arXiv research

We prove optimal subspace embedding conjecture up to sub-polylogarithmic factors.

New study reveals a polynomial penalty for adapting to unknown margin parameters in batched nonparametric bandits.

Mirzakhani volumes of moduli spaces are polylogarithmic.

Study shows sample complexity for multicalibration is Θ(ε^-3) with polylogarithmic factors.

New algorithm selects best distribution privately in nearly-linear time.

Study higher genus polylogarithms under Riemann surface degenerations.

Investigates webs related to cluster algebras and polylogarithms.

Paper solves no-swap regret minimization for combinatorial bandits with polylogarithmic dependence on N.

Improved bounds for estimating discrete distributions in KL divergence.

Efficiently estimates binary product distributions with privacy.

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for con…

Improved guarantees for misspecified kernelized bandit optimization.

Neural networks can achieve optimal sample complexity for learning single-index models.

A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we close the problem of computationally and sample effi…

New algorithms optimize without tuning, matching tuned SGD performance.

New DP optimization methods for sparse gradients, improving on existing algorithms.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the ba…

New algorithm reduces regret in online portfolio and quantum state learning.

The paper solves robust learning of Gaussian mixtures with nearly optimal guarantees.

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.

New bounds show current methods overestimate system parameter errors.

Sharp large deviations and Gibbs conditioning for portfolio credit risk models.

In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $γ\in(0,1)$ we provide an algorithm that computes an $ε$-optimal strategy with high-probability given $\tilde{O}((1 - γ)^{-3}…

Paper analyzes online tensorial ICA convergence with stochastic approximation.

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a given input matrix $A \in \mathbb{R}^{n \times d}$, $T(A)$ is the time needed to com…

QATS efficiently decodes HMMs with polylogarithmic complexity.

New method proves fast regret bounds for online RLHF with generalized preferences.

Algorithm optimizes collaborative learning among distributed clients using kernel-based bandits.

Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf \mathbf{M}}$, and a constant $-1 \leq p \leq 1$, our algorithm gives efficient access to a…

Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have dimension-independent bounds for the underlying $\mathit{continuous}$ processes under s…

In this paper, we give improved bounds for the computational complexity of computing with planar algebraic curves. More specifically, for arbitrary coprime polynomials $f$, $g \in \mathbb{Z}[x,y]$ and an arbitrary polynomial $h \in \mathbb{Z}[x,y]$, each of total degree less than $n$ and with integer coefficients of ab…

A new method for efficient Gaussian process inference using sparse approximations.

In this paper, we study local solutions F=(F1,..,Fn) of a general functional equation of the form F1(U1(x,y))+....+Fn(Un(x,y))=0. A such equation will be called an ``abelian functional equation'' (Afe). We will restrict ourselves to the case when the inner functions Ui's are real rational functions. First we prove that…

Paper solves robust convex problems with heavy-tailed noise.

Recent theoretical work has guaranteed that overparameterized networks trained by gradient descent achieve arbitrarily low training error, and sometimes even low test error. The required width, however, is always polynomial in at least one of the sample size $n$, the (inverse) target error $1/ε$, and the (inverse) fail…

We introduce the bilinear bandit problem with low-rank structure in which an action takes the form of a pair of arms from two different entity types, and the reward is a bilinear function of the known feature vectors of the arms. The unknown in the problem is a $d_1$ by $d_2$ matrix $\mathbfΘ^*$ that defines the reward…

Quantum computing offers a quadratic speedup for estimating non-linear functionals.

A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target error $ε^{-1}$, deep neural networks learned by (stochastic) gradient descent enjoy …

Private density estimation in Wasserstein distance for geographic populations.

New algorithm speeds up polynomial kernel approximations.

A new method clusters intersecting lines using hypergraphs.

New calibration measure SSCE ensures truthful prediction, unlike existing measures.

Improved GNN simulation of WL test with exponentially lower complexity.

The paper analyzes the convergence rates of Q-learning with entropy regularization and linear function approximation.

Kähler information manifolds for signal filters in weighted Hardy spaces are explored.

New algorithms minimize regret in both adversarial and stochastic contexts.

Gradient descent learns a neuron in noisy data.

AdaSDBO solves decentralized bilevel optimization without problem parameters, achieving competitive performance.