We use neural networks as control variates with geometric integration techniques.
problem Analytic integration of neural network approximations for variance reduction.
method Integration domain subdivision using computational geometry for MLPs with continuous piecewise linear activation functions.
result Neural networks can be used as control variates with geometric integration methods.
Improves cross-validation for biased data by adjusting risk estimator variance.
problem Cross-validation under sample selection bias produces suboptimal results.
method Introduces control variate to reduce variance of importance-weighted risk estimator.
result Control variate increases robustness to problematic weights.
Stacked Monte Carlo improves option pricing efficiency.
problem Evaluating option prices in various models.
method A stacking technique that approximates Monte Carlo draws using a specified function.
result Shows efficiency in European and Asian Call options in both constant and stochastic volatility models.
Paper improves variational inference convergence using many control variates.
problem High variance in gradient estimates hinders variational inference convergence.
method Develops a Bayesian risk minimization framework to combine many control variates.
result Combining many control variates significantly improves inference convergence.
Optimizes MCMC chains with neural control variates.
problem Reducing variance in Markov Chain Monte Carlo (MCMC) simulations.
method Uses neural networks as control variates to minimize asymptotic variance.
result Derives optimal convergence rate under various ergodicity assumptions.
New algorithm uses control variates to improve multi-armed bandit performance.
problem Stochastic multi-armed bandits with auxiliary reward information.
method Developed UCB-CV algorithm using control variates for mean estimation.
result UCB-CV algorithm provides tighter confidence bounds and smaller variance.
Improved confidence interval estimation with control variates.
problem Estimating confidence intervals with minimal samples.
method Designing an estimation algorithm using control variates and leveraging order statistics.
result Improved asymptotic efficiency compared to existing algorithms.
This paper develops scalable control variates for Monte Carlo methods using stochastic optimization.
problem Reducing variance in Monte Carlo estimators for large-scale problems.
method Control variates based on Stein operators, optimized through stochastic optimization.
result Novel theoretical results and empirical validations show effective variance reduction.
Develops diffusion samplers for target distributions with efficient score and density estimates.
problem Estimating scores and densities for time-varying distributions.
method Sequential Monte Carlo with diffusion paths and control variates.
result Effective samplers for time-varying distributions with theoretical guarantees and practical applications.
A new method reduces variance in training discrete latent variable models.
problem High variance in stochastic gradient estimators for discrete latent variable models.
method Double control variates for score function estimators using Taylor expansions.
result Our method can have lower variance compared to other estimators.
New method reduces inference variance for faster optimization.
problem High variance in black-box variational inference.
method Joint control variate addressing both data subsampling and Monte Carlo noise.
result Significantly reduced gradient variance, leading to faster optimization.
Combines control variates and adaptive importance sampling for Monte Carlo integration.
problem Improving Monte Carlo integration accuracy with control variates and adaptive sampling.
method A quadrature rule combining control variates and adaptive importance sampling.
result Non-asymptotic bound on the probabilistic error of the procedure.
The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.
problem Efficiency of control variates in reducing variance for Monte Carlo simulations.
method Study of a specific quadrature rule using nonparametric regression-adjusted control variates.
result A specific quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under sufficient smoothness assumptions.
Proposes neural networks for variance reduction in Monte Carlo estimation.
problem High variance in Monte Carlo estimations for complex functions.
method Uses neural networks to learn control variates from auxiliary random variables.
result Significant variance reduction in thermodynamic integration and reinforcement learning.
This work improves variational inference by reducing gradient variance.
problem Hard optimization of flexible variational distributions.
method Control variate based on quadratic approximation of the model's mean and covariance.
result Significant improvement in gradient variance and optimization convergence.
New method improves data-driven optimization by first-order statistical gains.
problem Unclear statistical benefits of data-driven optimization methods.
method Directionally perturbed empirical optimization (EO+) framework.
result First-order statistical improvements possible with geometrically effective side information.
ControlSHAP stabilizes Shapley value approximations using control variates.
problem High computational cost of exact Shapley values in blackbox models.
method ControlSHAP uses Monte Carlo control variates to stabilize Shapley value approximations.
result Significant reduction in Monte Carlo variability of Shapley estimates.
