1 Preference Elicitation in Single and Multiple User Settings Darius Braziunas, Craig Boutilier, 2005 (Boutilier, Patrascu, Poupart, Shuurmans, 2003, 2005) Nathanael Hyafil, Craig Boutilier, 2006a, 2006b Department of Computer Science University of Toronto

2 Overview  Preference Elicitation in A.I.  Single User Elicitation Foundations of Local queries [BB-05] Bayesian Elicitation [BB-05] Regret-based Elicitation [BPPS-03,05]  Multi-agent Elicitation (Mechanism Design) One-Shot Elicitation [HB-06b] Sequential Mechanisms[HB-06a]

3 Preference Elicitation in AI Luggage Capacity? Two Door? Cost? Engine Size? Color? Options? Shopping for a Car:

4 The Preference Bottleneck  Preference elicitation: the process of determining a user’s preferences/utilities to the extent necessary to make a decision on her behalf  Why a bottleneck? preferences vary widely large (multiattribute) outcome spaces quantitative utilities (the “numbers”) difficult to assess

5 Automated Preference Elicitation  The interesting questions: decomposition of preferences what preference info is relevant to the task at hand? when is the elicitation effort worth the improvement it offers in terms of decision quality? what decision criterion to use given partial utility info?

6 Overview  Preference Elicitation in A.I. Constraint-based Optimization Factored Utility Models Types of Uncertainty Types of Queries  Single User Elicitation  Multi-agent Elicitation (Mechanism Design)

7 Constraint-based Decision Problems  Constraint-based optimization (CBO): outcomes over variables X = {X 1 … X n } constraints C over X spell out feasible decisions generally compact structure, e.g., X 1 & X 2  ¬ X 3 add a utility function u: Dom(X) → R preferences over configurations

8 Constraint-based Decision Problems  Must express u compactly like C generalized additive independence (GAI)  model proposed by Fishburn (1967) [and BG95]  nice generalization of additive linear models given by graphical model capturing independence

9 Factored Utilities:GAI Models  Set of K factors f k over subset of vars X[k] “local” utility for each local configuration  [Fishburn67] u in this form exists iff lotteries p and q are equally preferred whenever p and q have the same marginals over each X[k] A B f 1 (A) a: 3 a: 1 f 2 (B) b: 3 b: 1 C f 3 (BC) bc: 12 bc: 2 … u(abc) = f 1 (a)+ f 2 (b)+ f 3 (bc)

10 Optimization with GAI Models  Optimize using simple IP (or Var Elim, or…) number of vars linear in size of GAI model AB f 1 (A) a: 3 a: 1 f 2 (B) b: 3 b: 1 C f 3 (BC) bc: 12 bc: 2 …

11 Difficulties in CBO  Utility elicitation: how do we assess individual user preferences? need to elicit GAI model structure (independence) need to elicit (constraints on) GAI parameters need to make decisions with imprecise parameters

12 Strict Utility Function Uncertainty  User’s actual utility u unknown  Assume feasible set F  U = [0,1] n allows for unquantified or “strict” uncertainty e.g., F a set of linear constraints on GAI terms  How should one make a decision? elicit info? u(red,2door,280hp) > 0.4 u(red,2door,280hp) > u(blue,2door,280hp)

13 f 2 (L,N) l,n: [2,4] l,n: [1,2] Strict Uncertainty Representation L N P Utility Function f 1 (L) l: [7,11] l: [2,5]

14 Bayesian Utility Function Uncertainty  User’s actual utility u unknown  Assume density P over U = [0,1] n  Given belief state P, EU of decision x is: EU(x, P) =  U (p x. u) P( u ) du  Decision making is easy, but elicitation harder? must assess expected value of information in query

15 f 2 (L,N) l,n: … Bayesian Representation L N P Utility Function f 1 (L) l:

16 Query Types  Comparison queries (is x preferred to x’ ?) impose linear constraints on parameters   k f k (x[k]) >  k f k (x’[k]) Interpretation is straightforward U

