Improved bounds on ideal vertices in right-angled hyperbolic polyhedra.
problem Finding bounds on ideal vertices in hyperbolic polyhedra.
method Improved Nikulin's inequality and Nonaka's lower bound.
result Shorter proofs and improved bounds on ideal vertices.
Uniform bounds for eigenvalues of Hodge Laplacian on manifolds with lower Ricci curvature.
problem Establishing bounds for eigenvalues of Hodge Laplacian under lower Ricci curvature.
method Using geometric assumptions including lower Ricci curvature, injectivity radius, and diameter bounds.
result Uniform eigenvalue bounds for the Hodge Laplacian and connection Laplacian.
Lower bounds on ribbon distance using Bar-Natan and α-Homology.
problem Calculating the minimum number of ribbon operations to unknot a knot.
method Bar-Natan Homology and α-Homology approaches.
result Lower bounds on ribbon distance via both Bar-Natan and α-Homology.
New study on regret lower bounds for multi-agent multi-armed bandit problems.
problem Understanding the limits of performance in multi-agent multi-armed bandit problems.
method Comprehensive study on different settings, establishing tight lower bounds.
result First comprehensive study on regret lower bounds across various settings.
Along the line of the Yang Conjecture, we give a new estimate on the lower bound of the first non-zero eigenvalue of a closed Riemannian manifold with negative lower bound of Ricci curvature in terms of the in-diameter and the lower bound of Ricci curvature.
There has been renewed recent interest in developing effective lower bounds for Dynamic Time Warping (DTW) distance between time series. These have many applications in time series indexing, clustering, forecasting, regression and classification. One of the key time series classification algorithms, the nearest neighbo…
In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower bound conjecture for triangulated spheres in the context of the lower bound theorem…
Lower bound found for Kähler manifold eigenvalues.
problem Finding bounds for eigenvalues on Kähler manifolds.
method Comparison results of Li and Wang applied to Kähler manifolds.
result Explicit lower bound of the first eigenvalue determined.
Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.
problem Conservative bandits and reinforcement learning problems.
method Reduction technique to calculate necessary and sufficient budget from baseline policy.
result Improved lower and upper bounds for various conservative settings.
Survey on gluing constructions under lower curvature bounds.
problem Understanding lower curvature bounds in various geometric contexts.
method Analyzes gluing constructions in smooth and non-smooth settings.
result Provides conjectures and theorems on synthetic lower Ricci curvature bounds.
The paper establishes bounds on scalar curvature on asymptotically flat manifolds.
problem Establishing scalar curvature bounds on asymptotically flat manifolds.
method Using Ricci-DeTurck flow and distributional scalar curvature, the paper derives bounds on scalar curvature.
result The scalar curvature lower bound under Ricci-DeTurck flow depends on the scalar curvature lower bound in the β-weak sense and time.
We prove non-asymptotic lower bounds on the expectation of the maximum of d independent Gaussian variables and the expectation of the maximum of d independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (…
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 …
Study sets lower bounds for Kähler manifolds' Laplacian eigenvalues.
problem Finding bounds for eigenvalues on Kähler manifolds.
method Establishes lower bounds using geometric data like dimension, diameter, and curvature.
result Proves bounds for Laplacian eigenvalues on Kähler manifolds.
New algorithms for private GLM estimation with minimax lower bounds.
problem Privacy in generalized linear models.
method Differentially private algorithms using projected gradient descent.
result Nearly rate-optimal performance with privacy-constrained minimax lower bounds.
Lower bounds for eigenvalues on Bakry-Emery manifolds proven.
problem Eigenvalue estimates on Bakry-Emery manifolds.
method Generalised maximum principle and heat kernel estimates.
result Lower bounds for all eigenvalues proven.
Estimates lower bounds for isoperimetric profiles and improves on previous estimates for specific manifolds.
problem Estimating lower bounds for isoperimetric profiles of specific Riemannian manifolds.
method Explicit lower bounds for isoperimetric profiles of Riemannian product manifolds.
result Improved lower bounds for isoperimetric profiles and Yamabe constants.
Sharp lower bound for Hodge Laplacian on Kähler hyperbolic manifolds.
problem Finding a sharp lower bound for the spectrum of the Hodge Laplacian.
method Explicitly expressed in terms of the supremum norm of the 1-form.
result Explicit spectral lower bounds for bounded symmetric domains.
