arXiv research

Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.

New study on regret lower bounds for multi-agent multi-armed bandit problems.

This paper sets out to provide a general framework for the pricing of average-type options via lower and upper bounds. This class of options includes Asian, basket and options on the volume-weighted average price. We demonstrate that in cases under discussion lower bounds allow for the dimensionality of the problem to …

Study bounds growth rate of irreducible meanders, showing proportion vanishes.

New bounds on continuous random variables' right-tail probabilities.

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.

In this note we provide several lower bounds for the volume of a geodesic ball within the injectivity radius in a $3$-dimensional Riemannian manifold assuming only upper bounds for the Ricci curvature.

We give lower and upper bounds for the first eigenvalue of geodesic balls in spherically symmetric manifolds. These lower and upper bounds are $C^{0}$-dependent on the metric coefficients. It gives better lower bounds for the first eigenvalue of spherical caps than those from Betz-Camera-Gzyl.

Paper establishes lower bounds for non-stationary kernelized bandits.

New lower bounds for gradient methods in strongly convex finite-sum optimization.

Lower bounds on curvature integral for manifolds with curvature constraints.

Improved upper bound for online calibrated forecasting of binary sequences.

Paper proves tight lower bounds for online multicalibration, separating it from marginal calibration.

The study sets limits on the complexity of Klein geometries.

Uniform bounds for eigenvalues of Hodge Laplacian on manifolds with lower Ricci curvature.

This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all have free fundamental group).

Exact bounds derived for neural network outputs with noisy inputs.

We give a lower bound on the number of non-simple closed curves on a hyperbolic surface, given upper bounds on both length and self-intersection number. In particular, we carefully show how to construct closed geodesics on pairs of pants, and give a lower bound on the number of curves in this case. The lower bound for …

We estimate risk measures in Markov cost processes with lower and upper bounds.

Method bounds tail probabilities of continuous RVs.

In this short note we consider a dynamic assortment planning problem under the capacitated multinomial logit (MNL) bandit model. We prove a tight lower bound on the accumulated regret that matches existing regret upper bounds for all parameters (time horizon $T$, number of items $N$ and maximum assortment capacity $K$)…

Lower bounds and upper bounds on sample complexity for identifying linear dynamical systems.

Improved regret bounds for bandits with expert advice.

We prove global and local upper bounds for the Hessian of log positive solutions of the heat equation on a Riemannian manifold. The metric is either fixed or evolves under the Ricci flow. These upper bounds supplement the well-known global lower bound.

We find upper and lower bounds for the first eigenvalue and the volume entropy of a noncompact real analytic Kähler manifold, in terms of Calabi's diastasis function and diastatic entropy, which are sharp in the case of the complex hyperbolic space. As a corollary we obtain explicit lower bounds for the first eigenvalu…

Study finds optimal regret bound for multi-armed bandit problem with expert advice.

New bounds for sequential tests under power-one error levels.

Sharp bounds for charged Hawking mass in electrostatic space-times.

Lower bounds found for nonconvex-strongly-concave min-max optimization problems.

Upper bound for conjugate radius in open manifolds with scalar curvature and spectrum constraints.

Sharp lower bound on GHHs' representation power of CPWL functions.

The study analyzes batched methods for early stopping in stochastic multi-armed bandits.

In the context of an incomplete market with a Brownian filtration and a fixed finite time horizon, this paper proves that for general dynamic convex risk measures, the buyer's and seller's risk indifference prices of a contingent claim are bounded from below and above by the dynamic lower and upper hedging prices, resp…

New bounds for Bayesian bandits show prior improves performance.

Study precise sample covariance error for Gaussian centered data.

Optimal sampling bounds for various classification losses under different regularization terms.

New bounds for SGD show improved performance in various settings.

Study on scalar curvature bounds and manifold topological complexity.

Sharp bounds established for Federated Averaging (FedAvg), improving convergence rates.

Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study many fundamental learning algorithms (e.g., $k$-nearest neighbors [Rogers and Wag…

New algorithms identify best policies in discounted linear MDPs efficiently.

New SQ lower bound shows complexity nearly matches known upper bound for smoothed agnostic learning.

The paper studies heat kernels on weighted Riemannian manifolds with curvature bounds.

Optimistic Hedge achieves optimal regret bounds in two-player zero-sum games.

In this paper, we will present some characterizations for the upper bound of the Bakry-Emery curvature on a Riemannian manifold by using functional inequalities on path space. Moreover, some characterizations for general lower and upper bounds of Ricci curvature are also given, which extends the recent results derived …

This work proves lower bounds on a greedy teaching set construction algorithm.

In the context of dealing with financial risk management problems it is desirable to have accurate bounds for option prices in situations when pricing formulae do not exist in the closed form. A unified approach for obtaining upper and lower bounds for Asian-type options, including options on VWAP, is proposed in this …

Sharp upper bounds on inscribed radius for metric spaces with convex boundary.