7,202 research outputs found
Sequential item pricing for unlimited supply
We investigate the extent to which price updates can increase the revenue of
a seller with little prior information on demand. We study prior-free revenue
maximization for a seller with unlimited supply of n item types facing m myopic
buyers present for k < log n days. For the static (k = 1) case, Balcan et al.
[2] show that one random item price (the same on each item) yields revenue
within a \Theta(log m + log n) factor of optimum and this factor is tight. We
define the hereditary maximizers property of buyer valuations (satisfied by any
multi-unit or gross substitutes valuation) that is sufficient for a significant
improvement of the approximation factor in the dynamic (k > 1) setting. Our
main result is a non-increasing, randomized, schedule of k equal item prices
with expected revenue within a O((log m + log n) / k) factor of optimum for
private valuations with hereditary maximizers. This factor is almost tight: we
show that any pricing scheme over k days has a revenue approximation factor of
at least (log m + log n) / (3k). We obtain analogous matching lower and upper
bounds of \Theta((log n) / k) if all valuations have the same maximum. We
expect our upper bound technique to be of broader interest; for example, it can
significantly improve the result of Akhlaghpour et al. [1]. We also initiate
the study of revenue maximization given allocative externalities (i.e.
influences) between buyers with combinatorial valuations. We provide a rather
general model of positive influence of others' ownership of items on a buyer's
valuation. For affine, submodular externalities and valuations with hereditary
maximizers we present an influence-and-exploit (Hartline et al. [13]) marketing
strategy based on our algorithm for private valuations. This strategy preserves
our approximation factor, despite an affine increase (due to externalities) in
the optimum revenue.Comment: 18 pages, 1 figur
A review of domain adaptation without target labels
Domain adaptation has become a prominent problem setting in machine learning
and related fields. This review asks the question: how can a classifier learn
from a source domain and generalize to a target domain? We present a
categorization of approaches, divided into, what we refer to as, sample-based,
feature-based and inference-based methods. Sample-based methods focus on
weighting individual observations during training based on their importance to
the target domain. Feature-based methods revolve around on mapping, projecting
and representing features such that a source classifier performs well on the
target domain and inference-based methods incorporate adaptation into the
parameter estimation procedure, for instance through constraints on the
optimization procedure. Additionally, we review a number of conditions that
allow for formulating bounds on the cross-domain generalization error. Our
categorization highlights recurring ideas and raises questions important to
further research.Comment: 20 pages, 5 figure
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