Lower bound found for volatility swap in SABR model.
problem Finding a lower bound for volatility swap in SABR model.
method Short time to maturity limit analysis of conditionally lognormal SABR model.
result Zero vanna implied volatility is a lower bound for volatility swap strike.
Lower bounds for geodesically convex optimization show curvature negatively impacts complexity.
problem Understanding the impact of curvature on the query complexity of geodesically convex optimization.
method Building on recent lower bounds, the study proposes and proves new lower bounds for various settings of geodesically convex optimization.
result Negative curvature is detrimental to the complexity of geodesically convex optimization.
Paper proves tight lower bounds for online multicalibration, separating it from marginal calibration.
problem Proving lower bounds for online multicalibration in relation to marginal calibration.
method Information-theoretic approach, constructing group families from orthonormal bases.
result Establishes tight lower bounds for online multicalibration, matching upper bounds up to logarithmic factors.
Paper establishes new lower bounds for MDPs with changing transition kernels.
problem Minimizing sample complexity and regret in non-stationary MDPs.
method Developed novel lower bounds and constructed hard MDPs.
result Proved Ω((H3SA/ε2)log(1/δ)) sample complexity lower bound. Lower bounds found for nonconvex-strongly-concave min-max optimization problems.
problem Finding stationary points in nonconvex-strongly-concave min-max optimization.
method Provided lower bounds for first-order oracle complexity.
result Lower bounds of Ω(√κε⁻²) for deterministic oracles and Ω(√κε⁻² + κ¹/₃ε⁻⁴) for stochastic oracles.
The paper proves inequalities under Bakry-Émery-Ricci curvature bounds.
problem Proving functional inequalities under lower Bakry-Émery-Ricci curvature bounds.
method Lower m-Bakry-Émery-Ricci curvature bounds with ε-range. result Proves Cheng type inequality and local Sobolev inequality.
Surveying Ricci flow for weak lower scalar curvature bounds.
problem Creating local definitions for weak lower scalar curvature bounds for C0 metrics. method Using Ricci flow to define and analyze weak lower scalar curvature bounds.
result Properties and applications of Ricci flow in defining weak lower scalar curvature bounds.
Abstract reviews known and open questions on spaces with lower Ricci bounds.
problem Understanding the structure and regularity of spaces with lower Ricci curvature bounds.
method Review of known results and presentation of open questions.
result Presentation of new open questions in the field.
Lower bound on stretch factor for periodic maps.
problem Finding a lower bound on stretch factors for periodic maps.
method Using core characteristic of end-periodic homeomorphisms, we derive a lower bound on the Handel-Miller stretch factor.
result The derived bound is sharp and measures topological complexity.
Proves equivalence of two types of Ricci curvature bounds.
problem Equivalence of distributional and synthetic Ricci curvature bounds.
method Analyzes weighted Riemannian manifolds with specific smoothness conditions.
result Proves equivalence of Ricci curvature bounds under given conditions.
Study eigenvalues of p-Laplacian on Kähler manifolds, proving lower bounds.
problem Eigenvalue problem for the p-Laplacian on Kähler manifolds.
method Lower bounds derived using dimension, diameter, curvature bounds.
result Sharp lower bounds for the first Dirichlet eigenvalue of the p-Laplacian.
Unified framework for lower bounds in interactive decision making.
problem Challenges in interactive decision making, especially bandits and reinforcement learning.
method Interactive Fano method and Fractional Covering Number.
result Unified characterization of learnability for stochastic bandit problems and tight lower bounds for interactive decision making.
The standard interpretation of importance-weighted autoencoders is that they maximize a tighter lower bound on the marginal likelihood than the standard evidence lower bound. We give an alternate interpretation of this procedure: that it optimizes the standard variational lower bound, but using a more complex distribut…
The paper improves regret lower bounds for communicating MDPs.
problem Regret lower bounds for communicating MDPs.
method Lower bound proof and optimization problem formulation.
result Regret lower bound becomes significantly more complex in communicating MDPs.
