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

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

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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

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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 ?

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

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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

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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

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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

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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

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

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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?

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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)

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

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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)

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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?)

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

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

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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

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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

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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

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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

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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

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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

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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

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

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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

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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

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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

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29 Results: Random Problems

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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

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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

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32 Questions?

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