arXiv research

New algorithms reduce communication for sparse mean estimation in noisy distributed systems.

Study exact community recovery in noisy SBM with limited queries.

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…

Federated learning for combinatorial multi-agent bandits reduces regret and speeds up with fewer communications.

We consider the non-stochastic version of the (cooperative) multi-player multi-armed bandit problem. The model assumes no communication at all between the players, and furthermore when two (or more) players select the same action this results in a maximal loss. We prove the first $\sqrt{T}$-type regret guarantee for th…

The pair-matching problem appears in many applications where one wants to discover good matches between pairs of entities or individuals. Formally, the set of individuals is represented by the nodes of a graph where the edges, unobserved at first, represent the good matches. The algorithm queries pairs of nodes and obs…

We consider a variant of the stochastic multi-armed bandit problem, where multiple players simultaneously choose from the same set of arms and may collide, receiving no reward. This setting has been motivated by problems arising in cognitive radio networks, and is especially challenging under the realistic assumption t…

Paper tackles federated learning with personalised bandit algorithms.

A new federated algorithm reduces regret in X-armed bandit problems.

New algorithms tackle adversarial multi-player bandits with forced-collision communication.

We study a multiplayer stochastic multi-armed bandit problem in which players cannot communicate, and if two or more players pull the same arm, a collision occurs and the involved players receive zero reward. We consider the challenging heterogeneous setting, in which different arms may have different means for differe…

In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node up…

Paper addresses robust federated linear bandits against Byzantine attacks.

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

Improved algorithm reduces communication rounds for distributed online learning.

Algorithm minimizes regret and converges to equilibria in Markov games.

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

Semi-decentralized federated learning combines device-to-server and device-to-device communications for faster convergence.

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…

Algorithm reduces regret in distributed kernel bandits with shared randomness.

Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of vertices. The main focus of the paper is on weak recovery of the community based on the …

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to…

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.

We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank structure of its updates to ac…

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.

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.