The paper offers methods to price complex options using upper and lower bounds.
problem Pricing complex options like Asian and basket options.
method Develops a general framework using lower and upper bounds.
result Lower bounds simplify the problem and provide reasonable approximations.
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.
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.
Upper and lower bounds for Steklov eigenvalues of submanifolds with fixed boundary.
problem Finding bounds for Steklov eigenvalues of submanifolds with prescribed boundary.
method General upper bound and sharp lower bounds for hypersurfaces of revolution.
result Each eigenvalue is uniquely minimized by the ball for hypersurfaces of revolution with connected boundary.
New bounds on continuous random variables' right-tail probabilities.
problem Finding precise upper and lower limits for right-tail probabilities of continuous random variables.
method Developed new bounds based on PDF, first derivative, and two parameters.
result The new bounds are tight for various continuous random variables.
Study bounds growth rate of irreducible meanders, showing proportion vanishes.
problem Understanding growth rate of irreducible meanders.
method Provided upper and lower bounds for growth rate.
result Proportion of irreducible meanders among prime meanders approaches 0 as n increases.
Lower bounds for geodesic ball volume in 3D with Ricci curvature constraints.
problem Finding volume bounds in 3D manifolds with Ricci curvature limits.
method Providing lower bounds for geodesic ball volume with upper bounds on Ricci curvature.
result Established lower bounds for geodesic ball volume under Ricci curvature constraints.
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.
Paper establishes lower bounds for non-stationary kernelized bandits.
problem Optimizing functions with noisy observations in non-stationary scenarios.
method Develops algorithm-independent lower bounds for time-varying functions under total variation constraints.
result First algorithm-independent lower bounds for time-varying kernelized bandits.
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 C^{0} 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.
New lower bounds for gradient methods in strongly convex finite-sum optimization.
problem Developing tight lower bounds for randomized gradient methods in finite-sum optimization.
method Deriving tight lower complexity bounds for SAG, SAGA, SVRG, SARAH, and related methods.
result Tight matches between lower bounds and upper bounds for various methods under specific conditions.
Efficient algorithm achieves tightest bounds for active learning.
problem Active learning of general concept classes.
method Efficient algorithm that realizes the tightest upper and lower bounds.
result Empirically demonstrates good performance of the algorithm.
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 ( T 2 / 3 − ε ) O(T^{2/3 - \varepsilon}) O ( T 2/3 − ε ) for calibrated forecasting, improving the O ( T 2 / 3 ) O(T^{2/3}) O ( T 2/3 ) bound of Foster & Vohra. 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.
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.
This paper establishes lower bounds for SGD's error, matching upper bounds.
problem Proving lower error bounds for SGD optimization algorithm.
method Analysis of mean square error for SGD with specific learning rates.
result Essentially matching lower and upper bounds for SGD's mean square error.
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.
The study sets limits on the complexity of Klein geometries.
problem Understanding the complexity of Klein geometries.
method Simple upper and lower bounds for the order of Klein geometries.
result Established upper and lower bounds for the order of Klein geometries.
New lower bounds nearly match existing upper bounds for boosted classifiers.
problem Understanding the generalization performance of boosted classifiers.
method Margin-based lower bounds on boosted classifiers.
result Lower bounds nearly match the k k k th margin bound, settling the generalization performance of boosted classifiers. 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.
problem Bounding the output distribution of neural networks with random inputs.
method Applying ReLU NNs to derive bounds for general NNs, then using these to find exact error guarantees.
result Exact upper and lower bounds for the output distribution of neural networks with random inputs.
The study sets up a framework to analyze parallel optimization problems with graph dependencies.
problem Analyzing the complexity of parallel stochastic optimization problems with graph dependencies.
method Developed a graph oracle-based framework to derive lower bounds and highlight gaps.
result Identified gaps between lower and upper bounds for specific parallel optimization settings.
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.
problem Estimating risk measures in infinite-horizon discounted costs within Markov processes.
method Truncation scheme and lower/upper bounds for CVaR and variance estimation.
result Upper and lower bounds for CVaR and variance estimation match up to logarithmic factors.
Method bounds tail probabilities of continuous RVs.
problem Bounding tail probabilities of continuous random variables.
method Setting continuous, positive, and strictly decreasing/increasing functions to derive upper and lower bounds.
result Provides tighter bounds than existing methods, including a novel asymptotic capacity bound for AWGN channel.
Lower bounds and upper bounds on sample complexity for identifying linear dynamical systems.
problem Identifying an unknown linear dynamical system with limited data.
method Sample complexity lower and upper bounds, persistent excitation condition, active learning algorithm.
result Lower and upper bounds share the same dependency on key problem parameters.
