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Key Concepts:
Terms in this set (73)
Agent
Perceives its environment through sensors
Achieves its goals by acting on its environment by using actuators
Single-Reflex Agents
Actions depends on its immediate precepts
Model-Based Agents
Actions depend on history/unperceived aspects of the world. It needs to maintain an internal world model.
Goal-Based Agents
Agents with variable goals and forms plans to achieve its goals.
Utility-based Agents
Agents that juggles multiple goals that are sometimes conflicting. Optimises utility over a range of goals.
Expected Utility
Utility + probability of success
Partially Observable Environment
Sensors of an agent don't fully describe an environment
Deterministic Environment
The next state is fully determined by current state + actions
Stochastic Enviroment
Random state changes
Episodic Environment
Next action is not dependant on last action (think mail sorting)
Sequential Environment
Next action is dependant on last action (think crossword)
Static Environment
Environment stays unchanged while agent deliberates (think crossword)
Dynamic Environment
Environment changes as agent deliberates (think chess)
Discrete Environment
Percepts, actions and episodes are discrete (think chess)
Continuous Environment
Percepts, actions and episodes are continuous (think robot car)
Single Agent Enviroment
In the environment, only one object can be modelled as an agent (think crossword)
Multi-Agent
In the environment, multiple objects can be modelled as agents (think poker)
Problem-Solving Agent
Agent that implements a "formulate, search, execute" design
Single-State Formulation
1. Initial state
2. Successor Function
3. Goal Test
4. Path Cost
Successor Function
S(x) = set of Actions-State pairs
Path Cost
C(x,a,y) = Cost of action a in state x to state y
Tree search Algorithms
An offline, simulated exploration of state spaces
(Search Strategy) Completeness
Search strategy finds a solution if one exists
Time Complexity
Number of nodes generated in a search strategy
Space Complexity
Maximum number of nodes in memory
Optimality
The finding of a least-cost solution when using a specific search strategy
Breadth-First Search
Expands shallowest unexpanded node.
Fifo queue (puts successors at the end of list)
(has space + time complexity problems)
Depth-First Search
Expands deepest unexpanded node.
Lifo queue (puts successor at front)
(not optimal or complete, time complexity problems)
Which search strategy to use when completeness/ optimal solutions is important?
Breadth-First Search
Which search strategy to use when solutions are dense/ low cost is important?
Depth-First Search
Depth-Limited search
Searches until for solution until depth i is reached
(not optimal or complete)
Iterative Deepening Search
Searches until depth i, and if no solution is found, then searches i+1 and repeats the process until solution is found
Minimax Search
Chooses state with the highest minimax value
(Example: if you=max, look at your possible moves and choose the state that will lead your opponent to choose the highest minimum choice.)
Alpha-Beta Pruning
MiniMax search but doesn't continue searching paths that are aren't optimal
Greedy Best-First Search
Expands the node that appears to optimal. Uses evaluation function f(n) = (heuristic)(estimated cost)
(not optimal or complete)
A* Search
Similar to Best-First but avoids already expensive paths using evaluation function f(n) = g(n) + h(n)
where f(n) = estimated total cost of path through n to goal, g(n) = cost so far, h(n) = heuristic
Knowledge Base
A set of sentences in a formal language
Entailment
Necessary truth of one sentence given another
(ie: KB including "Celtics won", "Hearts won" entails "Hearts won or Celtics won")
Inference
Deriving a sentence from another sentence
Soundness
Derivations produce only entailed sentences
Logical Completeness
Derivations produce all entailed sentence
Valid
A logical statement is true in all models
Satisfiable
A logical statement that is true in some model
Unsatisfiable
A logical statement that is always false
Proof Methods (2)
Application of Inference Rules and Model Checking
Application of Inference Rules
Sound generation of new sentences from old that typically requires a transformation of sentences into normal form (ie: resolution)
Model Checking
Truth table enumeration (ie: DPLL method or heuristic search in model space)
2 families of efficient algorithms for propositional inference
1. Complete back tracking search algorithms
2. Incomplete local search algorithms
DPLL
A complete back tracking search algorithm that determines if an input propositional logic sentence is satisfiable. works better than truth table enumeration by using Early Termination, Pure Symbol Heuristic and the Unit Clause
Early Termination
Improvement of DPLL that states:
1. A clause is true if one of its literals is true
2. A sentence is false if any of its clauses is false
Pure Symbol Heuristic
Improvement of DPLL that states:
A symbol is "pure" if it appears with the same sign throughout all clauses
(ie: (¬A v B)(¬A v C)(¬B v C) <- A and C are pure)
DPLL algorithm makes all literals that are pure, true
Unit Clause
Improvement of DPLL.
