Algorithm samples constrained stochastic differential equations.
problem Sampling stochastic differential equations with complex constraints.
method Pathspace Metropolis-adjusted manifold sampling.
result Demonstrated effectiveness in various constrained conditions.
Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estim…
New method improves zeroth-order stochastic optimization with adaptive sampling.
problem Optimization problems without gradient information.
method Adaptive sampling quasi-Newton method using finite differences.
result Significant improvement in performance with adaptive sample sizes.
New method for sampling from complex distributions using stochastic localization.
problem Sampling from unnormalized target densities in multi-modal distributions.
method Stochastic Localization via Iterative Posterior Sampling (SLIPS) framework.
result Approximate samples from target distribution and denoiser learned iteratively.
SA-Solver improves stochastic sampling from DPMs.
problem Efficient sampling from Diffusion Probabilistic Models (DPMs) is time-consuming.
method Proposes SA-Solver, an improved stochastic Adams method for solving diffusion SDE.
result SA-Solver achieves improved or comparable performance compared to SOTA methods for few-step sampling.
New sampling strategy improves TR algorithms for stochastic optimization.
problem Derivative-free stochastic optimization with Monte Carlo estimates.
method Stratified adaptive sampling to optimize MC sample size.
result Reduced sample complexity and superior efficiency confirmed.
New sampling method uses stochastic interpolants and FBSDEs.
problem Sampling from high-dimensional distributions with unnormalized densities.
method Stochastic interpolants and FBSDEs to define and solve diffusion process.
result Effective sampling from challenging distributions.
We study primal-dual type stochastic optimization algorithms with non-uniform sampling. Our main theoretical contribution in this paper is to present a convergence analysis of Stochastic Primal Dual Coordinate (SPDC) Method with arbitrary sampling. Based on this theoretical framework, we propose Optimality Violation-ba…
A new method speeds up sampling in diffusion models.
problem Slow sample generation in diffusion models.
method Proposed Splitting Integrators for fast stochastic sampling.
result Achieved FID score of 2.36 in 100 NFE, significantly faster than baselines.
New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.
problem Limited feedback in sequential learning problems.
method Developed a novel Thompson-sampling-based algorithm to sample from the posterior distribution exactly.
result Achieved logarithmic regret bound of O(log T) for a linearized variant of the problem.
NSFs learn SDE transition laws for efficient sampling.
problem Efficiently sampling between arbitrary time points in SDEs.
method Conditional normalising flows with architectural constraints.
result Up to two orders of magnitude speed-ups at large time gaps.
Improved convergence for non-log-concave sampling.
problem Sampling from non-log-concave distributions.
method Novel conductance analysis of SGLD with auxiliary Markov Chain.
result SGLD achieves ε-sampling error with fewer evaluations.
We show that stochastic interpolation flow maps are Lipschitz with a sharp constant.
problem High dimensional sampling and transport problems.
method Investigating stochastic interpolation flow for generating data samples.
result Stochastic interpolation flow maps are Lipschitz with a sharp constant matching optimal transport maps.
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Stochastic gradient descent optimizes Nyström samples for kernel matrix approximation.
problem Optimizing Nyström samples for kernel matrix approximation.
method Stochastic gradient descent applied to multisets of landmark points (Nyström samples) using a surrogate criterion (radial SKD).
result Local minimization of the radial SKD yields improved Nyström approximation accuracy.
Stochastic optimization techniques are standard in variational inference algorithms. These methods estimate gradients by approximating expectations with independent Monte Carlo samples. In this paper, we explore a technique that uses correlated, but more representative , samples to reduce estimator variance. Specifical…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo (MCMC) or Langevin Dynamics (LD) can suffer from slow mixing times there is a growin…
A new method interpolates between sampling and variational inference using stochastic mixtures.
problem Combining the strengths of sampling and variational inference methods.
method Develops a framework using stochastic mixtures of simple component distributions to interpolate between sampling and variational inference.
result Improves on both sampling and variational inference methods by reducing bias and variance.
Improved stochastic optimization outperforms standard methods.
problem Optimizing smooth, strongly convex functions with noisy data.
method Variance reduction strategy called VISOR.
result VISOR achieves optimal sample complexity and oracle complexity.
New method samples from time-integrated stochastic bridges using neural networks.
problem Sampling from time-integrated stochastic bridges with high accuracy and speed.
method Polynomial chaos expansion and artificial neural networks.
result Robust, data-driven Monte Carlo sampling with thousands of samples in milliseconds.
We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic function using finite differences within a common random number framework. We emplo…
New algorithm optimizes stochastic optimization with circular dependency.
problem Circular dependency between decision variable and importance sampling.
method Single-loop stochastic approximation algorithm based on Nesterov's dual averaging.
result Achieves minimal asymptotic variance and resolves circular optimization challenge.
YOASOVI improves stochastic VI for large models with fast, self-correcting sampling.
problem Efficiently performing stochastic Variational Inference on large Bayesian models.
method YOASOVI uses acceptance sampling to draw only one sample per iteration, improving convergence speed and accuracy.
result YOASOVI converges faster and more accurately than regular Monte Carlo and Quasi-Monte Carlo methods.
New technique reduces bias in CSO problems, improving sample complexity.
problem Reducing bias in conditional stochastic optimization problems.
method Introducing a stochastic extrapolation technique combined with variance reduction.
result Achieved significantly better sample complexity for nonconvex smooth objectives.
New method reduces variance in stochastic optimization with high confidence.
problem Achieving high-probability guarantees in stochastic optimization with weaker noise assumptions.
method Stochastic proximal point method combining proximal subproblem solver and probability booster.
result Demonstrates convergence with low sample complexity under bounded variance assumptions.
