ruihao zhu and kang g. shin
DESCRIPTION
Outline Background Design Goal Primers: differential privacy, exponential mech., truthfulness , revenue maximization Near Optimal Mechanism PASS Evaluation Results The talk will be divided into the following parts.TRANSCRIPT
Ruihao Zhu and Kang G. Shin
Differentially Private and Strategy-Proof Spectrum Auction with
Approximate Revenue Maximization Ruihao Zhu and Kang G. Shin
Department of Electrical Engineering and Computer Science,
University of Michigan, Ann Arbor Hello, ladies and gentlemen, I am
Ruihao Zhu, a senior student in University of Michigan. Today, I
will introduce my work, differentially private to all of you.
Outline Background Design Goal
Primers: differential privacy, exponentialmech., truthfulness ,
revenue maximization Near Optimal Mechanism PASS Evaluation Results
The talk will be divided into the following parts. Spectrum Need
Forecast Table of Results
This table comes from a whitepaper (Mobile Broadband: The Benefits
of Additional Spectrum) published by FCC in Oct On one hand, mobile
broadband traffic is growing dramatically; on the other hand,
spectrum is limited resource. FCC predicts that the spectrum
deficit is likely to approach 300 megahertz this year. FCC
whitepaper, Oct. 2010 Secondary Spectrum Market
Traditionally, static, long-term licenses Radio spectrum is not
fully utilized Unlicensed bands are getting crowded =>Dynamic
spectrum redistribution/auction needed! Traditional spectrum
allocation is carried out by the government in a static and long
term way. Therefore, radio spectrum is not fully utilized, and
unlicensed bands get crowded. Therefore, redistribution of idle
radio spectrum is highly important. Open markets, such as Spectrum
Bridge, have already appeared to improve spectrum utilization by
providing services for buying, selling, and leasing idle spectrum.
Unique Challenge in Spectrum Auctions
Spatial Reusability Bidders far away can use the same channel
Channel 1 Channel 2 Different from traditional goods, spectrum has
a unique characteristic. That is the spatial reusability, which
allows bidders far away enough from each other to use the same
channel. Traditional Spectrum Auctions
Auctioneer Channels Bidders However, spectrum valuations are the
private information of the bidders. It may disclose the bidders'
profits for serving their subscribers or their economic situations,
which are highly desirable information for rivals and stock market
speculators. Once the valuations are revealed to a corrupt
auctioneer, she may exploit such knowledge to her advantage.
Auctioneers Revenue Truthfulness Privacy in Spectrum Auctions
Channels are for short-term usage. Sequential auctions make
inference of bidding information possible even with secure channel.
spectrum valuations are the private information of the bidders. It
may disclose the bidders' profits for serving their subscribers or
their economic situations, which are highly desirable information
for rivals and stock market speculators. Once the valuations are
revealed to a corrupt auctioneer, she may exploit such knowledge to
her advantage. Privacy in Spectrum Auctions
spectrum valuations are the private information of the bidders. It
may disclose the bidders' profits for serving their subscribers or
their economic situations, which are highly desirable information
for rivals and stock market speculators. Once the valuations are
revealed to a corrupt auctioneer, she may exploit such knowledge to
her advantage. How to infer? Privacy in Spectrum Auctions,
contd
Single channel First time: & =2, =1.8 Second time: & =2.02,
=2.2 spectrum valuations are the private information of the
bidders. It may disclose the bidders' profits for serving their
subscribers or their economic situations, which are highly
desirable information for rivals and stock market speculators. Once
the valuations are revealed to a corrupt auctioneer, she may
exploit such knowledge to her advantage. 0.01% revenue for channel
cost Outline Background Design Goal
Primers: differential privacy, exponentialmech., truthfulness Near
Optimal Mechanism PASS Evaluation Results Goal Design a truthful
auction mechanism that maximizes auctioneers revenue while keeping
participants bidding prices confidential Bearing the concern in
mind, our goal here is design Outline Background Design Goal
Primers: differential privacy, exponentialmech., truthfulness,
revenue maximization Near Optimal Mechanism PASS Evaluation Results
Differential Privacy Differential privacyaims to provide means to
maximize the accuracy of queries from statistical databases while
minimizing the chances of identifying its records. Intuitively, it
means that a single change in the input dataset does not affect the
outcome much. Differential Privacy, contd
Defn. A mechanism Mis (,)-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(2) S]+ Differential Privacy
contd
Randomness (no deterministic DP): Input perturbation Exponential
mechanism Exponential Mechanism
Bids:=( 1 , 2,, ). = range of bids. Revenue: REV()= =1 . Choose
outcome x with probability Pr[x] exp(()/2). Logarithmic loss in
revenue (2)-differentially private Truthful (in Expectation)
