder Dont forget assignment 0 (survey). See
  courseworks

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• When solving problems, dig at the roots instead
  of just hacking at the leaves.
• Anthony J. D'Angelo, The College Blue Book

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Agenda

• Introduction of search as a problem-solving
  paradigm
• Uninformed search algorithms
• Example using the 8-puzzle
• Formulation of another example sodoku
• Transition to greedy search, one method for
  informed search

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Goal-based Agents

• Agents that work towards a goal
• Select the action that more likely achieve the
  goal
• Sometimes an action directly achieves a goal
  sometimes a series of actions are required

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Problem solving as search

• Goal formulation
• Problem formulation
• Actions
• States

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Uninformed

• Search through the space of possible solutions
• Use no knowledge about which path is likely to be
  best

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Characteristics

• Before actually doing something to solve a
  puzzle, an intelligent agent explores
  possibilities in its head
• Search mental exploration of possibilities
• Making a good decision requires exploring several
  possibilities
• Execute the solution once its found

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Formulating Problems as Search

• Given an initial state and a goal, find the
  sequence of actions leading through a sequence of
  states to the final goal state.
• Terms
• Successor function given action and state,
  returns action, successors
• State space the set of all states reachable from
  the initial state
• Path a sequence of states connected by actions
• Goal test is a given state the goal state?
• Path cost function assigning a numeric cost to
  each path
• Solution a path from initial state to goal state

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Example the 8-puzzle

• How would you use AI techniques to solve the
  8-puzzle problem?

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8-puzzle URLS

• http//www.permadi.com/java/puzzle8
• http//www.cs.rmit.edu.au/AI-Search/Product

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8 Puzzle

• States integer locations of tiles
• (0 1 2 3 4 5 6 7 B)
• (0 1 2)(3 4 5) (6 7 B)
• Action left, right, up, down
• Goal test is current state (0 1 2 3 4 5 6 7
  B)?
• Path cost same for all paths
• Successor function given up, (5 2 3 B 1 8 4 7
  6) -gt ?
• What would the state space be for this problem?

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What are we searching?

• State space vs. search space
• State represents a physical configuration
• Search space represents a tree/graph of possible
  solutions an abstract configuration
• Nodes
• Abstract data structure in search space
• Parent, children, depth, path cost, associated
  state
• Expand
• A function that given a node, creates all
  children nodes, using successsor function

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Data structures Searching data
AI Searching solutions
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Uninformed Search Strategies

• The strategy gives the order in which the search
  space is searched
• Breadth first
• Depth first
• Depth limited search
• Iterative deepening
• Uniform cost

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Breadth first Algorithm
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Depth-first Algorithm
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Complexity Analysis

• Completeness is the algorithm guaranteed to find
  a solution when there is one?
• Optimality Does the strategy find the optimal
  solution?
• Time How long does it take to find a solution?
• Space How much memory is needed to perform the
  search?

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Cost variables

• Time number of nodes generated
• Space maximum number of nodes stored in memory
• Branching factor b
• Maximum number of successors of any node
• Depth d
• Depth of shallowest goal node
• Path length m
• Maximum length of any path in the state space

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Can we combine benefits of both?

• Depth limited
• Select some limit in depth to explore the problem
  using DFS
• How do we select the limit?
• Iterative deepening
• DFS with depth 1
• DFS with depth 2 up to depth d

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Properties of the task environment?

• Fully observable
• Deterministic
• Episodic
• Static
• Discrete
• Single agent

• Partially observable
• Stochastic
• Sequential
• Dynamic
• Continuous
• Multiagent

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Three types of incompleteness

• Sensorless problems
• Contingency problems
• Adversarial problems
• Exploration problems

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End of Class Questions?
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Sodoku
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Informed Search
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Heuristics

• Suppose 8-puzzle off by one
• Is there a way to choose the best move next?
• Good news Yes!
• We can use domain knowledge or heuristic to
  choose the best move

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0 1 2
3 4 5
6 7
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Nature of heuristics

• Domain knowledge some knowledge about the game,
  the problem to choose
• Heuristic a guess about which is best, not
  exact
• Heuristic function, h(n) estimate the distance
  from current node to goal

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Heuristic for the 8-puzzle

• tiles out of place (h1)
• Manhattan distance (h2)
• Sum of the distance of each tile from its goal
  position
• Tiles can only move up or down ? city blocks

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0 1 2
3 4 5
6 7
Goal State
0 2 5
3 1 7
6 4
0 1 2
3 4 5
6 7
h11 h21
h15 h2111227
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Best first searches

• A class of search functions
• Choose the best node to expand next
• Use an evaluation function for each node
• Estimate of desirability
• Implementation sort fringe, open in order of
  desirability
• Today greedy search, A search

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Greedy search

• Evaluation function heuristic function
• Expand the node that appears to be closest to the
  goal

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Greedy Search

• OPEN start node CLOSED empty
• While OPEN is not empty do
• Remove leftmost state from OPEN, call it X
• If X goal state, return success
• Put X on CLOSED
• SUCCESSORS Successor function (X)
• Remove any successors on OPEN or CLOSED
• Compute heuristic function for each node
• Put remaining successors on either end of OPEN
• Sort nodes on OPEN by value of heuristic function
• End while

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End of Class Questions?