Related papers: Adaptive Maximization of Pointwise Submodular Func…
We consider the optimal transport problem between a set of $n$ red points and a set of $n$ blue points subject to a concave cost function such as $c(x,y) = \|x-y\|^{p}$ for $0< p < 1$. Our focus is on a particularly simple matching…
The subspace selection problem seeks a subspace that maximizes an objective function under some constraint. This problem includes several important machine learning problems such as the principal component analysis and sparse dictionary…
The Greedy algorithm is the simplest heuristic in sequential decision problem that carelessly takes the locally optimal choice at each round, disregarding any advantages of exploring and/or information gathering. Theoretically, it is known…
Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…
Maximizing a single submodular set function subject to a cardinality constraint is a well-studied and central topic in combinatorial optimization. However, finding a set that maximizes multiple functions at the same time is much less…
We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider…
``Composable core-sets'' are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove…
In this paper, we study the \underline{R}obust \underline{o}ptimization for \underline{se}quence \underline{Net}worked \underline{s}ubmodular maximization (RoseNets) problem. We interweave the robust optimization with the sequence networked…
In this paper, we study the tradeoff between the approximation guarantee and adaptivity for the problem of maximizing a monotone submodular function subject to a cardinality constraint. The adaptivity of an algorithm is the number of…
In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization in [BS18a] to quantify the information theoretic…
Unbalanced optimal transport (UOT) has recently gained much attention due to its flexible framework for handling un-normalized measures and its robustness properties. In this work, we explore learning (structured) sparse transport plans in…
In this work, we study the Submodular Cost Submodular Cover problem, which is to minimize the submodular cost required to ensure that the submodular benefit function exceeds a given threshold. Existing approximation ratios for the greedy…
When approaching to problems in computer science, we often encounter situations where a subset of a finite set maximizing some utility function needs to be selected. Some of such utility functions are known to be approximately submodular.…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
In this paper, we study the adaptive submodular cover problem under the worst-case setting. This problem generalizes many previously studied problems, namely, the pool-based active learning and the stochastic submodular set cover. The input…
Given a set of $n$ vectors in $\mathbb{R}^d$, the goal of the \emph{determinant maximization} problem is to pick $k$ vectors with the maximum volume. Determinant maximization is the MAP-inference task for determinantal point processes (DPP)…