Related papers: Algorithmic Discrepancy Minimization
Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative…
Motivated by learning of correlated equilibria in non-cooperative games, we perform a large deviations analysis of a regret minimizing stochastic approximation algorithm. The regret minimization algorithm we consider comprises multiple…
We introduce a new algorithmic framework for discrepancy minimization based on regularization. We demonstrate how varying the regularizer allows us to re-interpret several breakthrough works in algorithmic discrepancy, ranging from…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
The binary perceptron problem asks us to find a sign vector in the intersection of independently chosen random halfspaces with intercept $-\kappa$. We analyze the performance of the canonical discrepancy minimization algorithms of…
We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of…
With the widespread deployment of large-scale prediction systems in high-stakes domains, e.g., face recognition, criminal justice, etc., disparity in prediction accuracy between different demographic subgroups has called for fundamental…
We study discrepancy minimization for vectors in $\mathbb{R}^n$ under various settings. The main result is the analysis of a new simple random process in multiple dimensions through a comparison argument. As corollaries, we obtain bounds…
A multitude of classifiers can be trained on the same data to achieve similar performances during test time, while having learned significantly different classification patterns. This phenomenon, which we call prediction discrepancies, is…
Consider an infinite sequence of independent, uniformly chosen points from $[0,1]^d$. After looking at each point in the sequence, an overseer is allowed to either keep it or reject it, and this choice may depend on the locations of all…
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…
Though machine learning algorithms excel at minimizing the average loss over a population, this might lead to large discrepancies between the losses across groups within the population. To capture this inequality, we introduce and study a…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…
We study the online discrepancy minimization problem for vectors in $\mathbb{R}^d$ in the oblivious setting where an adversary is allowed fix the vectors $x_1, x_2, \ldots, x_n$ in arbitrary order ahead of time. We give an algorithm that…
We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of…
Recently, a Distribution Separation Method (DSM) is proposed for relevant feedback in information retrieval, which aims to approximate the true relevance distribution by separating a seed irrelevance distribution from the mixture one. While…
Recent advancements in machine learning and deep learning have brought algorithmic fairness into sharp focus, illuminating concerns over discriminatory decision making that negatively impacts certain individuals or groups. These concerns…
We formulate a comparison of minimal log discrepancies of a variety and its ambient space with appropriate boundaries in terms of motivic integration. It was obtained also by Ein and Musta\c{t}\v{a} independently.
For many computational problems involving randomness, intricate geometric features of the solution space have been used to rigorously rule out powerful classes of algorithms. This is often accomplished through the lens of the multi Overlap…