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Intelligent Environments

Intelligent Environments. Computer Science and Engineering University of Texas at Arlington. Decision-Making for Intelligent Environments. Motivation Techniques Issues. Motivation.

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Intelligent Environments

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  1. Intelligent Environments Computer Science and Engineering University of Texas at Arlington Intelligent Environments

  2. Decision-Making forIntelligent Environments • Motivation • Techniques • Issues Intelligent Environments

  3. Motivation • An intelligent environment acquires and applies knowledge about you and your surroundings in order to improve your experience. • “acquires”  prediction • “applies”  decision making Intelligent Environments

  4. Motivation • Why do we need decision-making? • “Improve our experience” • Usually alternative actions • Which one to take? • Example (Bob scenario: bedroom  ?) • Turn on bathroom light? • Turn on kitchen light? • Turn off bedroom light? Intelligent Environments

  5. Example • Should I turn on the bathroom light? • Issues • Inhabitant’s location (current and future) • Inhabitant’s task • Inhabitant’s preferences • Energy efficiency • Security • Other inhabitants Intelligent Environments

  6. Qualities of a Decision Maker • Ideal • Complete: always makes a decision • Correct: decision is always right • Natural: knowledge easily expressed • Efficient • Rational • Decisions made to maximize performance Intelligent Environments

  7. Agent-based Decision Maker • Russell & Norvig “AI: A Modern Approach” • Rational agent • Agent chooses an action to maximize its performance based on percept sequence Intelligent Environments

  8. Agent Types • Reflex agent • Reflex agent with state • Goal-based agent • Utility-based agent Intelligent Environments

  9. Reflex Agent Intelligent Environments

  10. Reflex Agent with State Intelligent Environments

  11. Goal-based Agent Intelligent Environments

  12. Utility-based Agent Intelligent Environments

  13. Intelligent Environments Decision-Making Techniques Intelligent Environments

  14. Decision-Making Techniques • Logic • Planning • Decision theory • Markov decision process • Reinforcement learning Intelligent Environments

  15. Logical Decision Making • If Equal(?Day,Monday) & GreaterThan(?CurrentTime,0600) & LessThan(?CurrentTime,0700) & Location(Bob,bedroom,?CurrentTime) & Increment(?CurrentTime,?NextTime) Then Location(Bob,bathroom,?NextTime) • Query: Location(Bob,?Room,0800) Intelligent Environments

  16. Logical Decision Making • Rules and facts • First-order predicate logic • Inference mechanism • Deduction: {A, A  B}  B • Systems • Prolog (PROgramming in LOGic) • OTTER Theorem Prover Intelligent Environments

  17. Prolog • location(bob,bathroom,NextTime) :- dayofweek(Day), Day = monday, currenttime(CurrentTime), CurrentTime > 0600, CurrentTime < 0700, location(bob,bedroom,CurrentTime), increment(CurrentTime,NextTime). • Facts: dayofweek(monday), ... • Query: location(bob,Room,0800). Intelligent Environments

  18. OTTER • (all d all t1 all t2 ((DayofWeek(d) & Equal(d,Monday) & CurrentTime(t1) & GreaterThan(t1,0600) & LessThan(t1,0700) & NextTime(t1,t2) & Location(Bob,Bedroom,t1)) -> Location(Bob,Bathroom,t2))). • Facts: DayofWeek(Monday), ... • Query: (exists r (Location(Bob,r,0800))) Intelligent Environments

  19. Actions • If Location(Bob,Bathroom,t1) Then Action(TurnOnBathRoomLight,t1) • Preferences among actions • If RecommendedAction(a1,t1) & RecommendedAction(a2,t1) & ActionPriority(a1) > ActionPriority(a2) Then Action(a1,t1) Intelligent Environments

  20. Persistence Over Time • If Location(Bob,room1,t1) & not Move(Bob,t1) & NextTime(t1,t2) Then Location(Bob,room1,t2) • One for each attribute of Bob! Intelligent Environments

  21. Logical Decision Making • Assessment • Complete? Yes • Correct? Yes • Efficient? No • Natural? No • Rational? Intelligent Environments

  22. Decision Making as Planning • Search for a sequence of actions to achieve some goal • Requires • Initial state of the environment • Goal state • Actions (operators) • Conditions • Effects (implied connection to effectors) Intelligent Environments

  23. Example • Initial: location(Bob,Bathroom) & light(Bathroom,off) • Goal: happy(Bob) • Action 1 • Condition: location(Bob,?r) & light(?r,on) Effect: Add: happy(Bob) • Action 2 • Condition: light(?r,off) • Effect: Delete: light(?r,off), Add: light(?r,on) • Plan: Action 2, Action 1 Intelligent Environments

  24. Requirements • Where do goals come from? • System design • Users • Where do actions come from? • Device “drivers” • Learned macros • E.g., SecureHome action Intelligent Environments

  25. Planning Systems • UCPOP (Univ. of Washington) • Partial Order Planner with Universal quanitification and Conditional effects • GraphPlan (CMU) • Builds and prunes graph of possible plans Intelligent Environments

  26. GraphPlan Example (:action lighton :parameters (?r) :precondition (light ?r off)) :effects (and (light ?r on) (not (light ?r off)))) Intelligent Environments

  27. Planning • Assessment • Complete? Yes • Correct? Yes • Efficient? No • Natural? Better • Rational? Intelligent Environments

  28. Decision Theory • Logical and planning approaches typically assume no uncertainty • Decision theory = probability theory + utility theory • Maximum Expected Utility principle • Rational agent chooses actions yielding highest expected utility • Averaged over all possible action outcomes • Weight utility of an outcome by its probability of occurring Intelligent Environments

