Related papers: R\'enyi-infinity constrained sampling with $d^3$ m…
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
We introduce a suite of new particle-based algorithms for sampling in constrained domains which are entirely learning rate free. Our approach leverages coin betting ideas from convex optimisation, and the viewpoint of constrained sampling…
A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We give algorithms for sampling several structured logconcave families to high accuracy. We further develop a reduction framework, inspired by proximal point methods in convex optimization, which bootstraps samplers for regularized…
The conventional channel resolvability problem refers to the determination of the minimum rate required for an input process so that the output distribution approximates a target distribution in either the total variation distance or the…
We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…
Multi-distribution learning (MDL), which seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions, has emerged as a unified framework in response to the evolving demand for robustness,…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to…
The divergence in the interaction term of the Calogero model can be prevented introducing a cutoff length parameter, this modification leads to a quasi-exactly solvable model whose eigenfunctions can be written in terms of Heun's…
This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in Durmus et al. (Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau, 2016)…
We analyze the convergence rate of the randomized Newton-like method introduced by Qu et. al. (2016) for smooth and convex objectives, which uses random coordinate blocks of a Hessian-over-approximation matrix $\bM$ instead of the true…
We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…
We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
Sharpness (of the loss minima) is a common measure to investigate the generalization of neural networks. Intuitively speaking, the flatter the landscape near the minima is, the better generalization might be. Unfortunately, the correlation…
Motivated by practical applications where stable long-term performance is critical-such as robotics, operations research, and healthcare-we study the problem of distributionally robust (DR) average-reward reinforcement learning. We propose…
We establish sharp exponential deviation estimates of the information content as well as a sharp bound on the varentropy for the class of convex measures on Euclidean spaces. This generalizes a similar development for log-concave measures…