New bounds for SGD show improved performance in various settings.
problem Improving convergence bounds for SGD with random permutations.
method Analyzing convergence of SGD with random reshuffling and arbitrary permutations.
result Tighter lower bounds for weighted average iterates in both convex and strongly-convex cases.
Improved upper bound for online calibrated forecasting of binary sequences.
problem Online calibrated forecasting of binary sequences.
method Introducing a variant of Qiao & Valiant's sign preservation game called sign preservation with reuse (SPR) and proving its equivalence to calibrated forecasting.
result Improved upper bound of O(T2/3−ε) for calibrated forecasting, improving the O(T2/3) bound of Foster & Vohra. Paper establishes lower bounds for Gaussian process bandit optimization under various perturbation models.
problem Lower bounds for Gaussian process bandit optimization in noisy and robust settings.
method Novel proof techniques for standard and robust settings, including deterministic strategies.
result Demonstrates inevitable joint dependence of cumulative regret on corruption level and time horizon in robust settings.
Paper proves first non-trivial PTF testing lower bounds for NGCA.
problem Proving lower bounds against PTF tests is challenging.
method Developed tools to prove PTF testing lower bounds for NGCA.
result First non-trivial PTF testing lower bounds for NGCA.
New self-imitation learning method improves performance in continuous control tasks.
problem Improving off-policy learning in continuous control tasks.
method Proposes a n-step lower bound to generalize lower-bound Q-learning and introduces a new family of self-imitation learning algorithms.
result n-step lower bound Q-learning achieves a better trade-off between bias and contraction rate, leading to improved performance.
Lower bounds set for infinite-precision transformers.
problem Understanding limitations of infinite-precision transformers.
method Used VC dimension technique to prove lower bounds.
result First lower bounds for two tasks: function composition and SUM2. Sharp lower bound on fold singularities self-intersections.
problem Finding a lower bound on the number of self-intersections of fold singularities.
method Established a sharp lower bound on the number of self-intersections of the boundary of an immersed surface, then applied this to fold singularities.
result Sharp lower bound on the number of self-intersections of fold singularities.
We obtain lower bounds for the first Laplacian eigenvalues of geodesic balls of spherically symmetric manifolds. These lower bounds are only C0 dependent on the metric coefficients.
New lower bounds for bilevel optimization with first-order oracles.
problem Complexity of bilevel optimization with first-order oracles.
method Development of hard instances and proof of lower bounds.
result Nontrivial lower bounds for first-order zero-respecting algorithms.
The paper sets lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.
problem Eigenvalues of the Laplace operator and clamped plate problem.
method Sharp lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.
result Sharp lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.
The paper sets lower bounds for sampling non-log-concave distributions using Fisher information.
problem Understanding the complexity of sampling non-log-concave distributions.
method Proves two lower bounds using Fisher information in the context of sampling.
result Lower bounds on the complexity of sampling non-log-concave distributions, ruling out high-accuracy algorithms.
The paper defines quasi-convex subsets in spaces with lower curvature bound.
problem Understanding the geometry of spaces with lower curvature bound.
method Introducing and exploring quasi-convex subsets in Alexandrov spaces.
result Quasi-convex subsets are a fundamental concept for comparing Riemannian and Alexandrov spaces.
Paper tightens lower bounds on decentralized training complexity.
problem Understanding and optimizing iteration complexity in decentralized training.
method Proved a tight lower bound on iteration complexity and proposed DeTAG algorithm.
result DeTAG achieves the theoretical lower bound with only a logarithmic gap.
Paper finds a lower bound for estimating low-rank matrices in logistic regression.
problem Estimating low-rank coefficient matrices in logistic regression.
method Derives a minimax lower bound on the risk.
result The bound depends on matrix dimensions, rank, and sample size.
Lower bounds on curvature integral for manifolds with curvature constraints.
problem Bounding curvature integrals under curvature constraints.
method Proving a lower bound for the curvature integral using dimension, upper curvature bounds, and injectivity radius.
result Uniformly bounded below integral of scalar curvature.
Lower bounds on cone density for nontrivial complements in low dimensions.
problem Finding density limits for minimal cones with nontrivial complements.
method Proving lower bounds on cone density for cones of dimensions less than seven with nontrivial complements.
result Established lower bounds on cone density for minimal cones with nontrivial complements in dimensions less than seven.