Differentially Private and Strategy-Proof Spectrum Auction - PowerPoint Presentation

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Differentially Private and Strategy-Proof Spectrum Auction with Approximate Revenue Maximization

Ruihao Zhu and Kang G. ShinDepartment of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor

1Slide2

Outline Background

Design GoalPrimers: differential privacy, exponential mech., truthfulness , revenue maximizationNear Optimal Mechanism

PASSEvaluation Results

2

2Slide3

Spectrum Need Forecast ‐ Table of Results

FCC whitepaper, Oct. 2010

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Secondary Spectrum MarketTraditionally,

static, long-term licensesRadio spectrum is not fully utilizedUnlicensed bands are getting crowded

=>Dynamic spectrum redistribution/auction needed!

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Unique Challenge in Spectrum AuctionsSpatial ReusabilityBidders far away can use the same channel

Channel 1

Channel 2

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Traditional Spectrum Auctions

Auctioneer

Channels

Bidders

Auctioneer’s

Revenue

Truthfulness

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Privacy in Spectrum AuctionsChannels are for

short-term usage.Sequential auctions make inference of bidding information possible even with secure channel.7Slide8

Privacy in Spectrum Auctions8

How to infer?Slide9

Privacy in Spectrum Auctions, cont’d

Single channel

First time:

Second

time:

9

0.01%

revenue for channel costSlide10

Outline Background

Design GoalPrimers: differential privacy, exponential mech., truthfulnessNear Optimal MechanismPASS

Evaluation Results

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GoalDesign a

truthful auction mechanism that maximizes auctioneer’s revenue

while keeping participants’ bidding prices confidential

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Outline Background

Design GoalPrimers: differential privacy, exponential mech., truthfulness, revenue maximizationNear Optimal Mechanism

PASSEvaluation Results

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Differential Privacy

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Differential Privacy, cont’d

Def’n. A mechanism

M is

-differential private if for any two data profiles D1 and D2 differing

on a single element, and all

S ⊆ Range(

M

),

Pr[

M

(D1)

∈ S] ≤ exp

(

)×

Pr[

M

(

) ∈ S

]+

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Differential Privacy cont’dRandomness

(no deterministic DP):Input perturbation

Exponential mechanism

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Exponential Mechanism

Bids

.

range of bids

.

Revenue

:

.

Choose outcome

x

with

probability

Pr

[

x

]

∝

exp

(

).

Logarithmic loss in revenue

-

differentially

private

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Truthful (in Expectation)

A bidder always maximize expected utility by bidding true valuation

, i.e.,

.

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Truthful Mechanism

A mechanism is truthful in expectation if and

only if, for any agent

and any fixed choice of bids by

the other

agents

1.

s winning probability is

monotone in

, where

is the probability that

wins when

his bid is

.

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Revenue Maximization

19

Bids

.

Bid PDFs and CDFs:

Virtual bid:

Virtual Revenue

:

.

Choose

outcome

x

to maximize

.

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Outline Background

Problem DefinitionPrimers: differential privacy, exponential mech., truthfulness, revenue maximizationNear Optimal Mechanism

PASSEvaluation Results

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Near Optimal Mechanismexponential mechanism

+ revenue maximization technique:Calculate virtual bidDetermine feasible allocations Select x

with probability

Pr

[

x

]

∝

exp

(

).

NP hard!

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Outline Background

Design GoalPrimers: differential privacy, exponential mech., truthfulness , revenue maximizationNear Optimal Mechanism

PASSEvaluation Results

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Illustrative Example

=1 channel

=5

bidders with

23

1

2

3

4

5

location

Interference rangeSlide24

PASS

Graph Partition

Random Selection and Allocation

Virtual Channel

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Graph Partition

Partition entire

area uniformly into

small hexagons

w

ith

side

length equal

half interference

range

.

2

3

1

4

25

5

PASSSlide26

2

3

1

4

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5

Virtual Channel

PASSSlide27

2

3

1

4

27

5

Random Selection and Allocation

.

PASSSlide28

2

3

1

4

28

5

Random Selection and Allocation

Taking

PASSSlide29

2

3

1

4

29

5

Random Selection and Allocation

Suppose bidder 1 is

s

elected.

PASSSlide30

2

3

1

4

30

5

Random Selection and Allocation

All the bidders conflict

with bidder 1 is removed

.

PASSSlide31

4

31

5

Random Selection and Allocation

Taking

PASSSlide32

4

32

5

Random Selection and Allocation

Suppose bidder 5 is

s

elected.

PASSSlide33

4

33

5

Random Selection and Allocation

All the bidders conflict

with bidder

5

is removed

.

PASSSlide34

Properties of PASS

Lemma 4. The size of the virtual channels bundle assigned to

each bidder is less than or equal to

12, which is optimal for hexagon partition.

Theorem 6.

With the probability of at

least

PASS can

generate a set of winners with a revenue of at

least

, where

is the optimal revenue.

Theorem 7. For any

PASS preserves

differential privacy.

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Outline Background

Design GoalPrimers: differential privacy, exponential mech., truthfulness , revenue maximizationNear Optimal MechanismPASS

Evaluation Results

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Revenue

Revenue of PASS (5 channels)

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Revenue of PASS (10 channels)

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RevenueSlide38

Revenue of PASS (15 channels)

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RevenueSlide39

Measuring Empirical

Privacy of PASS (5 channels)

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Privacy of PASS (10 channels)

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Measuring Empirical

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Privacy of PASS (15 channels)

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Measuring Empirical

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Conclusion

PASS: First

differentially private and truthful spectrum auction mechanism

with approximate revenue

maximization.

Theoretically proved

the properties in revenue and privacy.

I

mplemented PASS

and extensively evaluated its

performance.

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Thank you!

rhzhu@umich.edu

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