17 Query Types  Bound queries (is f k (x[k]) > v ?) response tightens bound on specific utility parameter can be phrased as a local standard gamble query U

18 Overview  Preference Elicitation in A.I.  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  Multi-agent Elicitation (Mechanism Design) One-Shot Elicitation Sequential Mechanisms

19 Difficulties with Bound Queries  Bound queries focus on local factors but values cannot be fixed without reference to others! seemingly “different” local prefs correspond to same u u(Color,Doors,Power) = u 1 (Color,Doors) + u 2 (Doors,Power) u(red,2door,280hp) = u 1 (red,2door) + u 2 (2door,280hp) u(red,4door,280hp) = u 1 (red,4door) + u 2 (4door,280hp)

20 Local Queries [BB05]  We wish to avoid queries on whole outcomes can’t ask purely local outcomes but can condition on a subset of default values  Conditioning set C(f) for factor f i (X i ) : variables that share factors with X i setting default outcomes on C(f) renders X i independent of remaining variables enables local calibration of factor values

21 Local Standard Gamble Queries  Local std. gamble queries use “best” and “worst” (anchor) local outcomes -- conditioned on default values of conditioning set bound queries on other parameters relative to these gives local value function v(x[i]) (e.g., v(ABC) )  Hence we can legitimately ask local queries:  But local Value Functions not enough: must calibrate: requires global scaling

22 Global Scaling  Elicit utilities of anchor outcomes wrt global best and worst outcomes the 2*m “best” and “worst” outcomes for each factor these require global std gamble queries (note: same is true for pure additive models)

23 Bound Query Strategies  Identify conditioning sets C i for each factor f i  Decide on “default” outcome  For each f i identify top and bottom anchors e.g., the most and least preferred values of factor i given default values of C i  Queries available: local std gambles: use anchors for each factor, C-sets global std gambles: gives bounds on anchor utilities

24 Overview  Preference Elicitation in A.I.  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  Multi-agent Elicitation (Mechanism Design) One-Shot Elicitation Sequential Mechanisms

25 Partial preference information Bayesian uncertainty  Probability distribution p over utility functions  Maximize expected (expected) utility MEU decision x* = arg max x E p [u(x)]  Consider: elicitation costs values of possible decisions optimal tradeoffs between elicitation effort and improvement in decision quality

26 Query selection  At each step of elicitation process, we can obtain more preference information make or recommend a terminal decision

27 Bayesian approach Myopic EVOI MEU(p) q1q1 q2q2... r 1,1 r 2,1 r 1,2 r 2,2... MEU(p 1,1 ) MEU(p 1,2 ) MEU(p 2,1 )MEU(p 2,2 )

28 Expected value of information  MEU(p) = E p [u(x*)]  Expected posterior utility: EPU(q,p) = E r|q,p [MEU(p r )]  Expected value of information of query q: EVOI(q) = EPU(q,p) – MEU(p) MEU(p) q1q1 q2q2... r 1,1 r 2,1 r 1,2 r 2,2... MEU(p 1,1 ) MEU(p 1,2 ) MEU(p 2,1 )MEU(p 2,2 )

29 Bayesian approach Myopic EVOI  Ask query with highest EVOI - cost  [Chajewska et al ’00] Global standard gamble queries (SGQ) “Is u(o i ) > l?” Multivariate Gaussian distributions over utilities  [Braziunas and Boutilier ’05] Local SGQ over utility factors Mixture of uniforms distributions over utilities

30 Local elicitation in GAI models [Braziunas and Boutilier ’05]  Local elicitation procedure Bayesian uncertainty over local factors Myopic EVOI query selection  Local comparison query “Is local value of factor setting x i greater than l”? Binary comparison query Requires yes/no response query point l can be optimized analytically

31 Experiments  Car rental domain: 378 parameters [Boutilier et al. ’03] 26 variables, 2-9 values each, 13 factors  2 strategies Semi-random query  Query factor and local configuration chosen at random  Query point set to the mean of local value function EVOI query  Search through factors and local configurations  Query point optimized analytically

