Related papers: Stochastic Monotone Submodular Maximization with Q…
In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…
We consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable…
A multidimensional optimization problem is formulated in the tropical mathematics setting as to maximize a nonlinear objective function, which is defined through a multiplicative conjugate transposition operator on vectors in a…
Subset selection tasks, arise in recommendation systems and search engines and ask to select a subset of items that maximize the value for the user. The values of subsets often display diminishing returns, and hence, submodular functions…
In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…
Meta-Learning has gained increasing attention in the machine learning and artificial intelligence communities. In this paper, we introduce and study an adaptive submodular meta-learning problem. The input of our problem is a set of items,…
Submodularity is an important property of set functions and has been extensively studied in the literature. It models set functions that exhibit a diminishing returns property, where the marginal value of adding an element to a set…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
We consider the problem of maximizing a non-negative submodular set function $f:2^N \rightarrow \mathbb{R}_+$ over a ground set $N$ subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack…
Suppose some objects are hidden in a finite set $S$ of hiding places which must be examined one-by-one. The cost of searching subsets of $S$ is given by a submodular function and the probability that all objects are contained in a subset is…
For the problem of maximizing a monotone, submodular function with respect to a cardinality constraint $k$ on a ground set of size $n$, we provide an algorithm that achieves the state-of-the-art in both its empirical performance and its…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…
In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
We investigate a more generalized form of submodular maximization, referred to as $k$-submodular maximization, with applications across social networks and machine learning domains. In this work, we propose the multilinear extension of…
We show that for the problem of minimizing (or maximizing) the ratio of two supermodular functions, no bounded approximation ratio can be achieved via polynomial number of queries, if the two supermodular functions are both monotone…
Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…
Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and…