Improved regret bounds for bandits with expert advice.
problem Optimizing decision-making in environments with expert advice.
method Proved lower and upper bounds for regret in restricted and standard feedback models.
result Proved a new upper bound of order K T ln ( N / K ) \sqrt{K T \ln(N/K)} K T ln ( N / K ) for the worst-case regret, matching a previously known lower bound. Upper and lower bounds derived for online learning with graph-structured feedback against adaptive adversaries.
problem Online learning with graph-structured feedback against adaptive adversaries.
method Analysis of Exp3 algorithm variants and lower bounds for specific adversary models.
result Upper bounds of O ~ ( T 2 / 3 ) \widetilde O(T^{2/3}) O ( T 2/3 ) and O ~ ( T 3 / 4 ) \widetilde O(T^{3/4}) O ( T 3/4 ) for strongly-observable and weakly-observable graphs, respectively. Study proves a tight lower bound for MNL-Bandit assortment selection problems.
problem Dynamic assortment planning under MNL bandit model with capacity constraints.
method Proved a tight lower bound on accumulated regret for all parameters.
result Tight lower bound matches existing upper bounds up to logarithmic factors.
Upper and lower bounds for magnetic Laplacian eigenvalues on manifolds.
problem Bounding eigenvalues of magnetic Laplacian on manifolds.
method Established upper and lower bounds using potential 1-forms and Weyl law compatibility.
result Sharp bounds for first eigenvalue in specific cases.
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.
problem Optimizing decision-making in a multi-armed bandit problem with expert advice.
method Proved a tight lower bound matching the upper bound of Kale (2014) for minimax expected regret.
result The minimax optimal expected regret is Θ(√(T K log (N/K))) for the problem.
New bounds for sequential tests under power-one error levels.
problem Determining stopping times for sequential tests with power-one error levels.
method Proved two lower bounds for stopping times under specific conditions.
result Upper and lower bounds for sequential tests are shown to be tight.
New bounds for prediction with experts using geometric stopping.
problem Online prediction with expert advice, focusing on geometric stopping.
method Potential-based framework, explicit bounds construction.
result First explicit lower and upper bounds in geometric stopping setting.
Sharp bounds for charged Hawking mass in electrostatic space-times.
problem Bounding charged Hawking mass in electrostatic space-times.
method Proving sharp lower bounds and upper bounds for the charged Hawking mass.
result Sharp lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times.
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.
Paper studies ranking from noisy comparisons with minimal assumptions.
problem Finding exact ranking from noisy comparisons with minimal assumptions.
method Adaptive comparisons, lower and upper bounds derivation.
result Nearly optimal pairwise ranking algorithms and extensions to listwise ranking.
Sharp lower bound on GHHs' representation power of CPWL functions.
problem Proving the minimum number of nestings for GHHs to represent arbitrary CPWL functions.
method Using a key lemma about finite sums of periodic functions, proving necessity of n nestings.
result Proving necessity of n nestings for GHHs to achieve universal representation power.
The study analyzes batched methods for early stopping in stochastic multi-armed bandits.
problem Early stopping in stochastic multi-armed bandits with fixed confidence.
method Instance-dependent lower bounds and a general batched algorithm with upper bounds.
result Upper and lower bounds on the number of batches and sample complexity.
Upper bound for conjugate radius in open manifolds with scalar curvature and spectrum constraints.
problem Bounding the conjugate radius of open manifolds with specific curvature and spectrum conditions.
method Established an upper bound using scalar curvature and bottom-of-spectrum constraints.
result For certain conditions, the conjugate radius is no more than π.
New bounds for Bayesian bandits show prior improves performance.
problem Improving regret bounds for Bayesian bandits.
method Upper confidence bound algorithm with finite-time logarithmic regret bounds.
result Derives O ( c Δ log n ) O(c_Δ\log n) O ( c Δ log n ) and O ( c h log 2 n ) O(c_h \log^2 n) O ( c h log 2 n ) upper bounds for Bayesian 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…
Study precise sample covariance error for Gaussian centered data.
problem Precise characterization of sample covariance error for Gaussian data.
method Developed a Random Duality Theory (RDT) framework to determine upper and lower bounds.
result Upper and lower bounds match in large-dimensional contexts, matching the spectral norm's limiting value.
Optimal sampling bounds for various classification losses under different regularization terms.
problem Achieving optimal sampling complexity for classification losses under different regularization terms.
method Proved optimal sampling bounds for a broad class of Lipschitz continuous classification loss functions under various regularization terms.
result Proved k 2 / ε 2 k^2/\varepsilon^2 k 2 / ε 2 upper and lower bounds for ∥ ⋅ ∥ 2 / k \|\cdot\|_2/k ∥ ⋅ ∥ 2 / k regularization, and k / ε 2 k/\varepsilon^2 k / ε 2 upper and lower bounds for ∥ ⋅ ∥ 1 / k \|\cdot\|_1/k ∥ ⋅ ∥ 1 / k regularization. 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.
Sharp bounds established for Federated Averaging (FedAvg), improving convergence rates.
problem Undetermined convergence rate of Federated Averaging (FedAvg) in Federated Learning.
method Developed novel iterate bias concept and proved sharp bounds on it, leading to improved convergence results.
result Lower bounds for FedAvg match existing upper bounds, showing no improvable capacity.
Upper and lower bounds on regret for noisy optimization of Brownian motion.
problem Optimizing a one-dimensional Brownian motion with noisy observations.
method Upper bound uses confidence bounds and Markov property; lower bound uses hypothesis testing reduction.
result Upper and lower bounds are tight up to a factor of O ( ( log T ) 1.5 ) O((\log T)^{1.5}) O (( log T ) 1.5 ) .