1 Regret-based Incremental Partial Revelation Mechanism Design Nathanaël Hyafil, Craig Boutilier AAAI 2006 Department of Computer Science University of Toronto

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

3 Mechanism Design  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

4 “Computational” Mechanism Design  The interesting questions: 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? how to deal with incentives ?

5 Overview  Mechanism Design Background  Incremental Partial Revelation Mechanism  Regret-based iPRMs  Experimental results  Conclusion / Future Work

6 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  Goal: implement social choice function f: T  X e.g., social welfare SW(x,t) =  v i (x, t i )  Quasi-linear utility: u i (x,  i,t i ) = v i (x, t i ) -  i  Our focus: social welfare maximization

7 Basic Mechanism Design  A mechanism m consists of three components: actions A i allocation function O: A  X payment functions p i : A  R  Mechanism is incentive compatible: In equilibrium, agents reveal truthfully  Ex-post IC Assume others tell the truth and agent i knows the others’ types Then agent i should tell the truth

8 Properties  Mechanism is efficient: maximizes social welfare given reported types:  -efficient: within  of optimal social welfare  Ex post individually rational: no agent can lose by participating  -IR: can lose at most 

9 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: incentive compatible in dominant strategies efficient, individually rational

10 Cost of Full Revelation  Communication costs  Computation costs  Cognitive costs  Privacy costs INTRACTABLE!  Partial revelation?

11 Partial Revelation  Full revelation: Not always necessary for optimal decision When necessary, not always worth the costs  Partial revelation: Elicit just enough to make optimal decision Trade-off elicitation costs with decision quality  Can we maintain incentives?

12 Existing Work on Partial Revelation [Conen,Hudson,Sandholm, Parkes, Nisan&Segal, Blumrosen&Nisan]  Most Work: require enough revelation to determine optimal allocation and VCG payments  hence can’t offer savings in general [Nisan&Segal05]  Exception: Priority games [Blumrosen&Nisan 02] specific settings (1-item, combinatorial auctions)

13 Overview  Mechanism Design Background  Incremental Partial Revelation Mechanism (iPRM)  Regret-based iPRMs  Experimental results  Conclusion / Future Work

14 Incremental Partial Revelation Mechanisms (iPRMs)  iPRM interacts with agents: set of queries Q i ( e.g. standard gamble:“v( car ) >5?”) response r  R i (q i ) interpreted as partial type  i (r)  T i (e.g. bounds on each parameter)  Formal Model (see paper)

15 iPRMs  Goal: Trade-off quality of alloc. with revelation costs Maintain acceptable incentives properties  At each step, given , choose between: Terminating (which allocation?) Eliciting (which query?)

16 Minimax Regret: Utility Uncertainty  Regret :  Max regret of x given  :  MMR-optimal allocation: x* = arg min x MR(x,  )

17 Overview  Mechanism Design Background  Incremental Partial Revelation Mechanism  Regret-based iPRMs  Experimental results  Conclusion / Future Work

18 Regret-based Elicitation  Find query to reduce MMR level?  Several heuristics proposed for preference elicitation. We adapt Current Solution Strategy (CSS) Focus elicitation on allocations involved in regret

19 Allocation Elicitation  Proposed allocation elicitation algorithm Using SW-regret computation and elicitation See paper for details  Allocation elicitation phase terminates with  -efficient allocation Partial type 

20 Incentive Properties  Let mechanism M = (x*, p i T ), with  -efficient allocation function x* payments: p i T (x* ;  ) = max t   p i VCG (x* ; t)  Theorem 1: M is  -efficient,  - ex post IR,  - ex post IC  =  +  (  )  (  ): bound on payment uncertainty

21 Approximate Incentives   : bound on utility gain  But gain from manipulation outweighed by costs of manipulation don’t know types of others must simulate mechanism  Formal, approximate IC  practical, exact IC

22 2 Phase Approach  Bound on manipulability:  +  (  ) : not a priori  If  (  ) too large: Elicit to reduce payment uncertainty Payment elicitation strategy: based on CSS (P-CSS)  Terminates with a priori bounds (  +  ) -IC  -IR,  -efficiency

23 Direct Optimization  Causes of manipulability: efficiency loss + payment uncertainty  MMR w.r.t. SW only accounts for efficiency loss  Should minimize global worst-case manipulability: u(best lie) - u(truth) efficiency loss bounded by worst-case manipulability  Formulate as regret optimization and elicitation ask queries that directly reduce global manipulability

24 Single Phase Approach  Theorem 2: For M = (x*, p i T ), If  =max worst case manipulability Then M is  -efficient  - ex post IC  - ex post IR

25 Overview  Mechanism Design Background  Incremental Partial Revelation Mechanism  Regret-based iPRMs  Experimental results  Conclusion / Future Work

26 Elicitation Strategies  Two Phase (2P): SW loss and payment uncertainty for elicitation and decisions   Two Phase (  2P): SW loss and payment uncertainty for elicitation Manipulability for decisions  Common-Hybrid (CH): Manipulability for elicitation and decisions  Myopically Optimal (MY): Simulate all queries, ask best

27 Test Domains  Car Rental Problem: 1 client, 2 dealers Car: 8 attributes, 2-9 values, ~12000 cars factored valuation/costs: 13 factors, size 1-4 Total 825 parameters  Small Random Problems: supplier-selection, 1 buyer, 2 sellers 81 parameters

28 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

29 Results: Random Problems

30 Conclusion  Theoretical model for iPRMs  Class of iPRMs with approximate incentives  Key point: Approximation  trade off cost vs. quality Formal, approximate IC  practical, exact IC  Applicable to general mechanism design  Empirically very effective

31 Current + Future Work  More heuristics + test domains  Formal model manipulation and revelation costs  formal, exact IC  explicit revelation/quality trade-off  Sequentially optimal elicitation  One-shot partial revelation mechanisms “Mechanism Design with Partial Revelation” draft 2006

32 Questions?