Related papers: Smoothed analysis of algorithms
The best known solutions for $k$-message broadcast in dynamic networks of size $n$ require $\Omega(nk)$ rounds. In this paper, we see if these bounds can be improved by smoothed analysis. We study perhaps the most natural randomized…
There is a significant gap between our theoretical understanding of optimization algorithms used in deep learning and their practical performance. Theoretical development usually focuses on proving convergence guarantees under a variety of…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…
Theoretical analyses of stochastic search algorithms, albeit few, have always existed since these algorithms became popular. Starting in the nineties a systematic approach to analyse the performance of stochastic search heuristics has been…
We perform a smoothed analysis of the termination phase of an interior-point method. By combining this analysis with the smoothed analysis of Renegar's interior-point algorithm by Dunagan, Spielman and Teng, we show that the smoothed…
We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…
We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…
Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…
We develop a framework that leverages the smoothed complexity analysis by Spielman and Teng to circumvent paradoxes and impossibility theorems in social choice, motivated by modern applications of social choice powered by AI and ML. For…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
For the prediction with experts' advice setting, we construct forecasting algorithms that suffer loss not much more than any expert in the pool. In contrast to the standard approach, we investigate the case of long-term forecasting of time…
Software analytics has been the subject of considerable recent attention but is yet to receive significant industry traction. One of the key reasons is that software practitioners are reluctant to trust predictions produced by the analytics…
The k-means method is one of the most widely used clustering algorithms, drawing its popularity from its speed in practice. Recently, however, it was shown to have exponential worst-case running time. In order to close the gap between…
The field of learning-augmented algorithms has gained significant attention in recent years. These algorithms, using potentially inaccurate predictions, must exhibit three key properties: consistency, robustness, and smoothness. In…
One of the primary goals of the mathematical analysis of algorithms is to provide guidance about which algorithm is the "best" for solving a given computational problem. Worst-case analysis summarizes the performance profile of an algorithm…