68 research outputs found
Budget Constrained Auctions with Heterogeneous Items
In this paper, we present the first approximation algorithms for the problem
of designing revenue optimal Bayesian incentive compatible auctions when there
are multiple (heterogeneous) items and when bidders can have arbitrary demand
and budget constraints. Our mechanisms are surprisingly simple: We show that a
sequential all-pay mechanism is a 4 approximation to the revenue of the optimal
ex-interim truthful mechanism with discrete correlated type space for each
bidder. We also show that a sequential posted price mechanism is a O(1)
approximation to the revenue of the optimal ex-post truthful mechanism when the
type space of each bidder is a product distribution that satisfies the standard
hazard rate condition. We further show a logarithmic approximation when the
hazard rate condition is removed, and complete the picture by showing that
achieving a sub-logarithmic approximation, even for regular distributions and
one bidder, requires pricing bundles of items. Our results are based on
formulating novel LP relaxations for these problems, and developing generic
rounding schemes from first principles. We believe this approach will be useful
in other Bayesian mechanism design contexts.Comment: Final version accepted to STOC '10. Incorporates significant reviewer
comment
Online Set Cover with Set Requests
We consider a generic online allocation problem that generalizes the classical online set cover framework by considering requests comprising a set of elements rather than a single element. This problem has multiple applications in cloud computing, crowd sourcing, facility planning, etc. Formally, it is an online covering problem where each online step comprises an offline covering problem. In addition, the covering sets are capacitated, leading to packing constraints. We give a randomized algorithm for this problem that has a nearly tight competitive ratio in both objectives: overall cost and maximum capacity violation. Our main technical tool is an online algorithm for packing/covering LPs with nested constraints, which may be of interest in other applications as well
Measuring Offline Advertisement Conversion
This disclosure describes techniques to measure the impact of exposure to an offline advertisement on subsequent online and offline actions. The system utilizes advertisement data, historical location data and user behavior data to estimate a test spatiotemporal region in which users are likely exposed to a particular offline advertisement and a control spatiotemporal region in which users are likely not exposed to the particular offline advertisement. The system uses statistical techniques to determine the impact of the particular advertisement by comparison of the behavior of the test population and the control population
When Are Two Lists Better than One?: Benefits and Harms in Joint Decision-making
Historically, much of machine learning research has focused on the
performance of the algorithm alone, but recently more attention has been
focused on optimizing joint human-algorithm performance. Here, we analyze a
specific type of human-algorithm collaboration where the algorithm has access
to a set of items, and presents a subset of size to the human, who
selects a final item from among those . This scenario could model content
recommendation, route planning, or any type of labeling task. Because both the
human and algorithm have imperfect, noisy information about the true ordering
of items, the key question is: which value of maximizes the probability
that the best item will be ultimately selected? For , performance is
optimized by the algorithm acting alone, and for it is optimized by the
human acting alone. Surprisingly, we show that for multiple of noise models, it
is optimal to set - that is, there are strict benefits to
collaborating, even when the human and algorithm have equal accuracy
separately. We demonstrate this theoretically for the Mallows model and
experimentally for the Random Utilities models of noisy permutations. However,
we show this pattern is reversed when the human is anchored on the algorithm's
presented ordering - the joint system always has strictly worse performance. We
extend these results to the case where the human and algorithm differ in their
accuracy levels, showing that there always exist regimes where a more accurate
agent would strictly benefit from collaborating with a less accurate one, but
these regimes are asymmetric between the human and the algorithm's accuracy
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