Related papers: Adaptive approximation of monotone functions

The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…

Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational…

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…

We address the problem of minimizing a smooth function $f^0(x)$ over a compact set $D$ defined by smooth functional constraints $f^i(x)\leq 0,~ i = 1,\ldots, m$ given noisy value measurements of $f^i(x)$. This problem arises in…

We consider minimizing the sum of three convex functions, where the first one F is smooth, the second one is nonsmooth and proximable and the third one is the composition of a nonsmooth proximable function with a linear operator L. This…

We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…

Motivated by the fact that in several cases a matching in a graph is stable if and only if it is produced by a greedy algorithm, we study the problem of computing a maximum weight greedy matching on weighted graphs, termed GreedyMatching.…

An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…

Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…

In this paper, we propose a new framework for designing fast parallel algorithms for fundamental statistical subset selection tasks that include feature selection and experimental design. Such tasks are known to be weakly submodular and are…

In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular…

We deal with monotonic regression of multivariate functions $f: Q \to \mathbb{R}$ on a compact rectangular domain $Q$ in $\mathbb{R}^d$, where monotonicity is understood in a generalized sense: as isotonicity in some coordinate directions…

We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent LP rounding algorithms and a hybrid algorithm…

We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle…

We consider the semi-infinite optimization problem: $f^*:=\min_{x\in X}\:\{f(x): g(x,y)\,\leq \,0,\:\forally\in Y_x\}$, where $f,g$ are polynomials and $X\subset R^n$ as well as $Y_\x\subset R^p$, $x\in X$, are compact basic semi-algebraic…

Greedy Sampling Methods (GSMs) are widely used to construct approximate solutions of Configuration Optimization Problems (COPs), where a loss functional is minimized over finite configurations of points in a compact domain. While effective…

Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These…

We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…

Approximating the roots of a holomorphic function in an input box is a fundamental problem in many domains. Most algorithms in the literature for solving this problem are conditional, i.e., they make some simplifying assumptions, such as,…