PEAS: Medical diagnosis system  Performance measure  Patient health, cost, reputation  Environment  Patients, medical staff, insurers, courts  Actuators  Screen display,  Sensors  Keyboard/mouse

Environment types PacmanBackgammonDiagnosisTaxi Fully or partially observable Single-agent or multiagent Deterministic or stochastic Static or dynamic Discrete or continuous Known or unknown

Agent design  The environment type largely determines the agent design  Partially observable => agent requires memory (internal state), takes actions to obtain information  Stochastic => agent may have to prepare for contingencies, must pay attention while executing plans  Multi-agent => agent may need to behave randomly  Static => agent has enough time to compute a rational decision  Continuous time => continuously operating controller

Agent types  In order of increasing generality and complexity  Simple reflex agents  Reflex agents with state  Goal-based agents  Utility-based agents

Simple reflex agents

A reflex Pacman agent in Python class TurnLeftAgent(Agent): def getAction(self, percept): legal = percept.getLegalPacmanActions() current = percept.getPacmanState().configuration.direction if current == Directions.STOP: current = Directions.NORTH left = Directions.LEFT[current] if left in legal: return left if current in legal: return current if Directions.RIGHT[current] in legal: return Directions.RIGHT[current] if Directions.LEFT[left] in legal: return Directions.LEFT[left] return Directions.STOP

Pacman agent contd.  Can we (in principle) extend this reflex agent to behave well in all standard Pacman environments?

Handling complexity  Writing behavioral rules or environment models more difficult for more complex environments  E.g., rules of chess (32 pieces, 64 squares, ~100 moves)  ~ pages as a state-to-state transition matrix (cf HMMs, automata) R.B.KB.RPPP..PPP..N..N…..PP….q.pp..Q..n..n..ppp..pppr.b.kb.r  ~ pages in propositional logic (cf circuits, graphical models)  …  1 page in first-order logic  x,y,t,color,piece On(color,piece,x,y,t)  …

Reflex agents with state

Goal-based agents

Utility-based agents

Summary  An agent interacts with an environment through sensors and actuators  The agent function, implemented by an agent program running on a machine, describes what the agent does in all circumstances  PEAS descriptions define task environments; precise PEAS specifications are essential  More difficult environments require more complex agent designs and more sophisticated representations

CS 188: Artificial Intelligence Search Instructor: Stuart Russell ]

Today  Agents that Plan Ahead  Search Problems  Uninformed Search Methods  Depth-First Search  Breadth-First Search  Uniform-Cost Search

Agents that plan ahead  Planning agents:  Decisions based on predicted consequences of actions  Must have a transition model: how the world evolves in response to actions  Must formulate a goal  Spectrum of deliberativeness:  Generate complete, optimal plan offline, then execute  Generate a simple, greedy plan, start executing, replan when something goes wrong

Video of Demo Replanning

Video of Demo Mastermind

Search Problems

 A search problem consists of:  A state space  For each state, a set Actions(s) of allowable actions  A transition model Result(s,a)  A step cost function c(s,a,s’)  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 E {N, E} 1 1

Search Problems Are Models

Example: Travelling in Romania  State space:  Cities  Actions:  Go to adjacent city  Transition model  Result(Go(B),A) = B  Step cost  Distance along road link  Start state:  Arad  Goal test:  Is state == Bucharest?  Solution?

What’s in a State Space?  Problem: Pathing  States: (x,y) location  Actions: NSEW  Transition model: update location  Goal test: is (x,y)=END  Problem: Eat-All-Dots  States: {(x,y), dot booleans}  Actions: NSEW  Transition model: update location and possibly a dot boolean  Goal test: dots all false The real world state includes every last detail of the environment A search state abstracts away details not needed to solve the problem MN states MN2 MN states

Quiz: Safe Passage  Problem: eat all dots while keeping the ghosts perma-scared  What does the state space have to specify?  (agent position, dot booleans, power pellet booleans, remaining scared time)

State Space Graphs and Search Trees

State Space Graphs  State space graph: A mathematical representation of a search problem  Nodes are (abstracted) world configurations  Arcs represent transitions resulting from actions  The goal test is a set of goal nodes (maybe only one)  In a state space graph, each state occurs only once!  We can rarely build this full graph in memory (it’s too big), but it’s a useful idea

More examples

Search Trees  A search tree:  A “what if” tree of plans and their outcomes  The start state is the root node  Children correspond to possible action outcomes  Nodes show states, but correspond to PLANS that achieve those states  For most problems, we can never actually build the whole tree “E”, 1.0“N”, 1.0 This is now / start Possible futures

