Related papers: Replicable Learning of Large-Margin Halfspaces
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
Most reinforcement learning algorithms take advantage of an experience replay buffer to repeatedly train on samples the agent has observed in the past. Not all samples carry the same amount of significance and simply assigning equal…
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…
This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation…
We analyze rates of uniform convergence for a class of high-order semi-Lagrangian schemes for first-order, time-dependent partial differential equations on embedded submanifolds of $\mathbb{R}^d$ (including advection equations on surfaces)…
We study the problem of similarity learning and its application to image retrieval with large-scale data. The similarity between pairs of images can be measured by the distances between their high dimensional representations, and the…
We study the task of testable learning of general -- not necessarily homogeneous -- halfspaces with adversarial label noise with respect to the Gaussian distribution. In the testable learning framework, the goal is to develop a…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algorithms, where $n$ is the size of the…
We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample…
Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…
We design a new distribution over $\poly(r \eps^{-1}) \times n$ matrices $S$ so that for any fixed $n \times d$ matrix $A$ of rank $r$, with probability at least 9/10, $\norm{SAx}_2 = (1 \pm \eps)\norm{Ax}_2$ simultaneously for all $x \in…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
Inspired by recent work on learning with distribution shift, we give a general outlier removal algorithm called iterative polynomial filtering and show a number of striking applications for supervised learning with contamination: (1) We…
We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…
We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus…
We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…