arXiv research

Logarithmic regret for continuous-time reinforcement learning.

Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.

Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.

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

Near-logarithmic regret per switch achieved for mixable/exp-concave losses.

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time versi…

The paper studies a 1D diffusion equation with nonlinear Robin boundary conditions and finds conditions for global and finite time blow-up or blow-down.

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…

We derive a logarithmic Sobolev inequality along the Ricci flow without any restriction on time, which depends only on the initial metric via rudimentary geometric data, assuming only that a certain first eigenvalue is positive. As a consequence we obtain a uniform Sobolev inequality along the Ricci flow without any re…

Study Higgs bundles on curves with punctures, extending spectral correspondence.

New loss function helps learn unstable dynamical systems.

New bounds for Bayesian bandits show prior improves performance.

Study heat flow on changing surfaces, proving existence and uniqueness.

This paper gives quantitative global estimates between a time dependent flow on a Riemannian manifold $\left( M\right)$ and the flow of a vector field constructed by truncating the formal Magnus expansion for the logarithm of the flow. As a corollary, we also find quantitative estimates between the composition of the …

Local logarithmic export distributions show non-zero skewness that changes with exporter and destination characteristics.

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

Applying logarithmic transformations along 2-tori, we construct a generalized complex structure J_n with n type changing luci for every $n\geq 0$ on genus 1-Lefschetz fibrations with a cusp neighborhood, which include elliptic surfaces with non-zero euler characteristic. Applying a technique of broken Lefschetz fibrati…

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…

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

Study robust utility maximization with uncertain continuous semimartingales.

We create a new online reduction of multiclass classification to binary classification for which training and prediction time scale logarithmically with the number of classes. Compared to previous approaches, we obtain substantially better statistical performance for two reasons: First, we prove a tighter and more comp…

Derives gradient estimate for a specific nonlinear parabolic equation on Finsler manifolds.

A decentralized policy achieves logarithmic regret for multi-agent MAB problems with communication constraints.

Honest traders can outperform insiders in a Black-Scholes market with positive probability.

This paper tightens the law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.

I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of…

For some class of geometric flows, we obtain the (logarithmic) Sobolev inequalities and their equivalence up to different factors directly and also obtain the long time non-collapsing and non-inflated properties, which generalize the results in the case of Ricci flow or List-Ricci flow or harmonic-Ricci flow. As applic…

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…

Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.

Logarithmic regret strategies for safe multi-armed bandits with safety risk constraints.

Rapid mixing of Langevin dynamics on Riemannian manifolds

Improved SVRG for quadratic functions achieves better performance and running times.

We study contextual bandits with budget and time constraints, referred to as constrained contextual bandits.The time and budget constraints significantly complicate the exploration and exploitation tradeoff because they introduce complex coupling among contexts over time.Such coupling effects make it difficult to obtai…

We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the case of the Gaussian logarithmic returns model by Harrison and Kreps, but we prove …

Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.

Researchers prove rigidity for log-Sobolev inequality on specific metric spaces.

Uniform heat kernel and diffusion bridge asymptotics for sub-Riemannian geometry.

E-LDA offers faster, interpretable LDA topic models.

Gradient flows for knot energies ensure long-term existence of knotted loops.

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 proposes FedQ-Advantage for federated Q-learning with near-optimal regret and low communication cost.

The common assumption of universal behavior in stock market data can sometimes lead to false conclusions. In statistical physics, the Hurst exponents characterizing long-range correlations are often closely related to universal exponents. We show, that in the case of time series of the traded value, these Hurst exponen…

Paper approximates Kelly betting for wealth growth.

Study rigidity by logarithmic capacity and related functions.

We study a phenomenological model for the continuous double auction, equivalent to two independent $M/M/1$ queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior …

The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly "amplify" the effective amount of data available. For a large variety of distri…

This paper investigates optimal trading strategies in a financial market with multidimensional stock returns where the drift is an unobservable multivariate Ornstein-Uhlenbeck process. Information about the drift is obtained by observing stock returns and expert opinions. The latter provide unbiased estimates on the cu…

New Dynkin condition for manifolds with boundary yields bi-Lipschitz equivalence and spectral properties.