arXiv research

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

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…

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…

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 sublinear sketches improve ANN and KDE for massive data streams.

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.

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

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

Study online learning in unknown Markov games with sublinear regret.

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…

New algorithm achieves sublinear regret in CMDPs without error cancellations.

Extends tracking guarantees for time-varying variational inequalities.

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.

LIBO optimizes repeated bandit tasks without prior knowledge or regret.

GP-UCB resolves sublinear regret for kernelized bandits.

New data structure identifies close match from multiple distributions.

Develops sublinear Morse theory in symmetric spaces.

Paper presents a faster classical algorithm for principal component regression.

The paper connects discrete choice models to multi-armed bandit algorithms with sublinear regret bounds.

An adversarial bandit problem with memory constraints is studied where only the statistics of a subset of arms can be stored. A hierarchical learning policy that requires only a sublinear order of memory space in terms of the number of arms is developed. Its sublinear regret orders with respect to the time horizon are …

New framework guides resource usage to achieve sublinear regret in adversarial settings.

Two-stage mechanism designs reduce regret in recommender systems with stochastic covariates.

The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is problematic as real-world problem sets continue to grow in categorical types, such as …

New algorithm improves game learning with randomised optimism.

The paper addresses pricing interest rate derivatives in markets with volatility uncertainty.

Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and state-space models still scales poorly; each MCMC transition takes linear time i…

Study on scheduling jobs with unknown types, achieving sublinear excess cost.

Paper proposes quantum methods for optimizing machine learning functions.

Greedy algorithm achieves sublinear regret for various distributions.

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strate…

Online learning algorithms are designed to learn even when their input is generated by an adversary. The widely-accepted formal definition of an online algorithm's ability to learn is the game-theoretic notion of regret. We argue that the standard definition of regret becomes inadequate if the adversary is allowed to a…

FPP preserves sublinear Morse boundaries in geodesic graphs.

The paper bounds eigenvalue multiplicities for hyperbolic surfaces using short geodesics.

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

Sublinear algorithms detect cliques in graphs with high probability.

For a large class of metric space X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdim X of X coincides with the covering dimension $\dim(ν_L X)$ of the Higson corona of X with respect to the sublinear coarse structure on X. Then we apply this fact to prove the equality AN-asdim(X …

We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally sho…