32 Experiments No. of queries Percentage utility error (w.r.t. true max utility)

33 Bayesian Elicitation: Future Work  GAI structure elicitation and verification  Sequential EVOI  Noisy responses

34 Overview  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  why MiniMax Regret (MMR) ?  Decision making with MMR  Elicitation with MMR  Multi-agent Elicitation (Mechanism Design)

35 Minimax Regret: Utility Uncertainty  Regret of x w.r.t. u:  Max regret of x w.r.t. F:  Decision with minimax regret w.r.t. F:

36 Why Minimax Regret?*  Appealing decision criterion for strict uncertainty contrast maximin, etc. not often used for utility uncertainty [BBB01,HS010] x x’ x x x x x Better u1u2u3u4u5u6

37 Why Minimax Regret?  Minimizes regret in presence of adversary provides bound worst-case loss robustness in the face of utility function uncertainty  In contrast to Bayesian methods: useful when priors not readily available can be more tractable; see [CKP00/02, Bou02] effective elicitation even if priors available [WB03]

38 Overview  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  why MiniMax Regret (MMR) ?  Decision making with MMR  Elicitation with MMR  Multi-agent Elicitation (Mechanism Design

39 Computing Max Regret  Max regret MR(x,F) computed as an IP number of vars linear in GAI model size number of (precomputed) constants (i.e., local regret terms) quadratic in GAI model size r( x[k], x’[k] ) = u T (x’[k] ) – u  (x[k] )

40 Minimax Regret in Graphical Models  We convert minimax to min (standard trick) obtain a MIP with one constraint per feasible config linearly many vars (in utility model size)  Key question: can we avoid enumerating all x’ ?

41 Constraint Generation  Very few constraints will be active in solution  Iterative approach: solve relaxed IP (using a subset of constraints) Solve for maximally violated constraint if any add it and repeat; else terminate

42 Constraint Generation Performance  Key properties: aim: graphical structure permits practical solution convergence (usually very fast, few constraints) very nice anytime properties considerable scope for approximation produces solution x* as well as witness x w

43 Overview  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  why MiniMax Regret (MMR) ?  Decision making with MMR  Elicitation with MMR  Multi-agent Elicitation (Mechanism Design)

44 Regret-based Elicitation [Boutilier, Patrascu, Poupart, Schuurmans IJCAI05; AIJ 06]  Minimax optimal solution may not be satisfactory  Improve quality by asking queries new bounds on utility model parameters  Which queries to ask? what will reduce regret most quickly? myopically? sequentially?  Closed form solution seems infeasible to date we’ve looked only at heuristic elicitation

45 Elicitation Strategies I  Halve Largest Gap (HLG) ask if parameter with largest gap > midpoint MMR(U) ≤ maxgap(U), hence n  log(maxgap(U)/  ) queries needed to reduce regret to  bound is tight like polyhedral-based conjoint analysis [THS03] f 1 (a,b) f 2 (b,c)

46 Elicitation Strategies II  Current Solution (CS) only ask about parameters of optimal solution x* or regret-maximizing witness x w intuition: focus on parameters that contribute to regret  reducing u.b. on x w or increasing l.b. on x* helps use early stopping to get regret bounds (CS-5sec) f 1 (a,b) f 2 (b,c)

47 Elicitation Strategies III  Optimistic-pessimistic (OP) query largest-gap parameter in one of:  optimistic solution x o  pessimistic solution x p  Computation: CS needs minimax optimization OP needs standard optimization HLG needs no optimization  Termination: CS easy Others ?

