Strategyproof Classification Under Constant Hypotheses: A Tale of ...

Reshef Meir, Ariel D. Procaccia, and Jeffrey S. Rosenschein

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

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

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)

Agent 1 Agent 2

+–

–

–

++

If all agents report truthfully, choose concept that minimizes global risk

Risk Minimization is not strategyproof: agents can benefit by lying

Agent 1 Agent 2

+–

–

–

+

+–

+

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

Agent 1

Agent 2

+ + +

+ +

– – –

+ +

Agent 1

Agent 2

+ + +

+ +

– – –

– –

Agent 1

Agent 2

+ + +– –

– – –

– –– –+

+

+ ++

Theorem: There is a randomized group SP 2-approximation mechanism

Theorem: No randomized SP mechanism achieves an approx ratio better than 2

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

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

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]