A bidder always maximize expected utility by bidding true
valuation, i.e., [ ( , )] [ ( , )]. 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 ; 2. = 0 , where
() is the probability that wins when his bid is . Revenue
Maximization Bids:=( 1 , 2 ,, ). Bid PDFs and CDFs:
= 1 , 2,, ,=( 1 , 2,, ) Virtual bid: )= (1 ( ))/ ( Virtual Revenue:
REV()= =1 . Choose outcome x to maximize REV. Outline Background
Problem Definition
Primers: differential privacy, exponentialmech., truthfulness,
revenue maximization Near Optimal Mechanism PASS Evaluation Results
Near Optimal Mechanism
exponential mechanism + revenue maximization technique: Calculate
virtual bid Determine feasible allocations Select x with
probability Pr[x] exp(()/2). NP hard! Outline Background Design
Goal
Primers: differential privacy, exponentialmech., truthfulness ,
revenue maximization Near Optimal Mechanism PASS Evaluation Results
Illustrative Example =1 channel
=5 bidders with( 1 )=20, ( 2 )=50,( 3 )=80, ( 4 )=70, ( 5 )=30
location 4 2 5 1. Partition the geographic region into hexagons
with unit side-length and color the region with 7 colors (as in the
figure). 2. Grouping: Bidders in the same color region are in the
same group and bidders in the same hexagon are in the same
subgroup. Interference range 1 3 Random Selection and
Allocation
PASS Graph Partition Virtual Channel 1. Partition the geographic
region into hexagons with unit side-length and color the region
with 7 colors (as in the figure). 2. Grouping: Bidders in the same
color region are in the same group and bidders in the same hexagon
are in the same subgroup. Random Selection and Allocation PASS
Partition entire area uniformly into small hexagons with
Graph Partition 4 Partition entire area uniformly into small
hexagons with sidelength equal half interference range. 5 2 In
bidder grouping, dear use a hexagon based graph partition technique
to divide the bidders into 7 groups, namely g1 to g7. each hexagon
here is called a subgroup. 1 3 PASS 1 ={ 6,7 , 7,12 } 2 ={ 6,7 } 3
={ 7,12 }
Virtual Channel 4 1 ={ 6,7 , 7,12 } 2 ={ 6,7 } 3 ={ 7,12 } 4 =
13,14 5 ={ 13,14 } 5 2 In bidder grouping, dear use a hexagon based
graph partition technique to divide the bidders into 7 groups,
namely g1 to g7. each hexagon here is called a subgroup. 1 3 Random
Selection and Allocation
PASS Random Selection and Allocation 4 exp( | |). 5 2 In bidder
grouping, dear use a hexagon based graph partition technique to
divide the bidders into 7 groups, namely g1 to g7. each hexagon
here is called a subgroup. 1 3 Random Selection and
Allocation
PASS Random Selection and Allocation 4 Taking =0.1 Pr W={1} exp(2/
2 ) Pr W={2} exp(5 ) Pr W={3} exp(8 ) Pr W={4} exp(7 ) Pr W={5}
exp(3 ) 5 2 In bidder grouping, dear use a hexagon based graph
partition technique to divide the bidders into 7 groups, namely g1
to g7. each hexagon here is called a subgroup. 1 3 Random Selection
and Allocation
PASS Random Selection and Allocation 4 Suppose bidder 1 is
selected. 5 2 In bidder grouping, dear use a hexagon based graph
partition technique to divide the bidders into 7 groups, namely g1
to g7. each hexagon here is called a subgroup. 1 3 Random Selection
and Allocation
PASS Random Selection and Allocation 4 All the bidders conflict
with bidder 1 is removed. 5 2 In bidder grouping, dear use a
hexagon based graph partition technique to divide the bidders into
7 groups, namely g1 to g7. each hexagon here is called a subgroup.
1 3 Random Selection and Allocation
PASS Random Selection and Allocation 4 Taking =0.1 Pr W={1,4} exp(7
) Pr W={1,5} exp(3 ) 5 In bidder grouping, dear use a hexagon based
graph partition technique to divide the bidders into 7 groups,
namely g1 to g7. each hexagon here is called a subgroup. Random
Selection and Allocation
PASS Random Selection and Allocation 4 Suppose bidder 5 is
selected. 5 In bidder grouping, dear use a hexagon based graph
partition technique to divide the bidders into 7 groups, namely g1
to g7. each hexagon here is called a subgroup. Random Selection and
Allocation
PASS Random Selection and Allocation 4 All the bidders conflict
with bidder 5 is removed. 5 In bidder grouping, dear use a hexagon
based graph partition technique to divide the bidders into 7
groups, namely g1 to g7. each hexagon here is called a subgroup.
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 least1 (1)PASS can generate a set of winners with a revenue of
at least 12 ( ln ), where is the optimal revenue. Theorem 7. For
any < 1 2 , PASS preserves ( 11 ln ,) differential privacy.
Outline Background Design Goal
Primers: differential privacy, exponentialmech., truthfulness ,
revenue maximization Near Optimal Mechanism PASS Evaluation Results
Revenue Revenue of PASS (5 channels) Revenue Revenue of PASS (10
channels) Revenue Revenue of PASS (15 channels) Measuring Empirical
Privacy of PASS (5 channels) Measuring Empirical Privacy of PASS
(10 channels) Measuring Empirical Privacy of PASS (15 channels)
Conclusion PASS: First differentially private and truthful spectrum
auction mechanism with approximate revenue maximization.
Theoretically proved the properties in revenue and privacy.
Implemented PASS and extensively evaluated its performance. Thank
you!