48 Results (Small Random) 10vars; < 5 vals 10 factors, at most 3 vars Avg 45 trials

49 Results (Car Rental, Unif) 26 vars; 61 billion configs 36 factors, at most 5 vars; 150 parameters Avg 45 trials

50 Results (Real Estate, Unif) 20 vars; 47 million configs 29 factors, at most 5 vars; 100 parameters Avg 45 trials

51 Results (Large Rand, Unif) 25 vars; < 5 vals 20 factors, at most 3 vars A 45 trials

52 Summary of Results  CS works best on test problems time bounds (CS-5): little impact on query quality always know max regret (or bound) on solution time bound adjustable (use bounds, not time)  OP competitive on most problems computationally faster (e.g., 0.1s vs 14s on RealEst) no regret computed so termination decisions harder  HLG much less promising

53 Interpretation  HLG: provable regret reduced very quickly  But: true regret faster (often to optimality) OP and CS restricted to feasible decisions CS focuses on relevant parameters

54 Conclusion – Single User  Local parameter elicitation Theoretically sound Computationally practical Easier to answer  Bayesian EVOI / Regret-based elicitation Good guides for elicitation Integrated in computationally tractable algorithms  Future Work: Sequential reasoning

55 Questions? References:  D. Braziunas and C. Boutilier: “Local Utility Elicitation in GAI Models”, UAI 2005  C. Boutilier, R. Patrascu, P. Poupart, D. Shuurmans: “Constraint-based Optimization and Utility Elicitation using the Minimax Decision Criterion”, Artificial Intelligence, 2006 (CP IJCAI 2005)

56 Preference Elicitation in Single and Multiple User Settings Part 2 Darius Braziunas, Craig Boutilier, 2005 (Boutilier, Patrascu, Poupart, Shuurmans, 2003, 2005) Nathanael Hyafil, Craig Boutilier, 2006a, 2006b Department of Computer Science University of Toronto

57 Overview  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  Multi-agent Elicitation Background: Mechanism Design Partial Revelation Mechanisms One-Shot Elicitation Sequential Mechanisms

58 Bargaining for a Car Luggage Capacity? Two Door? Cost? Engine Size? Color? Options? $$

59 Multiagent PE: Mechanism Design  Incentive to misrepresent preferences  Mechanism design tackles this: Design rules of game to induce behavior that leads to maximization of some objective (e.g., Social Welfare, Revenue,...) Objective value depends on private information held by self-interested agents  Elicitation + Incentives  Applications: Auctions, multi-attribute Negotiation, Procurement problems, Network protocols, Autonomic computing,...

60 Basic Social Choice Setup  Choice of x from outcomes X  Agents 1..n: type t i  T i and valuation v i (x, t i )  Type vectors: t  T and t -i  T -i  Goal: optimize social choice function f: T  X e.g., social welfare SW(x,t) =  v i (x, t i )  Assume payments and quasi-linear utility: u i (x,  i,t i ) = v i (x, t i ) -  i  Our focus: SW maximization, quasi-linear utility

61 Basic Mechanism Design  A mechanism m consists of three components: actions A i allocation function O: A  X payment functions p i : A  R  m induces a Bayesian game m implements social choice function f if  in equilibrium  : O(  (t)) = f(t) for all t  T

62 Incentive Compatibility (Truth-telling)  Dominant Strategy IC No matter what: agent i should tell the truth  Bayes-Nash IC Assume others tell the truth Assume agent i has Bayesian prior over others’ types Then, in expectation, agent i should tell the truth  Ex-Post IC Assume others tell the truth Assume agent i knows the others’ types Then agent i should tell the truth

63 Properties  Mechanism is Efficient: maximizes SW given reported types:  -efficient: within  of optimal SW  Ex Post Individually Rational: No agent can lose by participating  -IR: can lose at most 

64 Direct Mechanisms  Revelation principle: focus on direct mechanisms where agents directly and (in eq.) truthfully reveal their full types  For example, Groves scheme (e.g., VCG): choose efficient allocation and use payment function: implements SWM in dominant strategies incentive compatible, efficient, individually rational

65 Groves Schemes  Strong results: Groves is basically the “only choice” for dominant strategy implementation Roberts (1979): only social choice functions implementable in dominant strategies are affine welfare maximizers (if all valuations possible) Green and Laffont (1977): must use Groves payments to implement affine maximizers  Implications for partial revelation

66 Issues with Classical Mechanism Design  Computation Costs e.g., Winner Determination  Revelation Costs Communication Computation Cognitive Privacy