This work analyzes nonexpansive stochastic approximations with Markovian noise, proving convergence in reinforcement learning.
problem Applying stochastic approximation to reinforcement learning settings with nonexpansive operators.
method Investigates nonexpansive stochastic approximations with Markovian noise, providing asymptotic and finite sample analysis.
result First-time proof of convergence for classical tabular average reward temporal difference learning.
SGBD algorithm improves robustness in Bayesian sampling.
problem Inefficiency of existing MCMC algorithms in large datasets.
method Extends Barker MCMC to stochastic gradient framework, introducing bias-corrected version.
result SGBD is more robust to hyperparameter tuning and gradient noise.
SLIM efficiently solves overidentified models in a scalable manner.
problem Overidentified models with many moment conditions.
method Stochastic approximation framework using mini-batches and unbiased updates.
result SLIM solves overidentified models in under 1.4 hours, compared to 18 hours for full-sample GMM.
In this paper, we study a class of stochastic optimization problems, referred to as the \emph{Conditional Stochastic Optimization} (CSO), in the form of $\min_{x \in \mathcal{X}} \EE_ξf_ξ\Big({\EE_{η|ξ}[g_η(x,ξ)]}\Big)$, which finds a wide spectrum of applications including portfolio selection, reinforcement learning, …
We analyze SGAs for statistical inference via asymptotics, improving tuning methods.
problem Improper tuning of SGAs for optimization and sampling.
method Characterize large-sample asymptotics of SGAs via step-size and sample-size scaling limits.
result Iterate averaging with large step size is robust and asymptotically has covariance proportional to MLE's.
New method uses PDMPs with sub-sampling for efficient sampling from posterior distributions.
problem Efficient sampling from posterior distributions with limited data access.
method Approximate simulation of PDMPs with sub-sampling and stochastic gradient estimation.
result Stochastic-gradient PDMPs are efficient and robust compared to Langevin dynamics.
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
New algorithms solve complex multi-level optimization problems with improved efficiency.
problem Smooth stochastic multi-level composition optimization problems.
method Two algorithms using moving-average and linearized stochastic estimates.
result Achieved sample complexities of O(1/ε^4) and O(1/ε^6).
Itô maps provide a method for any-step SDE integration.
problem Stochastic dynamics
method Itô map formulation
result Empirical results on synthetic and image-generation benchmarks
New algorithm speeds up sampling from complex distributions.
problem Efficiently sampling from non-log-concave distributions.
method Stochastic Proximal Samplers (SPS) based on SGLD and MALA.
result SPS-SGLD and SPS-MALA achieve faster sampling with reduced gradient complexity.
Model shows screening for infectious disease is hard but Thompson sampling works well.
problem Optimal screening policy for infectious diseases is hard to find.
method Stochastic-control model with Thompson sampling for optimal performance.
result Thompson sampling provides optimal performance guarantees in screening for infectious diseases.
We convert deterministic flow models to stochastic samplers.
problem Deterministic flow models are sensitive to errors and cannot condition on intermediate states.
method Transform ODEs into SDEs with the same marginal distributions.
result Empirically outperforms deterministic samplers and controls generation diversity.
Bayesian approach to optimal transport with stochastic costs.
problem Inferring optimal transport plans with uncertain costs.
method Bayesian framework and Hamiltonian Monte Carlo (HMC) sampling.
result Inference of optimal transport plans under stochastic cost functions.
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient descent, using Monte Carlo approximation for the gradients. This enables variatio…
Proves minimax sample complexity for turn-based stochastic games.
problem Proving theoretical guarantees for reinforcement learning in turn-based stochastic games.
method Developing absorbing TBSG and reward perturbation techniques to handle statistical dependence.
result Empirical Nash equilibrium strategy approximates true Nash equilibrium in turn-based stochastic games.
New method converts and optimizes sampling schedules for generative models.
problem Optimizing sampling schedules for generative models like flows and diffusions.
method Unified framework for stochastic interpolants, including point mass schedules.
result Demonstrated efficient generation of images with fewer steps.
We analyze a new Markov chain model for better sampling and optimization.
problem Developing a new Markov chain model for improved sampling and optimization.
method We introduce a new class of Ito chains with arbitrary noise and inexact drift/diffusion coefficients, proving a bound in W2-distance. result Our analysis provides improved or first results for various applications like SGLD, sampling, and boosting.
Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to implement in many cases, and often performs better. In this paper, we provide comp…
(Mini-batch) Stochastic Gradient Descent is a popular optimization method which has been applied to many machine learning applications. But a rather high variance introduced by the stochastic gradient in each step may slow down the convergence. In this paper, we propose the antithetic sampling strategy to reduce the va…
New algorithm guarantees optimal convergence rate for stochastic optimization.
problem Optimal convergence rate for stochastic optimization algorithms.
method Regularized versions of Minimization by Incremental Surrogate Optimization (MISO) with arbitrary recurrent data sampling.
result Expected optimality gap converges at O(n−1/2) under general recurrent sampling schemes. Regularized SB process speeds up generative modeling.
problem Slow sampling and training times in SB-based models.
method Regularization terms to reduce timesteps and training time.
result Faster sampling speed for generative modeling.
Develops a new method for efficient stochastic bilevel optimization.
problem Stochastic bilevel optimization problems in machine learning applications.
method Single-Timescale stochAstic BiLevEl optimization (STABLE) method.
result Achieves the same order of sample complexity as stochastic gradient descent for single-level optimization.
New method improves stochastic kriging for high-dimensional simulations.
problem High-dimensional simulation models require prohibitive sample sizes and computational costs.
method Tensor Markov kernels and sparse grid experimental designs.
result Sample complexity grows only slightly with dimensionality, improving accuracy and efficiency.