If there is only 1 literal in a clause, then make the clause true
If all but one 1 literal is false then make the one literal true.
WalkSAT
Incomplete, local, search algorithm that uses min-conflict heuristic to minimise the number of unsatisfiable clauses. A balance between greediness and randomness.
Constraint Satisfaction Problems
Problems where:
-state = variables Xi with values from Di (i= 1...n)
-goal test = set of constraints specifying allowable combinations of values for variables
(ie: the Australian territories problem)
Standard Search Formulation
-Initial state: the empty assignment {}
-Successor function: assigns value to unassigned variable that doesn't conflict with current assignment
-Goal test: the current assignment is complete
Backtracking Search
Depth-First Search for CSPs with singular assignments
Forward Checking
Keeps track of remaining legal moves for unassigned variables and terminates search when any variable has no legal moves
Universal Quantifier (∀)
When used, ∀x.p is true in an interpretation iff P is true with x being each possible object in an interpretation
(Example: Everyone at UoE is smart:
∀x. At(x,UoE) ⇒ Smart(x) )
Existential quantification (∃)
When used, ∃x.P is true in an interpretation iff P is true with x being some possible object in the interpretation
( Example: Someone at UoE is smart:
∃x. At(x,UoE) ∧ Smart(x) )
Unification
Inference rule
We if we can find a substitution such that a(θ) = b(θ)
we can unify(a,b)
example:
King(x) and Greedy(x) match King(John) and Greedy(y)
θ= {x/John,y/John} works
Generalised Modus Ponens
if there is a bunch of definite clauses (p'1, p'2,...p'n ) and an entailment clause (p1 ∧ p2 ∧..pn ⇒ q)
if there is a unifer p'i θ = p'i θ ∀i
then we c an replace all the above clauses with: q(θ)
Forward Chaining
Starting from KB, using entailment clauses to chain forward to a new clause goal for KB
Backwards Chaining
Starting with goal clause and chain backwards using entailment clauses from KB to prove goal clause.
Ground Binary Resolution
If you have clauses (C v P), ( D v ¬P), it is the same as saying (C v D)
Non Binary Resolution
if there are clauses (C v P), (D v P'), then it is the same as saying (C v D)θ
(iff there is MGU θ for P and P')
Example: (¬rich(x) v unhappy(x)) , (rich(Ken))
= (unhappy (Ken))
Factoring
if you have clause (C v P1 v P2... v Pn) then it is the same as (C v P1)θ where θ is the MGU for all Pi
Planning Domain Definition Language
A planning language that allows you to describe states, actions and goals.
Precondition in PDDL
defines states in which action is executable
Forward State-Space Search (PDDL)
Start in initial state; consider action sequences until goal state is reached.
Backward State-Space Search (PDDL)
Start from goal state; consider action sequences until initial state is reached
Subgoal Decomposition
State space search heuristic where the original goal is broke into subgoals to more easily reach the main goal
Relaxed Problem
State space search heuristic that is a derivation of the original problem that ignores all preconditions and gets rid of negative effects
Partial-order planning
Least commitment strategy where you add actions to a plan without committing to a specific order of actions (unless necessary).
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