NCV uses neural networks to improve Monte Carlo integration.
problem Improving variance reduction in parametric Monte Carlo integration.
method NCV combines a normalizing flow and a neural network to approximate the integrand and solve the integral equation, with a neural importance sampler to estimate the difference.
result NCV achieves state-of-the-art performance in light transport simulation with reduced noise and negligible bias.
Proposes variance reduction techniques for sliced Wasserstein distance estimation.
problem Intractability of estimating sliced Wasserstein distances.
method Uses control variates based on Gaussian approximations of projected measures.
result Significant reduction in variance of SW distance estimators.
New method reduces variance in policy gradient estimation for reinforcement learning.
problem Large variance issue in policy gradient estimation.
method Action-dependent control variates using Stein's identity.
result Significantly improves sample efficiency of policy gradient methods.
New method reduces variance in Bayesian inverse problems.
problem High variance in Monte Carlo estimates for inverse problems.
method Conditional neural control variates based on Stein's identity.
result Substantial variance reduction across different inverse problems.
This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.
problem Pathwise gradient estimators in variational inference have high variance, leading to inefficient optimization.
method Apply zero-variance control variates to pathwise gradient estimators.
result Zero-variance control variates can significantly reduce the variance of pathwise gradient estimators without requiring complex assumptions.
Improved multi-step TD learning with control variates reduces variance and improves performance.
problem Variance in multi-step TD learning causes divergence in off-policy settings.
method Per-decision control variates for multi-step TD algorithms.
result Control variates significantly improve performance in both on and off-policy tasks.
New method reduces stochastic gradient MCMC's computational cost.
problem Stochastic gradient MCMC's high computational cost with large datasets.
method Control variates to reduce variance in noisy gradient estimates.
result Computational cost independent of dataset size under log-concavity.
A rule selects the best gradient estimator for faster convergence in machine learning.
problem Choosing the best gradient estimator for faster convergence in machine learning.
method Analyzed convergence rates of SGD as a function of time, resulting in a simple rule to select the best estimator.
result The selected estimator leads to the best optimization convergence guarantee, same for different SGD variants and objective types.
ES optimization improved by structured control variates.
problem Improving accuracy of Evolution Strategies in RL.
method RL-specific variance reduction through structured control variates.
result Structured control variates outperform general variance reduction methods.
Meta-CVs leverage task similarity to reduce variance with limited data.
problem Reducing variance in Monte Carlo estimators with few samples.
method Meta-learning control variates for related tasks.
result Meta-CVs lead to significant variance reduction in settings with limited data.
PPAT uses predictions to improve risk estimation in active testing.
problem Exploiting informative predictions from black-box models for efficient risk estimation.
method Combines LURE estimator with prediction-powered control variate.
result PPAT outperforms existing methods in risk estimation and uncertainty quantification.
Paper introduces a new method to solve complex PDEs efficiently.
problem Solving high-dimensional semilinear PDEs and BSDEs.
method Decomposes PDEs into linear and nonlinear parts, uses Deep BSDE solver with control variate method.
result Errors of the new method are much smaller than those of the original Deep BSDE solver.
StackMC improves Monte Carlo estimates by learning control variates from data.
problem Reducing error in Monte Carlo estimates, especially in high dimensions.
method StackMC uses in-sample/out-sample techniques to fit control variates to data samples, improving MC estimators without additional samples.
result StackMC significantly reduces estimation error across various MC sampling methods.
New method reduces training cost by using approximate gradients.
problem Training neural networks is computationally expensive.
method Uses control variates to approximate gradients without full backward pass.
result Efficacy demonstrated on a vision transformer classification task.
Neural SDEs reduce variance in stochastic simulations.
problem Efficiency of Monte Carlo simulations in finance.
method Use neural SDEs with control variates parameterized by neural networks.
result Prove optimality conditions for variance reduction in SDEs with infinite activity.
We reduce variance in Bures-Wasserstein variational inference.
problem High variance in Monte Carlo approximations of Bures-Wasserstein gradients.
method Control variates to reduce variance in the forward step.
result Proposed estimator reduces variance by orders of magnitude.
