Related papers: The Niceness of Unique Sink Orientations
For sink-free orientations in graphs of minimum degree at least $3$, we show that there is a deterministic approximate counting algorithm that runs in time $O((n^{73}/\varepsilon^{72})\log(n/\varepsilon))$, a near-linear time sampling…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
We develop algorithms for the optimization of convex objectives that have H\"older continuous $q$-th derivatives by using a $q$-th order oracle, for any $q \geq 1$. Our algorithms work for general norms under mild conditions, including the…
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices $\text{SO}(n)$. Such problems are nonconvex due to the constraint $X \in \text{SO}(n)$. Nonetheless, we show…
We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact}…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
Online strategic classification studies settings in which agents strategically modify their features to obtain favorable predictions. For example, given a classifier that determines loan approval based on credit scores, applicants may open…
Randomized smoothing, a method to certify a classifier's decision on an input is invariant under adversarial noise, offers attractive advantages over other certification methods. It operates in a black-box and so certification is not…
Link-analysis algorithms, such as PageRank, are instrumental in understanding the structural dynamics of networks by evaluating the importance of individual vertices based on their connectivity. Recently, with the rising importance of…
A commonly used heuristic in non-convex optimization is Normalized Gradient Descent (NGD) - a variant of gradient descent in which only the direction of the gradient is taken into account and its magnitude ignored. We analyze this heuristic…
In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…
Optimal experimental design (OED) concerns itself with identifying ideal methods of data collection, e.g.~via sensor placement. The \emph{greedy algorithm}, that is, placing one sensor at a time, in an iteratively optimal manner, stands as…
Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…
Two widely used randomized algorithms are the sketch-and-solve method for least-squares regression and the randomized SVD for low-rank approximation. These algorithms apply a random embedding to compress a target matrix, and they perform…
This paper studies the one-shot behavior of no-regret algorithms for stochastic bandits. Although many algorithms are known to be asymptotically optimal with respect to the expected regret, over a single run, their pseudo-regret seems to…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…
We study the performance of stochastic gradient descent (SGD) on smooth and strongly-convex finite-sum optimization problems. In contrast to the majority of existing theoretical works, which assume that individual functions are sampled with…
We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…