arXiv research

This work analyzes Gibbs samplers for Bayesian hierarchical models without dimensionality constraints.

Algorithm achieves optimal pricing with minimal exploration for dynamic markets.

New algorithm reduces complexity in multi-agent reinforcement learning.

New algorithms achieve decision calibration without sample complexity dependent on feature dimension.

New method proves dimension-free convergence for ULD in KL divergence.

New method bounds high-dimensional regression without estimating design covariance.

Unified bounds for iterative algorithms with Gaussian data matrices.

New rates for GLD and SGLD in infinite-dimensional spaces without dimensionality issues.

We study Smoothed Online Convex Optimization, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a $Ω(\sqrt{d})$ lower bound on the competitive ratio of any online algorithm, where $d$ is the dimension of the action space, we ask under what conditio…

Logistic regression gets a new, simpler uniform bound.

Paper improves Frank-Wolfe algorithm's efficiency bounds.

On a closed weighted Riemannian manifold with nonnegative Bakry-Émery Ricci curvature, it is shown that the ratio of the $k$-th to first eigenvalues of the weighted Laplacian is dominated by $641k^2$, using an argument via the Cheeger constant. While improving the previous exponential upper bound, the order of $k$ here…

New bounds for high-dimensional sparse linear bandits, balancing information and regret.

By using an explicit Bellman function, we prove a bilinear embedding theorem for the Laplacian associated with a weighted Riemannian manifold $(M,μ_φ)$ having the Bakry-Emery curvature bounded from below. The embedding, acting on the cartesian product of $L^p(M,μ_φ)$ and $L^q(T^*M,μ_φ)$, $1/p+1/q=1$, involves estimates…

We show how to take any two parameter-free online learning algorithms with different regret guarantees and obtain a single algorithm whose regret is the minimum of the two base algorithms. Our method is embarrassingly simple: just add the iterates. This trick can generate efficient algorithms that adapt to many norms s…

Paper develops probabilistic bounds for a stochastic gradient algorithm in non-convex problems.

This paper analyzes neural network classifiers' performance in binary classification.

In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for non-convex optimization problems. All proposed algorithms can escape from saddle poi…

In this paper, the author discusses the elliptic type gradient estimate for the solution of the time-dependent Schrödinger equations on noncompact manifolds. As its application, the dimension-free Harnack inequality and the Liouville type theorem for the Schrödinger equation are proved.

This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous $p$ decisions. This setting generalizes Smoothed Online Convex Optimization. The…

We study the regret minimization problem in the novel setting of generalized kernelized bandits (GKBs), where we optimize an unknown function $f^*$ belonging to a reproducing kernel Hilbert space (RKHS) having access to samples generated by an exponential family (EF) reward model whose mean is a non-linear function $μ(…

The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task. Predictive sparse coding algorithms recently have demonstrated impressive perform…

Unified framework for convergence of discrete diffusion models without state space size dependence.

Sharp inequality in spaces with non-negative Ricci curvature.

Graphs with nonnegative Bakry-Émery curvature have volume doubling and Poincaré inequalities.

Optimal sampling bounds for various classification losses under different regularization terms.

HAR regression improves performance on small datasets.

We investigate the fundamental principles that drive the development of scalable algorithms for network optimization. Despite the significant amount of work on parallel and decentralized algorithms in the optimization community, the methods that have been proposed typically rely on strict separability assumptions for o…

The paper derives Harnack inequalities for evolving Riemannian manifolds without dimensionality restrictions.

New private mean estimation method works well for anisotropic data.

New error bound for diffusion models without dimensionality constraints.

New sampling and diffusion models methods introduced without density function assumptions.

The paper provides generalization bounds for metric learning using neural network embeddings.

The study assesses ML model robustness under worst-case subpopulations.

We develop time-uniform confidence spheres for estimating means of random vectors.

We improve bounds for stochastic processes, especially those with heavy tails.

Low-precision streaming PCA estimates the leading eigenvector with limited precision.

In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation $\partial_t u=Lu$ associated with the time dependent Witten Laplacian on complete Riemannian manifolds equipped with a variant of the $(K, m)$-super Perelman Ricci flows and the $K$-super…

The goal of the paper is to sharpen and generalise bounds involving the Cheeger's isoperimetric constant $h$ and the first eigenvalue $λ_{1}$ of the Laplacian. A celebrated lower bound of $λ_{1}$ in terms of $h$, $λ_{1}\geq h^{2}/4$, was proved by Cheeger in 1970 for smooth Riemannian manifolds. An upper bound on $λ_{1…

New algorithm estimates transport maps with nearly optimal error.

In contextual continuum-armed bandits, the contexts $x$ and the arms $y$ are both continuous and drawn from high-dimensional spaces. The payoff function to learn $f(x,y)$ does not have a particular parametric form. The literature has shown that for Lipschitz-continuous functions, the optimal regret is $\tilde{O}(T^{\fr…

We consider minimizing a nonconvex, smooth function $f$ on a Riemannian manifold $\mathcal{M}$. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle points on the manifold). The rate of convergence depends as $1/ε^2$ o…

Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and high-dimensional models. A standard approach to mitigate this complexity consists i…

The paper introduces a new method for tail bounds of random vectors and matrices.

New algorithm reduces dimensionality in stochastic optimization.

MT-HAL learns features and task associations for multiple tasks with a shared sparse structure.

The paper uses deep neural networks to estimate and infer ATE without needing to know the dimension of the data.

Improved diffusion models for generative tasks without dimensionality constraints.