arXiv research

The paper shows how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.

New algorithm achieves sublinear regret in CMDPs without error cancellations.

New sublinear sketches improve ANN and KDE for massive data streams.

ERM with square loss achieves sublinear error for learnable function classes with smoothed data.

Two new algorithms reduce online kernel regression's computational cost while maintaining optimal regret bounds.

New algorithm reduces regret in noisy context bandits.

We study the problem of estimating the expected reward of the optimal policy in the stochastic disjoint linear bandit setting. We prove that for certain settings it is possible to obtain an accurate estimate of the optimal policy value even with a number of samples that is sublinear in the number that would be required…

Simplifies and optimizes learning from untrusted batches with structure.

New approach reduces simulator exploitation by improving strategic robustness.

In distributed statistical learning, $N$ samples are split across $m$ machines and a learner wishes to use minimal communication to learn as well as if the examples were on a single machine. This model has received substantial interest in machine learning due to its scalability and potential for parallel speedup. Howev…

New algorithm reduces prediction error in online learning without knowing base measure.

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric space. For example, the sublinear Higson corona of n-dimensional E…

Study finds exact limits for sparse regression with fewer observations than usual.

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too small to reliably learn any accurate model. Our first result applies to the settin…

New model for Knightian uncertainty with jumps.

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…

Study shows how much information can be learned from sparse signals with limited data.

New algorithm reduces neural net error in contextual bandits.

The paper uncovers the mathematical structure enabling value decomposition in multi-agent systems.

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…

New convergence rates found for PnP methods using MMSE denoisers.

New method reduces linear regret in high-dimensional bandit problems.

Method completes mixed matrix from complex surveys with heterogeneous missingness.

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …

The paper develops methods for time-varying constrained online convex optimization.

For $α\in (1,2)$, we present a generalized central limit theorem for $α$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, p…

New algorithms for constrained online optimization with memory and predictions.

We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in obtaining the next one, and b) recursive decoding, where the signal estimate from…

New algorithm reduces control error in systems with changing dynamics.

Memory-limited learning tackles adversarial bandits with reduced storage.

Sharp Liouville theorem for minimal graphs on manifolds with nonnegative Ricci curvature.

New method connects CAT(0) spaces to hyperbolic spaces.

We establish $L^{\infty}$ and $L^2$ error bounds for functions of many variables that are approximated by linear combinations of ReLU (rectified linear unit) and squared ReLU ridge functions with $\ell^1$ and $\ell^0$ controls on their inner and outer parameters. With the squared ReLU ridge function, we show th…

Study online learning in unknown Markov games with sublinear regret.

A new algorithm reduces memory usage for long token attention in streaming applications.

We consider stochastic gradient descent and its averaging variant for binary classification problems in a reproducing kernel Hilbert space. In the traditional analysis using a consistency property of loss functions, it is known that the expected classification error converges more slowly than the expected risk even whe…

Open problem seeks an online learning algorithm for binary classification.

Efficiently trains large GMMs with millions to billions of parameters.

Average signature of 2-bridge knots approximates sqrt(2c/π).

Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function cha…

We investigate the problems of identity and closeness testing over a discrete population from random samples. Our goal is to develop efficient testers while guaranteeing Differential Privacy to the individuals of the population. We describe an approach that yields sample-efficient differentially private testers for the…

Extends tracking guarantees for time-varying variational inequalities.

New bounds for adaptive control in high dimensions without fixed state space.

Geodesic loops escape from balls at a sublinear rate imply virtually abelian fundamental group.

Develops geometric foundations for sublinear Morse boundaries in mapping class groups and Teichmüller spaces.

LaPSRL achieves optimal regret for isoperimetric RL distributions.

New approach for distributed online optimization of non-convex losses with sublinear regret.