  29. Probability Theory • Random variables: X, Y, … • Prior probability: P(X) • Conditional probability: P(X|Y) • Joint probability distribution • P(X1,…,Xn) is an n-dimensional table of probabilities • Complete table allows computation of any probability • Complete table typically infeasible Intelligent Environments

  30. Probability Theory • Bayes rule • Example • More likely to know P(wet|rain) • In general, P(X|Y) =  * P(Y|X) * P(Y) •  chosen so that  P(X|Y) = 1 Intelligent Environments

  31. Bayes Rule (cont.) • How to compute P(rain|wet & thunder) • P(r | w & t) = P(w & t | r) * P(r) / P(w & t) • Know P(w & t | r) possibly, but tedious as evidence increases • Conditional independence of evidence • Thunder does not cause wet, and vice versa • P(r | w & t) =  * P(w|r) * P(t|r) * P(r) Intelligent Environments

  32. Where Do Probabilities Come From? • Statistical sampling • Universal principles • Individual beliefs Intelligent Environments

  33. Representation of Uncertain Knowledge • Complete joint probability distribution • Conditional probabilities and Bayes rule • Assuming conditional independence • Belief networks Intelligent Environments

  34. Belief Networks • Nodes represent random variables • Directed link between X and Y implies that X “directly influences” Y • Each node has a conditional probability table (CPT) quantifying the effects that the parents (incoming links) have on the node • Network is a DAG (no directed cycles) Intelligent Environments

  35. Belief Networks: Example Intelligent Environments

  36. Belief Networks: Semantics • Network represents the joint probability distribution • Network encodes conditional independence knowledge • Node conditionally independent of all other nodes except parents • E.g., MaryCalls and Earthquake are conditionally independent Intelligent Environments

  37. Belief Networks: Inference • Given network, compute P(Query | Evidence) • Evidence obtained from sensory percepts • Possible inferences • Diagnostic: P(Burglary | JohnCalls) = 0.016 • Causal: P(JohnCalls | Burglary) • P(Burglary | Alarm & Earthquake) Intelligent Environments

  38. Belief Network Construction • Choose variables • Discretize continuous variables • Order variables from causes to effects • CPTs • Specify each table entry • Define as a function (e.g., sum, Gaussian) • Learning • Variables (evidential and hidden) • Links (causation) • CPTs Intelligent Environments

  39. Combining Beliefs with Desires • Maximum expected utility • Rational agent chooses action maximizing expected utility • Expected utility EU(A|E) of action A given evidence E • EU(A|E) = i P(Resulti(A) | E, Do(A)) * U(Resulti(A)) • Resulti(A) are possible outcome states after executing action A • U(S) is the agent’s utility for state S • Do(A) is the proposition that action A is executed in the current state Intelligent Environments

  40. Maximum Expected Utility • Assumptions • Knowing evidence E completely requires significant sensory information • P(Result | E, Do(A)) requires complete causal model of the environment • U(Result) requires complete specification of state utilities • One-shot vs. sequential decisions Intelligent Environments

  41. Utility Theory • Any set of preferences over possible outcomes can be expressed by a utility function • Lottery L = [p1,S1; p2,S2; ...; pn,Sn] • pi is the probability of possible outcome Si • Si can be another lottery • Utility principle • U(A) > U(B)  A preferred to B • U(A) = U(B)  agent indifferent to A and B • Maximum expected utility principle • U([p1,S1; p2,S2; ...; pn,Sn]) = i pi * U(Si) Intelligent Environments

  42. Utility Functions • Possible outcomes • [1.0, $1000; 0.0, $0] • [0.5, $3000; 0.5, $0] • Expected monetary value • $1000 vs. $1500 • But depends on value $k • Sk = state of possessing wealth $k • EU(accept) = 0.5 * U(Sk+3000) + 0.5 * U(Sk) • EU(decline) = U(Sk+1000) • Will decline for some values of U, accept for others Intelligent Environments

  43. Utility Functions (cont.) • Studies show U(Sk+n) = log2n • Risk-adverse agents in positive part of curve • Risk-seeking agents in negative part of curve Intelligent Environments

  44. Decision Networks • Also called influence diagrams • Decision networks = belief networks + actions and utilities • Describes agent’s • Current state • Possible actions • State resulting from agent’s action • Utility of resulting state Intelligent Environments

  45. Example Decision Network Intelligent Environments

  46. Decision Network • Chance node (oval) • Random variable and CPT • Same as belief network node • Decision node (rectangle) • Can take on a value for each possible action • Utility node (diamond) • Parents are those chance nodes affecting utility • Contains utility function mapping parents to utility value or lottery Intelligent Environments

  47. Evaluating Decision Networks • Set evidence variables according to current state • For each action value of decision node • Set value of decision node to action • Use belief-net inference to calculate posteriors for parents of utility node • Calculate utility for action • Return action with highest utility Intelligent Environments

  48. Sequential Decision Problems • No intermediate utility on the way to the goal • Transition model • Probability of reaching state j after taking action a in state i • Policy = complete mapping from states to actions • Want policy maximizing expected utility • Computed from transition model and state utilities Intelligent Environments

  49. Example • P(intended direction) = 0.8 • P(right angle to intended) = 0.1 • U(sequence) = terminal state’s value - (1/25)*length(sequence) Intelligent Environments

  50. Example (cont.) Optimal Policy Utilities Intelligent Environments

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