67 Issues with Classical Mechanism Design  Full Revelation and “Quality” trade-off revelation costs with Social Welfare  Full Revelation and Incentives very dependent need “new” concepts

68 Overview  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  Multi-agent Elicitation Background: Mechanism Design Partial Revelation Mechanisms One-Shot Elicitation Sequential Mechanisms

69 Partial Revelation Mechanisms  Full revelation unappealing  A partial type is any subset  i  T i  A one-shot (direct) partial revelation mechanism each agent reports a partial type  i   i typically  i partitions type space, but not required  A truthful strategy: report  i s.t. t i   i  Goal: minimize revelation, computation, communication by suitable choice of partial types

70 Implications of Roberts  Partial revelation means we can’t generally maximize social welfare must allocate under type uncertainty  But if SCF is not an affine maximizer, we can’t expect dominant strategy implementation  What are some solutions? relax solution concept to BNE / Ex-Post relax solution concept to approx incentives incremental and “hope for” less than full elicitation relax conditions on Roberts results

71 Existing Work on PRMs [Conen,Hudson,Sandholm, Parkes, Nisan&Segal, Blumrosen&Nisan]  Most Approaches: require enough revelation to determine optimal allocation and VCG payments  hence can’t offer savings in general [Nisan&Segal05] Sequential, not one-shot specific settings (1-item, combinatorial auctions)  Priority games [Blumrosen&Nisan 02] genuinely partial and approximate efficiency but very restricted valuation space (1-item)

72 Preference Elicitation in MechDes  We move beyond this by allowing approximately optimal allocation specifically, regret-based allocation models  Avoid Roberts by relaxing solution concept: Bayes-Nash equilibrium? NO! [HB-06b] Ex-Post IC? NO ! [HB-06b] approximate, ex-post implementation

73 Partial Revelation MD: Impossibility Results  Bayes-Nash Equilibrium Theorem: [HB-06b]  Deterministic PRMs are Trivial  Randomized PRMs are Pseudo-Trivial Consequences:  max expected SW = same as best trivial  max expected revenue = same as best trivial  “Useless”  Ex-Post Equilibrium Same

74 Overview  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  Multi-agent Elicitation Background: Mechanism Design Partial Revelation Mechanisms One-Shot Elicitation Sequential Mechanisms

75 Regret-based PRMs  In any PRM, how is allocation to be chosen?  x*(  ) is minimax optimal decision for  A regret-based PRM: O(  )=x*(  ) for all   

76 Regret-based PRMs: Efficiency  Efficiency not possible with PRMs (unless MR=0) but bounds are quite obvious  Prop: If MR(x*(  ),  )   for all  , then regret- based PRM m is  -efficient for truthtelling agents. thus we can tradeoff efficiency for elicitation effort

77 Regret-based PRMs: Incentives  Can generalize Groves payments let f i (  i ) be an arbitrary type in  i  Thm: Let m be a regret-based PRM with partial types  and a partial Groves payment scheme. If MR(x*(  ),  )   for all  , then m is  -ex post incentive compatible

78 Regret-based PRMs: Rationality  Can generalize Clark payments as well  Thm: Let m be a regret-based PRM with partial types  and a partial Clark payment scheme. If MR(x*(  ),  )   for all  , then m is  -ex post individually rational.  A Clark-style regret-based PRM gives approximate efficiency, approximate IC (ex post) and approximate IR (ex post)

79 Approximate Incentives and IR  Natural to trade off efficiency for elicitation effort  Is approximate IC acceptable? computing a good “lie”?  Good?  Huge computation costs if incentive to deviate from truth is small enough, then formal, approximate IC ensures practical, exact IC  Is approximate IR acceptable? Similar argument  Thus regret-based PRMs offer scope to tradeoff as long as we can find a good set of partial types

80 Computation and Design/Elicitation  Minimax optimization given partial type vector  same techniques as for single agent varies with setting (experiments: CBO with GAI)  Designing the mechanism one-shot PRM: must choose partial types for each i sequential PRM: need elicitation strategy we apply generalization of CS to each task

