Related papers: Submodular Maximization with Nearly Optimal Approx…
Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…
We consider the problem of multi-objective maximization of monotone submodular functions subject to cardinality constraint, often formulated as $\max_{|A|=k}\min_{i\in\{1,\dots,m\}}f_i(A)$. While it is widely known that greedy methods work…
Constrained $k$-submodular maximization is a general framework that captures many discrete optimization problems such as ad allocation, influence maximization, personalized recommendation, and many others. In many of these applications,…
The goal of a typical adaptive sequential decision making problem is to design an interactive policy that selects a group of items sequentially, based on some partial observations, to maximize the expected utility. It has been shown that…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
This paper presents a polynomial-time $1/2$-approximation algorithm for maximizing nonnegative $k$-submodular functions. This improves upon the previous $\max\{1/3, 1/(1+a)\}$-approximation by Ward and \v{Z}ivn\'y~(SODA'14), where…
We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order.…
Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions,…
Adaptive submodularity is a fundamental concept in stochastic optimization, with numerous applications such as sensor placement, hypothesis identification and viral marketing. We consider the problem of minimum cost cover of…
In this paper, we demonstrate a formulation for optimizing coupled submodular maximization problems with provable sub-optimality bounds. In robotics applications, it is quite common that optimization problems are coupled with one another…
Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
Many large-scale machine learning problems--clustering, non-parametric learning, kernel machines, etc.--require selecting a small yet representative subset from a large dataset. Such problems can often be reduced to maximizing a submodular…
Submodularity is one of the most important properties in combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of a $k$-submodular function requires an exponential number of value oracle…
We study \emph{combinatorial procurement auctions}, where a buyer with a valuation function $v$ and budget $B$ wishes to buy a set of items. Each item $i$ has a cost $c_i$ and the buyer is interested in a set $S$ that maximizes $v(S)$…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising…