Paper derives an error bound for stochastic LTI systems.
problem Stochastic LTI systems with inputs in control engineering and econometrics.
method PAC-Bayesian-Like error bound derivation.
result Derived an error bound for stochastic LTI systems.
Proposes uncertain volatility models with fluctuating stochastic bounds for improved accuracy.
problem Improving accuracy in modeling volatility with fluctuating bounds.
method Introduces stochastic bounds that fluctuate according to a stochastic volatility process, applying perturbation analysis to reduce complexity.
result The method provides a significant computational advantage and performs well even with moderately slow varying bounds.
PAC-Bayesian bounds for stochastic LTI systems derived.
problem Error bounds for stochastic LTI systems.
method PAC-Bayesian theory applied to autonomous stochastic LTI models.
result Error bounds for stochastic LTI systems derived.
Stochastic approximation algorithms show exponential progress bounds.
problem Analyzing the convergence of stochastic approximation algorithms.
method Developed geometric ergodicity proofs to establish exponential concentration bounds.
result Proved faster convergence rates for specific algorithms.
Derives error bounds for stochastic iterative algorithms using Stein's method.
problem Bounding errors in stochastic iterative algorithms like SGD and SGLD.
method Uses infinite-dimensional Stein's method of exchangeable pairs to derive functional approximation error bounds.
result Establishes non-asymptotic error bounds for algorithm sample paths and variance of iterate averages.
High-probability bound for distributed stochastic approximation tracking error.
problem Analyzing the convergence of distributed stochastic approximation schemes.
method Analysis using ODE approach to stochastic approximation.
result High probability bound for tracking error between iterates and limiting differential equation.
New bounds show linear predictors rarely overfit with certain optimization methods.
problem Bounding test error for linear predictors with stochastic optimization methods.
method Coupling argument for fixed point methods like stochastic and batch mirror descent.
result Locally-adapted rates that depend on predictor properties, not global problem structure.
New bounds for online convex optimization between stochastic and adversarial settings.
problem Understanding optimization tasks that are neither i.i.d. nor fully adversarial.
method Establishing novel regret bounds exploiting smoothness of expected losses.
result Regret bounds match expected rates in the fully i.i.d. case and gracefully deteriorate in the fully adversarial case.
New method bounds stochastic subgradient methods with heavy-tailed noise.
problem Bounding stochastic subgradient methods under heavy-tailed noise.
method Clipped version of projected stochastic subgradient method.
result Near optimal any-time and finite horizon bounds for averaging schemes.
Proposes SPFB method for optimizing partition functions in stochastic learning.
problem Optimizing partition functions in stochastic learning settings.
method Stochastic Gradient Bound (SPFB) method based on upper-bounding the partition function with a quadratic surrogate.
result Sub-linear convergence rate of SPFB method and efficient training of deep learning models.
Lower bounds on queries needed for finding stationary points in non-convex optimization.
problem Finding ε ε ε -stationary points in non-convex stochastic optimization. method Proving lower bounds on the number of queries required by stochastic first-order methods.
result Lower bounds on the number of queries required to find ε ε ε -stationary points are tight and optimal. Improved online convex optimization bounds between stochastic and adversarial settings.
problem Understanding optimization tasks that are neither i.i.d. nor fully adversarial.
method Establishing novel regret bounds exploiting smoothness of expected losses.
result Regret bounds improve on previous results by reducing dependence on maximum gradient length to variance of gradients.
New algorithm optimizes PAC-Bayes bound without surrogate loss.
problem Mismatch between optimisation objective and generalisation bound in stochastic neural networks.
method Proposes a novel training algorithm that optimizes the PAC-Bayesian bound directly.
result Empirical results show improved performance over existing PAC-Bayesian training methods.
PAC-Bayesian framework for fairness in stochastic and deterministic classifiers.
problem Theoretical guarantees on fairness for balancing predictive risk and fairness constraints.
method PAC-Bayesian framework for both stochastic and deterministic classifiers, covering a broad class of fairness measures.
result Derives generalization bounds for fairness, demonstrating tightness with empirical evaluation.
Study reveals mutual information is crucial for understanding algorithm performance in stochastic convex optimization.
problem Uncertainty in capturing the exceptional performance of learning algorithms using existing information-theoretic generalization bounds.
method Examined the relationship between mutual information and generalization in stochastic convex optimization.
result Mutual information is necessary for true risk minimization in stochastic convex optimization, indicating existing bounds fall short.
New algorithms solve stochastic variational inequalities without bounded variance assumption.
problem Solving stochastic variational inequalities without bounded variance assumption.
method Developed algorithms for two classes of problems: monotone and structured nonmonotone VIs.
result Oracle complexity of O(ε^-4) for solving VIs with unbounded domains and possibly unbounded variance.