81 (One-shot) Partial Type Optimization  Designing PRM: must pick partial types we focus on bounds on utility parameters  A simple greedy approach Let  be current partial type vectors (initially {T} ) Let  =(  1,…  i,…  n )   be partial type vector with greatest MMR Choose agent i and suitable split of partial type  i into  ’ i and  ’’ i Replace all   [  i ] by pair of vectors:  i   ’ i ;  ’’ i Repeat until bound  is acceptable

82 The Mechanism Tree (  ’ 1,…  i,…  n )(  ’’ 1,…  i,…  n ) (  ’ 1,…  ’ i,… )(  ’ 1,…  ’’ i,… )(  ’’ 1,…  ’ i,… )(  ’’ 1,…  ’’ i,… ) (  1,…  i,…  n )

83 A More Refined Approach  Simple model has drawbacks exponential blowup (“naïve” partitioning) split of  i useful in reducing regret in one partial type vector , but is applied at all partial type vectors  Refinement apply split only at leaves where it is “useful”  keeps tree from blowing up, saves computation new splits traded off against “cached” splits once done, use either naïve/variable resolution types for each agent

84 Naïve vs. Variable Resolution ii p1p1 p2p2 ii p1p1 p2p2

85 Heuristic for Choosing Splits  Adopt variant of current solution strategy  Let  be partial type vector with max MMR optimal solution x* regret-maximizing witness x w only split on parameters of utility functions of optimal solution x* or regret-maximizing witness x w intuition: focus on parameters that contribute to regret  reducing u.b. on x w or increasing l.b. on x* helps pick agent-parameter pair with largest gap

86 Preliminary Empirical Results  Very preliminary results use only very naïve algorithm single buyer, single seller 16 goods specified by 4 boolean variables valuation/cost given by GAI model  two factors, two vars each (buyer/seller factors are different)  thus 16 values/costs specified by 8 parameters  no constraints on feasible allocations

87 Preliminary Empirical Results

88 Overview  Single User Elicitation Foundations of Local queries Bayesian Elicitation Regret-based Elicitation  Multi-agent Elicitation Background: Mechanism Design Partial Revelation Mechanisms One-Shot Elicitation Sequential Mechanisms

89 Sequential PRMs  Optimization of one-shot PRMs unable to exploit conditional “queries” e.g., if seller cost of x greater than your upper bound, needn’t ask you for your valuation of x  Sequential PRMs incrementally elicit partial type information apply similar heuristics for designing query policy incentive properties somewhat weaker: opportunity to manipulate payments by altering the query path  thus additional criteria can be used to optimize

90 Sequential PRMs: Definition  Set of queries Q i response r  R i (q i ) interpreted as partial type  i (r)  T i history h: sequence of query-response pairs possibly followed by allocation (terminal)  Sequential mechanism m maps: nonterminal histories to queries/allocations terminal histories to set of payment functions p i  Revealed partial type  i (h): intersect.  i (r), r in h  m is partial revelation if exists realizable terminal h s.t.  i (h) admits more than one type t i

91 Sequential PRMs: Properties  Strategies  i (h i,q i,t i ) selects responses  i is truthful if t i   i (  i (h i,q i,t i )) truthful strategies must be history independent  (Determ.) strategy profile  induces history h if h is terminal, then quasi-linear utility realized if history is unbounded, then assume utility = 0  Regret-based PRM allocation defined as in one- shot

92 Max VCG Payment Scheme  Assume terminal history h let  be revealed PTV at h, x*(  ) be allocation  Max VCG payment scheme: where VCG payment is:

93 Incentive Properties  Suppose we elicit type info until MMR allocation has max regret   and we use “max VCG”  Define:  Thm: m is  -efficient,  -ex post IR and (  +  ( x*(  )))-ex post IC. weaker results due to possible payment manipulation

94 Elicitation Approaches Two Phases:  Standard max regret based approaches give us bounds on efficiency , no a priori  bounds  Regret-based followed by payment elicitation once  small enough, elicit additional payment information until max  is small enough

