3,189 research outputs found
Learning Theory and Algorithms for Revenue Optimization in Second-Price Auctions with Reserve
Second-price auctions with reserve play a critical role for modern search
engine and popular online sites since the revenue of these companies often
directly de- pends on the outcome of such auctions. The choice of the reserve
price is the main mechanism through which the auction revenue can be influenced
in these electronic markets. We cast the problem of selecting the reserve price
to optimize revenue as a learning problem and present a full theoretical
analysis dealing with the complex properties of the corresponding loss
function. We further give novel algorithms for solving this problem and report
the results of several experiments in both synthetic and real data
demonstrating their effectiveness.Comment: Accepted at ICML 201
Learning to bid in revenue-maximizing auctions
We consider the problem of the optimization of bidding strategies in
prior-dependent revenue-maximizing auctions, when the seller fixes the reserve
prices based on the bid distributions. Our study is done in the setting where
one bidder is strategic. Using a variational approach, we study the complexity
of the original objective and we introduce a relaxation of the objective
functional in order to use gradient descent methods. Our approach is simple,
general and can be applied to various value distributions and
revenue-maximizing mechanisms. The new strategies we derive yield massive
uplifts compared to the traditional truthfully bidding strategy
A General Theory of Sample Complexity for Multi-Item Profit Maximization
The design of profit-maximizing multi-item mechanisms is a notoriously
challenging problem with tremendous real-world impact. The mechanism designer's
goal is to field a mechanism with high expected profit on the distribution over
buyers' values. Unfortunately, if the set of mechanisms he optimizes over is
complex, a mechanism may have high empirical profit over a small set of samples
but low expected profit. This raises the question, how many samples are
sufficient to ensure that the empirically optimal mechanism is nearly optimal
in expectation? We uncover structure shared by a myriad of pricing, auction,
and lottery mechanisms that allows us to prove strong sample complexity bounds:
for any set of buyers' values, profit is a piecewise linear function of the
mechanism's parameters. We prove new bounds for mechanism classes not yet
studied in the sample-based mechanism design literature and match or improve
over the best known guarantees for many classes. The profit functions we study
are significantly different from well-understood functions in machine learning,
so our analysis requires a sharp understanding of the interplay between
mechanism parameters and buyer values. We strengthen our main results with
data-dependent bounds when the distribution over buyers' values is
"well-behaved." Finally, we investigate a fundamental tradeoff in sample-based
mechanism design: complex mechanisms often have higher profit than simple
mechanisms, but more samples are required to ensure that empirical and expected
profit are close. We provide techniques for optimizing this tradeoff
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