TITLE: A Dynamic Near-Optimal Algorithm for Online Linear Programming

SPEAKER: Professor Yinyu Ye

ABSTRACT:

A natural optimization model that formulates many online
resource allocation and revenue

management problems is the online linear program (LP) where the
constraint matrix is revealed

column by column along with the objective function. We provide a
near-optimal algorithm for

this surprisingly general class of online problems under the
assumption of random order of arrival
and some mild conditions on the size of the LP right-hand-side input.
Our learning-based algorithm works by dynamically updating a threshold price vector at
geometric time intervals, where
the dual prices learned from revealed columns in the previous period
are used to determine the
sequential decisions in the current period. Our algorithm has a
feature of learning by doing, and the prices are updated at a carefully chosen pace that is neither
too fast nor too slow. In
particular, our algorithm doesn't assume any distribution information
on the input itself, thus
is robust to data uncertainty and variations due to its dynamic
learning capability. Applications
of our algorithm include many online multi-resource allocation and
multi-product revenue management
problems such as online routing and packing, online combinatorial
auctions, adwords
matching, inventory control and yield management.


Joint work with Shipra Agrawal and Zizhuo Wang.