Related papers: Submodular Maximization under the Intersection of …
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…
The problem of monotone submodular maximization has been studied extensively due to its wide range of applications. However, there are cases where one can only access the objective function in a distorted or noisy form because of the…
We consider the problem of maximizing a monotone submodular function under a knapsack constraint. We show that, for any fixed $\epsilon > 0$, there exists a polynomial-time algorithm with an approximation ratio $1-c/e-\epsilon$, where $c…
Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. Streaming algorithms for submodule maximization have gained attention in recent years, allowing for…
We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms…
Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
We study the problem of maximizing a non-negative monotone $k$-submodular function $f$ under a knapsack constraint, where a $k$-submodular function is a natural generalization of a submodular function to $k$ dimensions. We present a…
Multi-armed bandit problems are the predominant theoretical model of exploration-exploitation tradeoffs in learning, and they have countless applications ranging from medical trials, to communication networks, to Web search and advertising.…
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…
We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…
The adversarial Bandit with Knapsack problem is a multi-armed bandits problem with budget constraints and adversarial rewards and costs. In each round, a learner selects an action to take and observes the reward and cost of the selected…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
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…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…
Submodular maximization has been widely used in many multi-robot task planning problems including information gathering, exploration, and target tracking. However, the interplay between submodular maximization and communication is rarely…
Finding the $r\times r$ submatrix of maximum volume of a matrix $A\in\mathbb R^{n\times n}$ is an NP hard problem that arises in a variety of applications. We propose a new greedy algorithm of cost $\mathcal O(n)$, for the case $A$…
The Submodular Welfare Maximization problem (SWM) captures an important subclass of combinatorial auctions and has been studied extensively from both computational and economic perspectives. In particular, it has been studied in a natural…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…