strategyproof classification under constant hypotheses: a tale of
TRANSCRIPT
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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 Xi = {xi1,xi2,...} X For each xik Xi agent i has a label yik { , } Agent i reports labels y’i1,y’i2,... Mechanism receives reported labels and
outputs c+ (constant ) or c (constant ) Risk of i: Ri(c) = |{k: c(xik) yik}| Global risk: R(c) = |{i,k: c(xik) yik}| = i Ri(c)
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Agent 1 Agent 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 1 Agent 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
![Page 12: Strategyproof Classification Under Constant Hypotheses: A Tale of](https://reader033.vdocument.in/reader033/viewer/2022060200/5598cff41a28ab87338b4812/html5/thumbnails/12.jpg)
Each agent assigns a label to every point of X. Each agent holds a distribution over X Ri(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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