A wide range of AI problems, such as sensor placement, active learning, and network influence maximization, require sequentially selecting elements from a large set with the goal of optimizing the utility of the selected subset. Moreover, each element that is picked may provide stochastic feedback, which can be used to make smarter decisions about future selections. Finding efficient policies f...

In this paper, a non-monotone adaptive trust region method for the system of non-linear equations is proposed, in part, which is based on the technique in [9]. The local and global convergence properties of non-monotone adaptive trust region method are proved under favorable conditions. Some numerical experiments show that the method is effective.

In this paper, we present a new trust region method for unconstrained nonlinear programming in which we blend adaptive trust region algorithm by non-monotone strategy to propose a new non-monotone trust region algorithm with automatically adjusted radius. Both non-monotone strategy and adaptive technique can help us introduce a new algorithm that reduces the number of iterations and function ev...

The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objective function. More generally, adaptive seeding is a stochastic optimization framework where the c...

In this paper we run two important methods for solving some well-known problems and make a comparison on their performance and efficiency in solving nonlinear systems of equations‎. ‎One of these methods is a non-monotone adaptive trust region strategy and another one is a scaled trust region approach‎. ‎Each of methods showed fast convergence in special problems and slow convergence in other o...

We give a poly(logn, 1/ε)-query adaptive algorithm for testing whether an unknown Boolean function f : {−1, 1}n → {−1, 1}, which is promised to be a halfspace, is monotone versus ε-far from monotone. Since non-adaptive algorithms are known to require almost Ω(n) queries to test whether an unknown halfspace is monotone versus far from monotone, this shows that adaptivity enables an exponential i...

For positive integers n,d, the hypergrid [n]d is equipped with the coordinatewise product partial ordering denoted by ≺. A function f : [n]d → N is monotone if ∀x ≺ y, f (x)≤ f (y). A function f is ε-far from monotone if at least an ε fraction of values must be changed to make f monotone. Given a parameter ε , a monotonicity tester must distinguish with high probability a monotone function from...

1 Overview 1.1 Last time • Proper learning for P implies property testing of P (generic, but quite inefficient) • Testing linearity (over GF[2]), i.e. P = {all parities}: (optimal) O 1-query 1-sided non-adaptive tester. • Testing monotonicity (P = {all monotone functions}: an efficient O n-query 1-sided non-adaptive tester.

Suppose we are given a submodular function f over a set of elements, and we want to maximize its value subject to certain constraints. Good approximation algorithms are known for such problems under both monotone and non-monotone submodular functions. We consider these problems in a stochastic setting, where elements are not all active and we can only get value from active elements. Each elemen...

Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue via viral marketing. The massive instances occurring in modern-day applications can render existing algorithms prohibitively slow. Moreover, frequently those are also inherently stochastic. Focusing on these challenges, we revisit the classic ...