Related papers: Algorithms and Complexity for Functions on General…
In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving…
We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
There is currently a rapid increase in the number of challenge problem, benchmarking datasets and algorithmic optimization tests for evaluating AI systems. However, there does not currently exist an objective measure to determine the…
We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…
In this work, we study online submodular maximization, and how the requirement of maintaining a stable solution impacts the approximation. In particular, we seek bounds on the best-possible approximation ratio that is attainable when the…
We establish sharp non-asymptotic probabilistic bounds for the star discrepancy of double-infinite random matrices -- a canonical model for sequences of random point sets in high dimensions. By integrating the recently proved…
Many systems of interest in cryptography consist of equations of the same degree. Under the assumption that the degree of regularity is finite, we prove upper bounds on the degree of regularity of a system of equations of the same degree,…
Iteration complexities for optimizing smooth functions with first-order algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are then achieved using fixed step sizes. But many…
We study the notion of a generalization bound being uniformly tight, meaning that the difference between the bound and the population loss is small for all learning algorithms and all population distributions. Numerous generalization bounds…
Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain…
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
We consider shape optimization problems for general integral functionals of the calculus of variations, defined on a domain $\Omega$ that varies over all subdomains of a given bounded domain $D$ of ${\bf R}^d$. We show in a rather…
We prove that every online learnable class of functions of Littlestone dimension $d$ admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the…
Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
The domain of an optimization problem is seen as one of its most important characteristics. In particular, the distinction between continuous and discrete optimization is rather impactful. Based on this, the optimizing algorithm, analyzing…
We focus on the optimal value for various information-theoretical tasks. There are several studies for the asymptotic expansion for these optimal values up to the order $\sqrt{n}$ or $\log n$. However, these expansions have errors of the…