Algorithm reduces variance in causal effect estimation from multiple datasets.
problem Unidentifiable average treatment effect in observational data due to selection bias.
method Constructs control variates using datasets where ATE is not identifiable to reduce variance.
result Significant reduction in variance of ATE estimate using control variates.
KF-LAX uses KFAC to improve sample efficiency in reinforcement learning.
problem Sample efficiency and low variance in gradient-based optimization methods.
method Kronecker-factored curvature estimation (KFAC) applied to RELAX gradient estimator.
result Improved performance on synthetic and Atari games.
New method uses Hessian to track gradients, improving variance reducing stochastic methods.
problem Improving variance reducing stochastic methods for faster convergence.
method Proposes a modified SVRG method using the Hessian for better control variates and accurate approximations.
result Demonstrates faster theoretical convergence and effectiveness on various problems.
Calibrates hybrid LSV models with stochastic rates using particle method and control variates.
problem Calibrating complex foreign exchange models with stochastic volatility and stochastic rates.
method Combines particle method with variance reduction techniques and control variates.
result Accelerates convergence in calibration process for a wide class of hybrid LSV models.
New method uses model comparison signals to improve LLM evaluation accuracy.
problem Limited benchmark sizes and model stochasticity in evaluating LLMs' mathematical reasoning.
method Combines standard labeled outcomes with model comparison signals to design a statistically efficient evaluation framework.
result Semiparametric estimator achieves the semiparametric efficiency bound and substantially improves ranking accuracy.
Improved A2C method with lower variance.
problem Reducing variance in deep policy gradient methods.
method Using control variate theory, derived a new A2C formulation with lower variance.
result New A2C method has lower variance and improved performance.
Paper introduces control variate to reduce variance in off-policy reinforcement learning.
problem High variance in off-policy reinforcement learning.
method Introduces control variate technique to Expected Sarsa(λ) and proposes ES(λ)-CV algorithm.
result Proposed ES(λ)-CV algorithm has lower variance than Expected Sarsa(λ).
A new method using spherical harmonics approximates the Sliced-Wasserstein distance.
problem Approximating the Sliced-Wasserstein distance between probability measures.
method Spherical Harmonics Control Variates (SHCV) method for Monte Carlo approximation of the SW distance.
result SHCV method provides an improved rate of convergence compared to Monte Carlo for general measures.
A new weighted MLMC method improves efficiency in Monte Carlo simulations.
problem Improving efficiency in Monte Carlo simulations with correlated coarse level approximations.
method Generalization of MLMC to any number of levels with control variates and weights.
result Significant efficiency improvements possible, especially when coarse level approximations are poorly correlated.
Improves gradient estimation for discrete distributions with variance reduction techniques.
problem Excessive variance in gradient estimation for discrete distributions.
method Stein operators for discrete distributions and control variates.
result Substantially lower variance in gradient estimation.
DTM improves dLLM fine-tuning stability and performance.
problem Intractable sequence-level marginal likelihoods for masked diffusion models.
method Discrete Tilt Matching (DTM) recasts dLLM fine-tuning as state-level matching of local unmasking posteriors under reward tilting.
result DTM yields strong gains on Sudoku and Countdown while remaining competitive on MATH500 and GSM8K.
Develops numerical methods for pricing exchange options in a market with limited liquidity.
problem Pricing European style exchange options in a market with finite liquidity.
method Integrates price impact into the dynamics of correlated assets using a controlled variate approach.
result Numerical pricing methods for exchange options are developed and validated.
New method reduces variance in complex probabilistic model optimization.
problem High variance in stochastic optimisation of complex models.
method Use recognition network to approximate optimal control variate for each mini-batch.
result Sub-optimal variance reduction is improved with new approach.
REBAR reduces gradient variance in discrete latent models.
problem High variance in gradient estimates for models with discrete latent variables.
method Introduces a continuous relaxation of discrete variables and a novel control variate to produce low-variance, unbiased gradient estimates.
result State-of-the-art variance reduction on generative modeling tasks, leading to faster convergence.
In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level zero. We show that, under a proper choice of control variates, one can reduce t…