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Reshef Meir, Ariel D. Procaccia, and Jeffrey S. Rosenschein
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A very simple example of mechanism design in a decision making setting 8 slides An investigation of incentives in a general machine learning setting 2 slides
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ECB makes Yes/no decisions at European level Decisions based on reports from national banks National bankers gather positive/negative data from local institutions Bankers might misreport their data in order to sway the central decision
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Set of n agents Agent i controls points X i = {x i1,x i2,...} X For each x ik X i agent i has a label y ik { , } Agent i reports labels y’ i1,y’ i2,... Mechanism receives reported labels and outputs c + (constant ) or c (constant ) Risk of i: R i (c) = |{k: c(x ik ) y ik }| Global risk: R(c) = |{i,k: c(x ik ) y ik }| = i R i (c)
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Agent 1Agent 2 + + – – – – – – + + + +
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If all agents report truthfully, choose concept that minimizes global risk Risk Minimization is not strategyproof: agents can benefit by lying
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Agent 1Agent 2 + + – – – – – – + + + + – – + +
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VCG works (but is not interesting). Mechanism gives -approximation if returns concept with risk at most times optimal Mechanism 1: 1. Define i as positive if has majority of + labels, negative otherwise 2. If at least half the points belong to positive agents return c +, otherwise return c - Theorem: Mechanism 1 is a 3-approx group strategyproof mechanism Theorem: No (deterministic) SP mechanism achieves an approx ratio better than 3
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Agent 1 Agent 2 + + + + + + + + + + – – – – – – + + + + Agent 1 Agent 2 + + + + + + + + + + – – – – – – – – – – Agent 1 Agent 2 + + + + + + – – – – – – – – – – – – – – – – – – + + + + + + + + + +
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Theorem: There is a randomized group SP 2- approximation mechanism Theorem: No randomized SP mechanism achieves an approx ratio better than 2
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A very simple example of mechanism design in a decision making setting 8 slides An investigation of incentives in a general machine learning setting 2 slides
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Each agent assigns a label to every point of X. Each agent holds a distribution over X R i (c) = prob. of point being mislabeled according to agent’s distribution R(c) = average individual risk Each agent’s distribution is sampled, sample labeled by the agent Theorem: Possible to achieve almost 2- approximation in expectation under rationality assumption
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Classification: Richer concept classes Currently have strong results for linear threshold functions over the real line Other machine learning models Regression learning [Dekel, Fischer, and Procaccia, in SODA 2008]
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