arXiv research

New algorithms achieve logarithmic regret in learning linear quadratic control systems.

Logarithmic-time schedules boost large-scale language model training efficiency.

Oracle-efficient algorithms reduce combinatorial semi-bandit regret to logarithmic time.

Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.

An efficient algorithm for Riemannian logarithm on Stiefel manifold family.

Paper proposes efficient cost functions for automated market makers in DeFi.

Characterizes the local diffeomorphism structure of the exponential in the set of skew-symmetric matrices.

Develops a new option pricing model under G-expectation framework.

We present a logarithmic-scale efficient convolutional neural network architecture for edge devices, named WaveletNet. Our model is based on the well-known depthwise convolution, and on two new layers, which we introduce in this work: a wavelet convolution and a depthwise fast wavelet transform. By breaking the symmetr…

A new method for efficiently computing derivatives of skew-symmetric matrix exponentials.

We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal…

Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core of which amounts to evaluating the logarithm of the marginal likelihood (LML) o…

The Dantzig selector has received popularity for many applications such as compressed sensing and sparse modeling, thanks to its computational efficiency as a linear programming problem and its nice sampling properties. Existing results show that it can recover sparse signals mimicking the accuracy of the ideal procedu…

Efficient algorithm for contextual bandits with first-order guarantees.

We study the decades-old problem of online portfolio management and propose the first algorithm with logarithmic regret that is not based on Cover's Universal Portfolio algorithm and admits much faster implementation. Specifically Universal Portfolio enjoys optimal regret $\mathcal{O}(N\ln T)$ for $N$ financial instrum…

We study the problem of regret minimization for distributed bandits learning, in which $M$ agents work collaboratively to minimize their total regret under the coordination of a central server. Our goal is to design communication protocols with near-optimal regret and little communication cost, which is measured by the…

Paper analyzes and improves KL-regularized RL for LLMs with logarithmic regret.

A new interpolation method speeds up neural ODE training.

New algorithm reduces online logistic regression regret without exponential constant.

In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…

New algorithm reduces switching costs in RL beyond linear MDPs.

Paper presents a new framework for covariance matrix estimation with geometric insights.

Greedy algorithm achieves sublinear regret for various distributions.

A new method for estimating probabilities and risks using Markov processes.

Quantum RL algorithm achieves logarithmic regret for exploration.

This paper focuses on projection-free methods for solving smooth Online Convex Optimization (OCO) problems. Existing projection-free methods either achieve suboptimal regret bounds or have high per-iteration computational costs. To fill this gap, two efficient projection-free online methods called ORGFW and MORGFW are …

Efficiently calibrates epidemiological models using Bayesian optimization.

Study rigidity by logarithmic capacity and related functions.

Dynamic pricing improves DeFi lending efficiency by reducing regret to logarithmic levels.

New algorithms achieve logarithmic regret in KL-regularized Markov games.

In this short communication we introduce the quick clustering algorithm (QUIST), an efficient hierarchical clustering algorithm based on sorting. QUIST is a poly-logarithmic divisive clustering algorithm that does not assume the number of clusters, and/or the cluster size to be known ahead of time. It is also insensiti…

Study real logarithms of semi-simple matrices, focusing on differential structure.

Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.

Logarithmic connections on principal bundles over normal varieties are studied.

We present a new method to solve certain $\bar{\partial}$-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a $\bar{\partial}$-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness…

Local logarithmic Brunn-Minkowski holds for zonoids.

Study of diffusion annealed Langevin dynamics for generative models.

Efficient algorithms for sparse parameter recovery in mixture models.

New framework for logarithmically divergent integrals on manifolds with corners.

Directly proves logarithmic systolic growth for all hyperbolic surfaces.

Logarithmic separation profile in hyperbolic groups shows hierarchical structure.

Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.

We propose a novel, efficient approach for distributed sparse learning in high-dimensions, where observations are randomly partitioned across machines. Computationally, at each round our method only requires the master machine to solve a shifted ell_1 regularized M-estimation problem, and other workers to compute the g…

This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however we show that, if we choose as cost function the logarithm of the determinant of t…

Investment and consumption strategy optimized under uncertain conditions.

The paper constructs a Saito basis for a specific class of divisors and applies it to logarithmic Poisson geometry.

Extended logarithm for solvable elements in mapping class groups.

Efficient algorithms identify true hypothesis from many options with minimal actions.