Related papers: Tight Dynamic Problem Lower Bounds from Generalize…

Algorithm-dependent generalization error bounds are central to statistical learning theory. A learning algorithm may use a large hypothesis space, but the limited number of iterations controls its model capacity and generalization error.…

We pose the fine-grained hardness hypothesis that the textbook algorithm for the NFA Acceptance problem is optimal up to subpolynomial factors, even for dense NFAs and fixed alphabets. We show that this barrier appears in many variations…

Many real-world decision problems require solving, again and again, combinatorial optimization instances drawn from a common distribution. A recent line of structured learning methods exploits this regularity by learning policies that pair…

Minimizing the sum of a convex function and a composite function appears in various fields. The generalized Levenberg--Marquardt (LM) method, also known as the prox-linear method, has been developed for such optimization problems. The…

Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the…

Grammar compression is a general compression framework in which a string $T$ of length $N$ is represented as a context-free grammar of size $n$ whose language contains only $T$. In this paper, we focus on studying the limitations of…

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

Maximum bipartite matching (MBM) is a fundamental problem in combinatorial optimization with a long and rich history. A classic result of Hopcroft and Karp (1973) provides an $O(m \sqrt{n})$-time algorithm for the problem, where $n$ and $m$…

Previous approaches to systematic state-space exploration for testing multi-threaded programs have proposed context-bounding and depth-bounding to be effective ranking algorithms for testing multithreaded programs. This paper proposes two…

We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is…

We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of stable set polytope. We apply it to majority functions and…

This article derives lower bounds on the convergence rate of continuous-time gradient-based optimization algorithms. The algorithms are subjected to a time-normalization constraint that avoids a reparametrization of time in order to make…

Given query access to an undirected graph $G$, we consider the problem of computing a $(1\pm\epsilon)$-approximation of the number of $k$-cliques in $G$. The standard query model for general graphs allows for degree queries, neighbor…

A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…

In fully dynamic clustering problems, a clustering of a given data set in a metric space must be maintained while it is modified through insertions and deletions of individual points. In this paper, we resolve the complexity of fully…

Safety is a fundamental challenge in reinforcement learning (RL), particularly in real-world applications such as autonomous driving, robotics, and healthcare. To address this, Constrained Markov Decision Processes (CMDPs) are commonly used…

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…

In this article, we propose a novel and general dimension-hopping MCMC methodology that can update all the parameters as well as the number of parameters simultaneously using simple deterministic transformations of some low-dimensional…

We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and…

The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…