Related papers: Adaptivity Gaps for Stochastic Probing: Submodular…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
We investigate a graph probing problem in which an agent has only an incomplete view $G' \subsetneq G$ of the network and wishes to explore the network with least effort. In each step, the agent selects a node $u$ in $G'$ to probe. After…
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…
We investigate the approximability of several classes of real-valued functions by functions of a small number of variables ({\em juntas}). Our main results are tight bounds on the number of variables required to approximate a function…
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…
Budget feasible mechanism considers algorithmic mechanism design questions where there is a budget constraint on the total payment of the mechanism. An important question in the field is that under which valuation domains there exist budget…
In partial function extension, we are given a partial function consisting of $n$ points from a domain and a function value at each point. Our objective is to determine if this partial function can be extended to a function defined on the…
Stochastic Boolean Function Evaluation is the problem of determining the value of a given Boolean function f on an unknown input x, when each bit of x_i of x can only be determined by paying an associated cost c_i. The assumption is that x…
We propose a new concept named adaptive submodularity ratio to study the greedy policy for sequential decision making. While the greedy policy is known to perform well for a wide variety of adaptive stochastic optimization problems in…
We consider the problem of sequentially maximizing an unknown function $f$ over a set of actions of the form $(s,\mathbf{x})$, where the selected actions must satisfy a safety constraint with respect to an unknown safety function $g$. We…
In stochastic combinatorial optimization, algorithms differ in their adaptivity: whether or not they query realized randomness and adapt to it. Dean et al. (FOCS '04) formalize the adaptivity gap, which compares the performance of fully…
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…
We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…
We consider the Stochastic Boolean Function Evaluation (SBFE) problem in the well-studied case of $k$-of-$n$ functions: There are independent Boolean random variables $x_1,\dots,x_n$ where each variable $i$ has a known probability $p_i$ of…
The goal of a sequential decision making problem is to design an interactive policy that adaptively selects a group of items, each selection is based on the feedback from the past, in order to maximize the expected utility of selected…
Running machine learning algorithms on large and rapidly growing volumes of data is often computationally expensive, one common trick to reduce the size of a data set, and thus reduce the computational cost of machine learning algorithms,…
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…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
We consider the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where the objective $f$ is not accessed as a value oracle but instead subject to noisy queries. We introduce a versatile adaptive sampling…
In this paper, we propose and study the cascade submodular maximization problem under the adaptive setting. The input of our problem is a set of items, each item is in a particular state (i.e., the marginal contribution of an item) which is…