New algorithm tackles adversarial contextual bandits using stochastic smoothing.
problem Adversarial contextual bandit problems.
method Stochastic smoothing perspective and random perturbation based algorithms.
result Zero-order bound of O ( T ) O(\sqrt{T}) O ( T ) and first-order bound of O ( L T ∗ 2 / 3 ) O(L^{*2/3}_{T}) O ( L T ∗ 2/3 ) for the proposed algorithm. The paper analyzes generalization bounds for NC-SC/NC-C stochastic minimax optimization.
problem Generalization analysis of nonconvex-(strongly)-concave stochastic minimax optimization.
method Established algorithm-agnostic and algorithm-dependent generalization bounds via uniform convergence and stability arguments.
result Sample complexities and generalization bounds for NC-SC and NC-C settings.
New methods bound uncertainties in large, noisy data for robust SVM classification.
problem Uncertainty in large, noisy data for robust SVM classification.
method Formulate robust optimization problem with bounding schemes for random features using Random Fourier Features and Nyström methods. Solve with stochastic approximation techniques.
result Efficient solutions for large, noisy data classification.
Paper develops bounds for stochastic approximation with averaging.
problem Establish high-probability bounds for averaged stochastic approximation.
method Develops a general framework for non-asymptotic concentration bounds.
result Derives sharp bounds for averaged iterates and tightens existing results.
Stochastic Bayesian Neural Network improves scalability and performance.
problem Challenges in calculating posterior distribution in Bayesian Neural Networks.
method Maximizes Evidence Lower Bound using Stochastic Evidence Lower Bound objective function.
result Demonstrates improved performance and scalability over previous algorithms.
SGD generalization bounds derived from information theory.
problem Understanding generalization of SGD for non-convex functions.
method Combining information-theoretic bounds with perturbation analysis.
result Upper bounds on SGD's generalization error based on gradient variance and function smoothness.
Two new algorithms solve privacy-constrained SVI and SSP problems.
problem Privacy-constrained stochastic variational inequality and saddle-point problems.
method Proposed Noisy Stochastic Extragradient (NSEG) and Noisy Inexact Stochastic Proximal Point (NISPP) algorithms.
result Optimal risk bounds for weak gap function with sampling with replacement.
New bounds on adaptivity cost in stochastic optimization.
problem Understanding the cost of changing strategies in stochastic optimization.
method Proving impossibility results for adaptivity in non-smooth stochastic convex optimization.
result Lower bounds on the price of adaptivity for different levels of uncertainty.
Proposes new rule for ranking investment prospects over long horizons.
problem Ranking investment prospects over long horizons considering bounded risk aversion.
method Introduces asymptotic fractional-order stochastic dominance with bounded relative risk aversion.
result Establishes equivalent conditions for the new rule under lognormal returns without mean non-negativity constraint.
Paper establishes convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
problem Analyzing convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
method Novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing length.
result First almost sure convergence rate and maximal concentration bound with exponential tails for contractive stochastic approximation algorithms with Markovian noise.
Unified algorithm for optimizing rewards in stochastic path problems.
problem Optimizing rewards in stochastic path problems with unknown reward scales.
method A simple optimistic algorithm with regret guarantees.
result Regret bound matches best known results for SSP with all non-positive rewards.
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.
SGD handles label noise with bounds improving over SGLD.
problem Label noise in non-convex optimization.
method Stochastic gradient descent with uniform dissipativity and smoothness conditions, using Wasserstein distance and algorithmic stability.
result Generalization error bounds with a rate of n − 2 / 3 n^{-2/3} n − 2/3 , better than SGLD's n − 1 / 2 n^{-1/2} n − 1/2 . Unified analysis of perturbation-based strategies in stochastic and adversarial bandit problems.
problem Optimality of perturbation-based strategies in multi-armed bandit problems.
method Unified regret analysis for stochastic and adversarial settings, using perturbations of sub-Weibull and bounded support.
result Unified bounds for perturbations in both stochastic and adversarial settings, with optimal perturbations of Frechet-type.
We provide bounds on control learning error in stochastic systems.
problem Learning optimal controls in stochastic environments with uncontrolled parts.
method Dynamic programming and mean-field interpretation of neural networks.
result Non-asymptotic bounds on generalization error for stable overparametrised settings.
Method solves complex optimization problems with high probability bounds.
problem Nonlinear equality constrained stochastic optimization problems.
method Step-search sequential quadratic programming method.
result High-probability bound on iteration complexity for first-order stationarity.
Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.
problem Optimizing convex and Lipschitz functions with heavy-tailed noise.
method Develops tail bounds for optimization error of Stochastic Mirror Descent.
result Tail bounds extend to heavier-tailed noise regimes without diameter constraints.
