126 research outputs found
An Efficient Bandit Algorithm for Realtime Multivariate Optimization
Optimization is commonly employed to determine the content of web pages, such
as to maximize conversions on landing pages or click-through rates on search
engine result pages. Often the layout of these pages can be decoupled into
several separate decisions. For example, the composition of a landing page may
involve deciding which image to show, which wording to use, what color
background to display, etc. Such optimization is a combinatorial problem over
an exponentially large decision space. Randomized experiments do not scale well
to this setting, and therefore, in practice, one is typically limited to
optimizing a single aspect of a web page at a time. This represents a missed
opportunity in both the speed of experimentation and the exploitation of
possible interactions between layout decisions.
Here we focus on multivariate optimization of interactive web pages. We
formulate an approach where the possible interactions between different
components of the page are modeled explicitly. We apply bandit methodology to
explore the layout space efficiently and use hill-climbing to select optimal
content in realtime. Our algorithm also extends to contextualization and
personalization of layout selection. Simulation results show the suitability of
our approach to large decision spaces with strong interactions between content.
We further apply our algorithm to optimize a message that promotes adoption of
an Amazon service. After only a single week of online optimization, we saw a
21% conversion increase compared to the median layout. Our technique is
currently being deployed to optimize content across several locations at
Amazon.com.Comment: KDD'17 Audience Appreciation Awar
An Upper Bound on the Size of Obstructions for Bounded Linear Rank-Width
We provide a doubly exponential upper bound in on the size of forbidden
pivot-minors for symmetric or skew-symmetric matrices over a fixed finite field
of linear rank-width at most . As a corollary, we obtain a
doubly exponential upper bound in on the size of forbidden vertex-minors
for graphs of linear rank-width at most . This solves an open question
raised by Jeong, Kwon, and Oum [Excluded vertex-minors for graphs of linear
rank-width at most . European J. Combin., 41:242--257, 2014]. We also give a
doubly exponential upper bound in on the size of forbidden minors for
matroids representable over a fixed finite field of path-width at most .
Our basic tool is the pseudo-minor order used by Lagergren [Upper Bounds on
the Size of Obstructions and Interwines, Journal of Combinatorial Theory Series
B, 73:7--40, 1998] to bound the size of forbidden graph minors for bounded
path-width. To adapt this notion into linear rank-width, it is necessary to
well define partial pieces of graphs and merging operations that fit to
pivot-minors. Using the algebraic operations introduced by Courcelle and
Kant\'e, and then extended to (skew-)symmetric matrices by Kant\'e and Rao, we
define boundaried -labelled graphs and prove similar structure theorems for
pivot-minor and linear rank-width.Comment: 28 pages, 1 figur
On the pathwidth of almost semicomplete digraphs
We call a digraph {\em -semicomplete} if each vertex of the digraph has at
most non-neighbors, where a non-neighbor of a vertex is a vertex such that there is no edge between and in either direction.
This notion generalizes that of semicomplete digraphs which are
-semicomplete and tournaments which are semicomplete and have no
anti-parallel pairs of edges. Our results in this paper are as follows. (1) We
give an algorithm which, given an -semicomplete digraph on vertices
and a positive integer , in time either
constructs a path-decomposition of of width at most or concludes
correctly that the pathwidth of is larger than . (2) We show that there
is a function such that every -semicomplete digraph of pathwidth
at least has a semicomplete subgraph of pathwidth at least .
One consequence of these results is that the problem of deciding if a fixed
digraph is topologically contained in a given -semicomplete digraph
admits a polynomial-time algorithm for fixed .Comment: 33pages, a shorter version to appear in ESA 201
Qd-tree: Learning Data Layouts for Big Data Analytics
Corporations today collect data at an unprecedented and accelerating scale,
making the need to run queries on large datasets increasingly important.
Technologies such as columnar block-based data organization and compression
have become standard practice in most commercial database systems. However, the
problem of best assigning records to data blocks on storage is still open. For
example, today's systems usually partition data by arrival time into row
groups, or range/hash partition the data based on selected fields. For a given
workload, however, such techniques are unable to optimize for the important
metric of the number of blocks accessed by a query. This metric directly
relates to the I/O cost, and therefore performance, of most analytical queries.
Further, they are unable to exploit additional available storage to drive this
metric down further.
In this paper, we propose a new framework called a query-data routing tree,
or qd-tree, to address this problem, and propose two algorithms for their
construction based on greedy and deep reinforcement learning techniques.
Experiments over benchmark and real workloads show that a qd-tree can provide
physical speedups of more than an order of magnitude compared to current
blocking schemes, and can reach within 2X of the lower bound for data skipping
based on selectivity, while providing complete semantic descriptions of created
blocks.Comment: ACM SIGMOD 202
Obstructions for Matroids of Path-Width at most k and Graphs of Linear Rank-Width at most k
International audienceEvery minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field , the list contains only finitely many -representable matroids, due to the well-quasi-ordering of -representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)]. But this proof is non-constructive and does not provide any algorithm for computing these -representable excluded minors in general. We consider the class of matroids of path-width at most for fixed . We prove that for a finite field , every -representable excluded minor for the class of matroids of path-width at most~ has at most elements. We can therefore compute, for any integer and a fixed finite field , the set of -representable excluded minors for the class of matroids of path-width , and this gives as a corollary a polynomial-time algorithm for checking whether the path-width of an -represented matroid is at most . We also prove that every excluded pivot-minor for the class of graphs having linear rank-width at most has at most vertices, which also results in a similar algorithmic consequence for linear rank-width of graphs
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