51 research outputs found
Data Summarization beyond Monotonicity: Non-monotone Two-Stage Submodular Maximization
The objective of a two-stage submodular maximization problem is to reduce the
ground set using provided training functions that are submodular, with the aim
of ensuring that optimizing new objective functions over the reduced ground set
yields results comparable to those obtained over the original ground set. This
problem has applications in various domains including data summarization.
Existing studies often assume the monotonicity of the objective function,
whereas our work pioneers the extension of this research to accommodate
non-monotone submodular functions. We have introduced the first constant-factor
approximation algorithms for this more general case
Constrained Submodular Maximization: Beyond 1/e
In this work, we present a new algorithm for maximizing a non-monotone
submodular function subject to a general constraint. Our algorithm finds an
approximate fractional solution for maximizing the multilinear extension of the
function over a down-closed polytope. The approximation guarantee is 0.372 and
it is the first improvement over the 1/e approximation achieved by the unified
Continuous Greedy algorithm [Feldman et al., FOCS 2011]
Non-monotone Submodular Maximization with Nearly Optimal Adaptivity and Query Complexity
Submodular maximization is a general optimization problem with a wide range
of applications in machine learning (e.g., active learning, clustering, and
feature selection). In large-scale optimization, the parallel running time of
an algorithm is governed by its adaptivity, which measures the number of
sequential rounds needed if the algorithm can execute polynomially-many
independent oracle queries in parallel. While low adaptivity is ideal, it is
not sufficient for an algorithm to be efficient in practice---there are many
applications of distributed submodular optimization where the number of
function evaluations becomes prohibitively expensive. Motivated by these
applications, we study the adaptivity and query complexity of submodular
maximization. In this paper, we give the first constant-factor approximation
algorithm for maximizing a non-monotone submodular function subject to a
cardinality constraint that runs in adaptive rounds and makes
oracle queries in expectation. In our empirical study, we use
three real-world applications to compare our algorithm with several benchmarks
for non-monotone submodular maximization. The results demonstrate that our
algorithm finds competitive solutions using significantly fewer rounds and
queries.Comment: 12 pages, 8 figure
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