New oracles improve stochastic optimization with noisy or biased measurements.
problem Optimizing functions with noisy or biased measurements.
method Introduced biased gradient oracles for stochastic optimization, analyzed RSG and SGD algorithms with these oracles.
result Derived non-asymptotic bounds for convergence rates of algorithms with biased gradient oracles.
Study shows how SGD's implicit regularization relates to ridge regression.
problem Least squares regression optimization with mini-batch SGD.
method Analyzes stochastic gradient flow as a continuous-time model of SGD.
result Bound on excess risk of SGD flow over ridge regression, revealing how parameters drive risk.
The study extends stochastic completeness to landmark spaces with any number of landmarks.
problem Stochastic completeness for landmark spaces with arbitrary numbers of landmarks.
method Volume growth criterion and eigenvalue bounds for geodesic balls.
result Stochastic completeness for landmark spaces with any number of landmarks is proven.
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.
Paper develops probabilistic bounds for a stochastic gradient algorithm in non-convex problems.
problem Stochastic optimization in non-convex finite sum problems.
method Develops a new dimension-free Azuma-Hoeffding type bound for a martingale difference sequence.
result Empirical results show superior probabilistic performance of Prob-SARAH compared to other algorithms.
The paper provides bounds for pricing Guaranteed Annuity Options under stochastic interest and mortality rates.
problem Valuation of Guaranteed Annuity Options in a correlated stochastic environment.
method Employing doubly stochastic stopping times and a change of measure, the authors derive general price bounds for GAOs.
result Derivation of general price bounds for GAOs using a conditioning approach for the lower bound and arithmetic-geometric mean inequality for the upper bound.
Paper improves generalization bounds for noisy stochastic algorithms.
problem Improving generalization bounds for noisy stochastic algorithms.
method Introduces Exponential Family Langevin Dynamics (EFLD) and establishes data-dependent expected stability based generalization bounds.
result Sharp generalization bounds with O(1/n) sample dependence and gradient discrepancy.
Study shows Stochastic Mirror Descent optimizes convex problems with infinite noise variance.
problem Optimizing convex problems with infinite noise variance.
method Stochastic Mirror Descent algorithm with uniformly convex mirror maps.
result Demonstrates convergence rate quantified in terms of iterations, dimensionality, and geometric parameters.
New method achieves optimal performance without needing problem parameters.
problem Parameter-free stochastic optimization in non-convex and convex settings.
method Simple hyperparameter search technique for non-convex setting, and method with stochastic gradients for convex setting.
result Fully parameter-free methods can outperform state-of-the-art algorithms in both non-convex and convex settings.
New algorithm optimizes multi-armed bandit performance in stochastic and adversarial settings.
problem Optimizing multi-armed bandit performance in both stochastic and adversarial environments.
method Follow-the-regularized-leader method with adaptive learning rates.
result First BOBW algorithm with gap-variance-dependent regret bounds in adversarial settings.
New algorithm finds approximate stationary points in non-convex optimization.
problem Finding approximate stationary points in non-convex stochastic optimization.
method Design of an algorithm using O ( ε − 3 ) O(ε^{-3}) O ( ε − 3 ) stochastic gradient and Hessian-vector products. result Optimal rate of O ( ε − 3 ) O(ε^{-3}) O ( ε − 3 ) for finding ε ε ε -approximate stationary points, matching lower bounds. Adapts Bayesian optimization for uncertain outcomes using stochastic sampling.
problem Optimizing with uncertain or stochastic outcomes in scientific and engineering problems.
method Proposes SSBO, a new framework that handles uncertainty and myopic decision making.
result SSBO techniques effectively optimize standard and applied problems.
New bounds link generalization to stochastic optimizer's lower tail exponents.
problem Understanding the impact of stochastic optimization algorithms on generalization in non-convex settings.
method Proves novel bounds linking generalization to the lower tail exponent of the transition kernel of stochastic optimizers, both discrete- and continuous-time.
result Empirical results show correlations between generalization error and lower tail exponents.
Bayesian bandit algorithms with approximate inference improve regret bounds in stochastic linear bandits.
problem Theoretical justification for Bayesian bandit algorithms with approximate inference in stochastic linear bandits.
method Proposed a theoretical framework to analyze approximate inference impact and conducted frequentist regret analysis on LinTS and LinBUCB.
result LinTS and LinBUCB preserve their original regret upper bounds with larger constant terms in approximate inference settings.
Lower bounds show many sampling algorithms need many gradient queries.
problem Sampling from strongly log-concave densities in high dimensions.
method Information theory and stochastic gradient methods.
result Lower bound on number of gradient queries needed.