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Lirong Xia

Basic search. Lirong Xia. Reminder. TA OH Joe Johnson (mainly in charge of the project): Wed 12:30-1:30 pm, Amos Eaton 217 Hongzhao Huang (everything else): Thur 12:30-1:30 pm, Amos Eaton 125 Project0 due on next Tuesday Jan 28 midnight LMS working! 2 points

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Lirong Xia

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  1. Basic search Lirong Xia

  2. Reminder • TA OH • Joe Johnson (mainly in charge of the project): Wed 12:30-1:30 pm, Amos Eaton 217 • HongzhaoHuang (everything else): Thur 12:30-1:30 pm, Amos Eaton 125 • Project0 due on next Tuesday Jan 28 midnight • LMS working! • 2 points • submission instruction changed, if you have uploaded project 0, please re-submit it • Sign up on piazza by Jan 28 midnight (1 point) • Try your best to use piazza for Q/A • You are encouraged to stop me and ask questions in class

  3. Last class

  4. Welcome back to the earth

  5. Today’s schedule • Rational agents • Search problems • State space graph vs search trees • Uninformed search • Depth first search (DFS) algorithm • Breadth first search (BFS) algorithm

  6. Rational Agents Agent • An agent is an entity that perceives and acts. • A rational agent selects actions that maximize its utility function. • Characteristics of the percepts, environment, and action space dictate techniques for selecting rational actions. Actuators Sensors Percepts Actions Environment

  7. Pacman as an Agent Agent Sensors Percepts Environment ? Actuators Actions

  8. Reflex vs goal-based Agents • Reflex agents: • Act on how the world IS • Do not consider the future consequences of their actions • Goal-based agents: • Plan ahead • Act on how the world WOULD BE • Must have a model of how the world evolves in response to actions • We will be interested in goal-based agents in this class

  9. When goal = search for something

  10. More general than you may think

  11. Can we teach agents how to search for all of these?

  12. WARNING: leisure time is over!Let’s do science

  13. Search Problems • A search problem consists of: • A state space …… • A successor function (with actions, costs) • 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

  14. What’s in a State Space? The world state specifies every last detail of the environment A search state keeps only the details needed (abstraction) • Problem: Pathing • States: (x,y) location • Actions: NSEW • Successor: adjacent locations • Goal test: is (x,y) = END • Problem: Eat-All-Dots • States: {(x,y), dot booleans} • Actions: NSEW • Successor: updated location and dot booleans • Goal test: dots all false

  15. State Space Sizes? • World state: • Agent positions: 120 • Food count: 30 • Ghost positions: 12 • Agent facing: NSEW • How many • World states? • States for pathing? • States for eat-all-dots?

  16. 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 is memory (so we don’t) Ridiculously tiny search graph for a tiny search problem

  17. Search 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

  18. Generic search algorithm • Fringe = set of nodes generated but not expanded = nodes we know we still have to explore • fringe := {node corresponding to the initial state} • loop: • if fringe empty, declare failure • choose and remove a node v from fringe • check if v’s state s is a goal state; if so, declare success • if not, expand v, insert resulting nodes into fringe • Key question in search: Which of the generated nodes do we expand next?

  19. Example 2: Capital Region Cohoes • State space: • Cities • Successor function: • Roads: Go to adjacent city with cost = dist • Start state: • Cohoes • Goal test: • Is state == Delmar • Solution? 4.4 Latham 4.1 4 Troy 3.1 5.3 10.7 Loudonville 8 4.3 Guilderland 8.7 Albany 1.5 Rensselaer 5.2 Delmar

  20. Another Search Tree Cohoes Latham Troy Cohoes Troy Loudonville Cohoes Latham Loudonville La T C La Lo A • Search: • Expand out possible plans • Maintain a fringe of unexpanded plans • Try to expand as few tree nodes as possible

  21. State Graphs vs. Search Trees State graph Search trees • State graphs: a representation of the search problem • each node is an abstract of the state of the world • Search tree: a tool that helps us to find the solution • each node represents an entire path in the graph • tree nodes are constructed on demand and we construct as little as possible

  22. States 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 and a cost • The same problem state may be achieved by multiple search tree nodes Problem States Search Nodes

  23. Uninformed search • Uninformed search: given a state, we only know whether it is a goal state or not • Cannot say one nongoal state looks better than another nongoal state • Can only traverse state space blindly in hope of somehow hitting a goal state at some point • Also called blind search • Blind does not imply unsystematic!

  24. Breadth-first search

  25. Example b a Start c d e GOAL

  26. Properties of breadth-first search • Ignores the cost • May expand more nodes than necessary • BFS is complete: if a solution exists, one will be found • BFS finds a shallowest solution • Not necessarily an optimal solution • If every node has b successors (the branching factor), shallowest solution is at depth d, then fringe size will be at least bd at some point • This much space (and time) required 

  27. Fixed BFS • Never expand a node whose state has been visited • Fringe can be maintained as a First-In-First-Out (FIFO) queue (class Queue in util.py) • Maintain a set of visited states • fringe := {node corresponding to initial state} • loop: • if fringe empty, declare failure • choose and remove the top node v from fringe • check if v’s state s is a goal state; if so, declare success • if v’s state has been visited before, skip • if not, expand v, insert resulting nodes whose states have not been visited into fringe • This is the BFS you should implement in project 1

  28. Depth-first search

  29. Example b a Start c d e GOAL

  30. Properties of depth-first search • Ignores cost • Not complete (might cycle through nongoal states) • If solution found, generally not optimal/shallowest • If every node has b successors (the branching factor), and we search to at most depth m, fringe is at most bm • Much better space requirement  • Actually, generally don’t even need to store all of fringe • Time: still need to look at every node • bm + bm-1 + … + 1 (for b>1, O(bm)) • Inevitable for uninformed search methods…

  31. Fixed DFS • Never expand a node whose state has been visited • Fringe can be maintained as a Last-In-First-Out (LIFO) queue (class Stack in util.py) • Maintain a set of visited states • fringe := {node corresponding to initial state} • loop: • if fringe empty, declare failure • choose and remove the top node v from fringe • check if v’s state s is a goal state; if so, declare success • if v’s state has been visited before, skip • if not, expand v, insert resulting nodes whose states have not been visited into fringe • This is the DFS you should implement in project 1

  32. You can start to work on Project 1 now • Read the instructions on course website and the comments in search.py first • Q1: DFS • LIFO • Q2: BFS • FIFO • Due in two weeks (Feb 7) • Check util.py for LIFO and FIFO implementation • Use piazza for Q/A

  33. Dodging the bullets • The auto-grader is very strict • 0 point for expanding more-than-needed states • no partial credit • Hint 1: do not include print "Start:", problem.getStartState() in your formal submission • comment out all debuging commands • Hint 2: remember to check if a state has been visited before • Hint 3: return a path from start to goal. You should pass the local test before submission (details and instructions on project 1 website)

  34. Reminder • TA OH • Joe Johnson (mainly in charge of the project): Wed 12:30-1:30 pm, Amos Eaton 217 • HongzhaoHuang (everything else): Thur 12:30-1:30 pm, Amos Eaton 125 • Project0 due on next Tuesday Jan 28 midnight • LMS working! • 2 points • submission instruction changed, if you have uploaded project 0, please re-submit it • Project1 due on Feb 7 midnight • Sign up on piazza by Jan 28 midnight (1 point) • Try your best to use piazza for Q/A • You are encouraged to stop me and ask questions in class

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