Derives optimal control conditions using calculus of variations.
problem Optimizing Markov control in stochastic control problems.
method Calculus of variations approach to derive necessary conditions.
result Solves the Merton portfolio optimization problem.
Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A popular approach used to reduce gradient's variance involves the use of control varia…
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 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.
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.
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.
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.
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.
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.
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.
Paper improves variance control in importance weighted variational bounds.
problem Improving the variance of gradient estimators for IWAE.
method Develops a novel control variate that grows SNR as √K for large K.
result Empirically, the method yields superior variance reduction for generative models.
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.
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.
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates approaches are well-known to reduce the variance of the estimation. These control v…
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.
Study develops a data-based model for in-cylinder pressure and cyclic variations in RCCI engines.
problem Lack of models capturing cyclic variations in combustion concepts like RCCI.
method Combines Principle Component Decomposition and Gaussian Process Regression.
result Model predicts combustion measures with high accuracy, especially peak-pressure rise-rate.
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.
New control theory for self-path-dependent problems solves unique constraints.
problem Optimal control with self-path-dependent constraints in stochastic systems.
method Introduces new HJB equations for variational inequalities with historical maximum controls.
result Value functions are viscosity solutions to HJB equations under Lipschitz conditions.
Investigates optimal strategies for behavioral control problems with finite variation controls.
problem Behavioral singular stochastic control problems with finite variation controls.
method Abstract framework, applied to storage management and portfolio investment problems, using CPT preferences and Skorokhod representation theorem.
result Existence of optimal strategies for various goal functionals, including CPT preferences.
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.
VarGrad reduces variance in ELBO gradient estimation for variational inference.
problem Improving the variance of gradient estimators in variational inference.
method VarGrad uses a new log-variance loss to estimate the ELBO gradient, achieving lower variance than the score function method.
result VarGrad offers a lower variance gradient estimator compared to other methods.
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.
It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly with dataset size. A popular class of methods for solving this issue is stochastic gradient MCMC. These methods use a noisy estimate of the gradient of the log posterior, which reduces the per iteration computational cost of the algorithm. Despi…
Causal effect estimation relies on separating the variation in the outcome into parts due to the treatment and due to the confounders. To achieve this separation, practitioners often use external sources of randomness that only influence the treatment called instrumental variables (IVs). We study variables constructed …
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.
GCVAE improves disentanglement in VAEs while balancing reconstruction error.
problem Improving disentanglement in VAEs while maintaining low reconstruction error.
method Introduces three controllable Lagrangian hyperparameters to optimize reconstruction and KL divergence loss.
result GCVAE outperforms state-of-the-art models in disentanglement while balancing reconstruction.
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.
The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S^n following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler-Lagrange equations is established. This problem…
Policy gradient methods have achieved remarkable successes in solving challenging reinforcement learning problems. However, it still often suffers from the large variance issue on policy gradient estimation, which leads to poor sample efficiency during training. In this work, we propose a control variate method to effe…
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.
Revisits VIC method to correct intrinsic reward bias in stochastic environments.
problem Intrinsic reward bias in VIC leading to suboptimal solutions.
method Proposes two methods based on transitional probability model and Gaussian mixture model to correct bias.
result Achieves maximal empowerment through corrected intrinsic reward.
New comparison shows differences in how value is incorporated in AIF and CAI.
problem Clarifying the relationship between Active Inference and Control-as-Inference.
method Formal comparison of AIF and CAI frameworks.
result Primary difference is how value is incorporated into generative models.
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.
ControlVAE improves VAE performance by adding a controller to tune hyperparameters.
problem Existing VAE models struggle with KL vanishing and low reconstruction quality.
method ControlVAE combines a controller inspired by automatic control theory with VAE to improve performance.
result ControlVAE achieves better disentangling and reconstruction quality than existing methods.
Paper uses VAEs to control IVS features for financial modeling.
problem Generating realistic IVSs with desired characteristics.
method Variational autoencoder architecture with controllable latent variables.
result Controlled generation of IVSs with specified features.
New insights into cascade feedback linearization of control systems.
problem Obtaining a cascade feedback linearization for invariant control systems.
method Introducing truncated versions of operators from the calculus of variations to prove new theorems.
result Established new geometry and foundational theorems for future work.
Generating versatile and appropriate synthetic speech requires control over the output expression separate from the spoken text. Important non-textual speech variation is seldom annotated, in which case output control must be learned in an unsupervised fashion. In this paper, we perform an in-depth study of methods for…
New method approximates diffusion process posteriors using moment functions.
problem Approximating posteriors of stochastic differential equations.
method Constructs variational process as controlled prior, approximates posterior with moment functions, uses natural gradient descent.
result Richer variational approximations for state-dependent diffusion terms.
The paper proves index theorems for graph-based optimal control problems.
problem Optimal control problems on graphs with constraints.
method Proves Morse index theorems for a broad class of variational problems on graphs.
result Formulas compute the difference of Hessians related to different graphs or boundary conditions.
A key challenge for gradient based optimization methods in model-free reinforcement learning is to develop an approach that is sample efficient and has low variance. In this work, we apply Kronecker-factored curvature estimation technique (KFAC) to a recently proposed gradient estimator for control variate optimization…
New method for handling multi-dimensional singular controls with jump costs in mean-field problems.
problem Handling jump costs in multi-dimensional singular controls.
method Introducing two-layer parametrisations to interpolate jumps on both distributional and pathwise levels.
result Derivation of a DPP and characterisation of the value function as a minimal super-solution to a quasi-variational inequality.
New method guides pretrained diffusion models without additional training.
problem Guidance methods for diffusion models often require extra training or are task-specific.
method Variational Control using Diffusion Trajectory Matching (DTM)
result Achieves state-of-the-art results on various problems.
Autonomous agents can learn by imitating teacher demonstrations of the intended behavior. Hierarchical control policies are ubiquitously useful for such learning, having the potential to break down structured tasks into simpler sub-tasks, thereby improving data efficiency and generalization. In this paper, we propose a…
Exploration in environments with continuous control and sparse rewards remains a key challenge in reinforcement learning (RL). Recently, surprise has been used as an intrinsic reward that encourages systematic and efficient exploration. We introduce a new definition of surprise and its RL implementation named Variation…
Paper introduces RCaI, a risk-sensitive control method using Rényi divergence.
problem Risk-sensitive control in reinforcement learning.
method RCaI extends CaI using Rényi divergence variational inference.
result Risk-sensitive optimal policy can be obtained by solving a soft Bellman equation.