State Space Graphs vs. Search Trees

Quiz: State Space Graphs vs. Search Trees S G b a Consider this 4-state graph: Important: Lots of repeated structure in the search tree! How big is its search tree (from S)? S a b G G ab G aGb

Tree Search

Search Example: Romania

Searching with a Search Tree  Search:  Expand out potential plans (tree nodes)  Maintain a frontier of partial plans under consideration  Try to expand as few tree nodes as possible

General Tree Search  Important ideas:  Frontier  Expansion  Exploration strategy  Main question: which frontier nodes to explore? function TREE-SEARCH(problem) returns a solution, or failure initialize the frontier using the initial state of problem loop do if the frontier is empty then return failure choose a leaf node and remove it from the frontier if the node contains a goal state then return the corresponding solution expand the chosen node, adding the resulting nodes to the frontier

Depth-First Search

S a b d p a c e p h f r q qc G a q e p h f r q qc G a S G d b p q c e h a f r q p h f d b a c e r Strategy: expand a deepest node first Implementation: Frontier is a LIFO stack

Search Algorithm Properties

 Complete: Guaranteed to find a solution if one exists?  Optimal: Guaranteed to find the least cost path?  Time complexity?  Space complexity?  Cartoon of search tree:  b is the branching factor  m is the maximum depth  solutions at various depths  Number of nodes in entire tree?  1 + b + b 2 + …. b m = O(b m ) … b 1 node b nodes b 2 nodes b m nodes m tiers

Depth-First Search (DFS) Properties … b 1 node b nodes b 2 nodes b m nodes m tiers  What nodes does DFS expand?  Some left prefix of the tree.  Could process the whole tree!  If m is finite, takes time O(b m )  How much space does the frontier take?  Only has siblings on path to root, so O(bm)  Is it complete?  m could be infinite, so only if we prevent cycles (more later)  Is it optimal?  No, it finds the “leftmost” solution, regardless of depth or cost

Breadth-First Search

S a b d p a c e p h f r q qc G a q e p h f r q qc G a S G d b p q c e h a f r Search Tiers Strategy: expand a shallowest node first Implementation: Frontier is a FIFO queue

Breadth-First Search (BFS) Properties  What nodes does BFS expand?  Processes all nodes above shallowest solution  Let depth of shallowest solution be s  Search takes time O(b s )  How much space does the frontier take?  Has roughly the last tier, so O(b s )  Is it complete?  s must be finite if a solution exists, so yes!  Is it optimal?  Only if costs are all 1 (more on costs later) … b 1 node b nodes b 2 nodes b m nodes s tiers b s nodes

Quiz: DFS vs BFS

 When will BFS outperform DFS?  When will DFS outperform BFS? [Demo: dfs/bfs maze water (L2D6)]

Video of Demo Maze Water DFS/BFS (part 1)

Video of Demo Maze Water DFS/BFS (part 2)

Iterative Deepening … b  Idea: get DFS’s space advantage with BFS’s time / shallow-solution advantages  Run a DFS with depth limit 1. If no solution…  Run a DFS with depth limit 2. If no solution…  Run a DFS with depth limit 3. …..  Isn’t that wastefully redundant?  Generally most work happens in the lowest level searched, so not so bad!

Finding a least-cost path BFS finds the shortest path in terms of number of actions. It does not find the least-cost path. We will now cover a similar algorithm which does find the least-cost path. START GOAL d b p q c e h a f r

Uniform Cost Search

S a b d p a c e p h f r q qc G a q e p h f r q qc G a Strategy: expand a cheapest node first: Frontier is a priority queue (priority: cumulative cost) S G d b p q c e h a f r Cost contours 2

… Uniform Cost Search (UCS) Properties  What nodes does UCS expand?  Processes all nodes with cost less than cheapest solution!  If that solution costs C* and arcs cost at least , then the “effective depth” is roughly C*/   Takes time O(b C*/  ) (exponential in effective depth)  How much space does the frontier take?  Has roughly the last tier, so O(b C*/  )  Is it complete?  Assuming best solution has a finite cost and minimum arc cost is positive, yes!  Is it optimal?  Yes! (Proof next lecture via A*) b C*/  “tiers” c  3 c  2 c  1

Uniform Cost Issues  Remember: UCS explores increasing cost contours  The good: UCS is complete and optimal!  The bad:  Explores options in every “direction”  No information about goal location  We’ll fix that soon! Start Goal … c  3 c  2 c  1

Video of Demo Empty UCS

Video of Demo Maze with Deep/Shallow Water --- DFS, BFS, or UCS? (part 1)

Video of Demo Maze with Deep/Shallow Water --- DFS, BFS, or UCS? (part 2)

Video of Demo Maze with Deep/Shallow Water --- DFS, BFS, or UCS? (part 3)

Search Gone Wrong?