Related papers: Approximation Algorithms for Min-max-min Robust Op…
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…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…
In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
Consider the following problem: given a set system (U,I) and an edge-weighted graph G = (U, E) on the same universe U, find the set A in I such that the Steiner tree cost with terminals A is as large as possible: "which set in I is the most…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…
In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This…
Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which…
In two-stage robust optimization the solution to a problem is built in two stages: In the first stage a partial, not necessarily feasible, solution is exhibited. Then the adversary chooses the "worst" scenario from a predefined set of…
In this paper, we provide a generic anytime lower bounding procedure for minmax regret optimization problems. We show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by Chassein and Goerigk…
Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing…
Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of…
We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the…
In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
In this paper, we consider the unconstrained submodular maximization problem. We propose the first algorithm for this problem that achieves a tight $(1/2-\varepsilon)$-approximation guarantee using $\tilde{O}(\varepsilon^{-1})$ adaptive…
For many optimization problems in machine learning, finding an optimal solution is computationally intractable and we seek algorithms that perform well in practice. Since computational intractability often results from pathological…