95 Elicitation Approaches Direct optimization:  global manipulability: u(best lie) - u(truth)  ask queries that directly reduce global manipulability  can be formulated as regret-style optimization  analogous query strategies possible

96 Test Domains  Car Rental Problem: 1 client, 2 dealers GAI valuation/costs: 13 factors, size 1-4 Car: 8 attributes, 2-9 values Total 825 parameters  Small Random Problems: supplier-selection, 1 buyer, 2 sellers 81 parameters

97 Results: Car Rental Initial regret: 99% of opt SW Zero-regret: 71/77 queries Avg remaining uncertainty: 92% vs 64% at zero-manipulability Avg nb params queried: 8% relevant parameters reduces revelation improves decision quality

98 Results: Random Problems

99 Contributions  Theoretical framework for Partial Revelation Mech Design  One-shot mechanisms generalize VCG to PRMs (allocation + payments) v. general payments: secondary objectives algorithm to design partial types  Sequential mechanisms slightly different model, but similar results algorithm to design query strategy  Viewpoint: why approximate incentives are useful Approximate decision  trade off cost vs. quality Formal, approximate IC ensures practical, exact IC  Applicable to general Mechanism Design problems  Empirically very effective

100 PRMs: Future Work  Further investigate splitting / elicitation heuristics  More experimentation Larger problems Combinatorial Auctions  Formal model manipulability cost  formal, exact IC  Formal model revelation costs  explicit revelation vs efficiency trade-off  Sequentially optimal elicitation

101 Questions ? References:  Nathanael Hyafil and Craig Boutilier “Regret-based Incremental Partial Revelation Mechanisms”, AAAI 2006 “One-shot Partial Revelation Mechanisms”, Working Paper, 2006

102 Extra Slides - Part 1

103 Fishburn [1967]: Default Outcomes  Define default outcome:  For any x, let x[I] be restriction of x to vars I, with remaining replaced by default values:  Utility of x can be written [F67]: sum of utilities of certain related “key” outcomes

104 Key Outcome Decomposition  Example: GAI over I={ABC}, J={BCD}, K={DE}  u(x) = u(x[I]) + u(x[J]) + u(x[K]) - u(x[I  J]) - u(x[I  K]) - u(x[J  K]) + u(x[I  J  K])  u(abcde) = u(x[abc]) + u(x[bcd]) + u(x[de]) - u(x[bc]) - u(x[]) - u(x[d]) + u(x[])  u(abcde) = u(abcd 0 e 0 ) + u(a 0 bcde 0 ) + u(a 0 b 0 c 0 de) - u(a 0 bcd 0 e 0 ) - u(a 0 b 0 c 0 de 0 )

105 Canonical Decompostion [F67]  This leads to canonical decompostion of u: u 1 (x 1, x 2 )u 2 (x 2, x 3 ) u(abcde) = u(abcd 0 e 0 ) + u(a 0 bcde 0 ) - u(a 0 bcd 0 e 0 ) + u(a 0 b 0 c 0 de) - u(a 0 b 0 c 0 de 0 ) e.g., I={ABC}, J={BCD}, K={DE}

106 Local Queries  Thus, if for some y (where Y =X \ X i \ C(X i ) ) then for all y’ hence we can legitimately ask local queries:

107 Implications for Minimax Regret  Complicates MMR utility of outcome depends linearly on GAI parameters but GAI parameters depend on bounds induced by two types of queries: quadratic constraints  Local pairwise regret notion can be modified To compute r x[k]x’[k]  set values: v x’[k] to u.b. and v x[k] to l.b.  If v x’[k] ↑ > v x[k] ↓: max u( x T [k]) and min u(x  [k])  otherwise do the opposite

108 Bayesian Utility Function Uncertainty  User’s actual utility u unknown  Assume density P over U = [0,1] n  Given belief state P, EU of decision x is:  Decision making is easy, but elicitation harder? must assess expected value of information in query

109 Extra Slides - Part 2