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.
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.
We solve a complex trade execution problem by simplifying it into a known LQ control problem.
problem Optimal trade execution with stochastic price impact and resilience.
method Extending the problem to progressively measurable processes and reducing it to a LQ stochastic control problem.
result The solution to the LQ problem traces back to the solution of the original trade execution problem.
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.
Study optimal consumption with drawdown limits over a fixed time frame.
problem Maximizing utility with consumption limits during a fixed period.
method Extended utility maximization problem with drawdown constraint, using PDE arguments and dual transform.
result Existence and uniqueness of classical solution to HJB variational inequality, with explicit free boundaries.
Study on natural actor-critic for POMDPs with finite memory.
problem Learning in partially observed Markov decision processes with noisy observations.
method Finite actor-critic method with multi-step temporal difference learning.
result First non-asymptotic global convergence for POMDPs with function approximation.
Improved Least-Squares Monte Carlo with finite-difference ansatz.
problem Improving accuracy and stability in option pricing.
method Constructing an ansatz using finite-difference solution for conditional expected continuation payoffs.
result Reduces mean squared error and final pricing error.
We develop a method to learn neural network activations with controlled Lipschitz constant.
problem Increase neural network capacity while controlling Lipschitz constant.
method Variational framework to learn activation functions with piecewise-linear constraints.
result Proves existence of solutions with continuous and piecewise-linear activations.
The paper analyzes rates for a modified gradient descent method using Stein variational gradients.
problem Improving the accuracy of gradient descent methods for complex target distributions.
method Derives finite-particle rates for regularized Stein variational gradient descent (R-SVGD).
result Establishes explicit non-asymptotic bounds for time-averaged empirical measures.
We study a multiplicative transient price impact model for an illiquid financial market, where trading causes price impact which is multiplicative in relation to the current price, transient over time with finite rate of resilience, and non-linear in the order size. We construct explicit solutions for the optimal contr…
Paper optimizes aquaculture feeding and harvesting strategies for profit maximization.
problem Maximizing farm profit through optimal feeding and harvesting decisions under stochastic price dynamics.
method Developed a simplified aquaculture model and two numerical solution approaches: finite difference scheme and PINN-based method combined with DeepOS algorithm.
result PINN-based method achieves comparable accuracy to finite differences but is more scalable.
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.
We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determi…
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.
Paper tackles utility maximization with job-switching and retirement constraints.
problem Maximizing utility with job-switching and retirement constraints.
method Dual-martingale approach and double obstacle problem theory.
result Characterization of optimal job-switching strategy and wealth boundaries.
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.
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under some assumptions on the underlying process and the utility function. The resultin…
Develops variational framework for LQG risk-sensitive MFGs with major-minor interactions.
problem Risk-sensitive optimal control in LQG systems with major-minor interactions.
method Variational approach, nonlinear necessary and sufficient condition of optimality, equivalent risk-neutral measure, Markovian closed-loop best-response strategies.
result Derives optimal control strategies for LQG risk-sensitive MFGs with major-minor interactions, establishing Nash and ε \varepsilon ε -Nash equilibria. A new method for estimating causal parameters from observables reduces the need for finite moment conditions.
problem Estimating causal parameters from observational data with unknown or infinite moment conditions.
method Variational Method of Moments (VMM) for a general class of estimators, including kernel and neural net-based methods.
result VMM estimators are consistent, asymptotically normal, and semiparametrically efficient.
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.
The present paper is devoted to the study of a bank salvage model with finite time horizon and subjected to stochastic impulse controls. In our model, the bank's default time is a completely inaccessible random quantity generating its own filtration, then reflecting the unpredictability of the event itself. In this fra…
Study optimizes pricing under uncertainty and capacity constraints.
problem Optimizing pricing decisions under demand uncertainty and capacity constraints.
method Analyzes linear demand, stochastic noise, and finite capacity; uses certified demand forecasts and control variates.
result Certified demand forecasts reduce regret from O ( T ) O(\sqrt{T}) O ( T ) to O ( log T ) O(\log T) O ( log T ) under certain conditions. 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.
Variational inference improves hierarchical imitation learning of control programs.
problem Learning structured control policies from demonstrations.
method Variational inference for discovering hierarchical structure in observation-action traces.
result Variational inference leads to more efficient and generalized control policies.
Paper provides finite-sample guarantees for Wasserstein DRO without dimensionality curse.
problem Tackles empirical success of Wasserstein DRO in operations and ML with performance guarantees.
method Develops non-asymptotic framework for analyzing out-of-sample performance and generalization bound.
result First finite-sample guarantee for generic Wasserstein DRO problems without curse of dimensionality.
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.
Study optimal stopping for diffusion processes with unknown primitives, applying RL and martingale methods.
problem Optimal stopping for diffusion processes with unknown model primitives.
method Continuous-time reinforcement learning framework, variational inequality formulation, stochastic optimal control, entropy regularizer, semi-analytical optimal Bernoulli distribution, policy improvement theorem, policy iterations.
result Demonstrated high accuracy in learning value functions and characterizing free boundaries for various optimal stopping problems.
A Closer Look at Disentangling in β-VAE shows non-monotonic inference performance.
problem Learning disentangled representations from data.
method Generalization of VAE using variational inference with hyperparameter β.
result Non-monotonic inference performance in β-VAE with a finite optimal β.
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.
Study optimizes trading in multiple assets with cross-effects.
problem Optimizing trade execution in multiple assets with cross-impact effects.
method Formulated as a stochastic control problem, extended to progressively measurable controls, solved using linear-quadratic control theory.
result Cross-hedging effects can be optimal, e.g., trading in an asset without an initial position.
Paper studies central bank's strategy to control systemic risk in interbank system.
problem Minimizing average distance between log-monetary reserves and target levels.
method Weak formulation, Ekeland's variational principle, Gamma-convergence, stochastic Fokker-Planck-Kolmogorov equation.
result Proves convergence of optimal strategies as number of banks increases.
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.
Optimization geometrodynamics simplifies adaptive optimizer dynamics.
problem Hidden states in adaptive optimizers complicate gradient-based learning.
method Develops a variational theory to eliminate hidden states and compose across hierarchies.
result Yields interaction curvature that integrates to finite contrasts.
A new method removes biases in data integration by using surrogate control outcomes.
problem Data integration methods can be biased due to data-dependent processes.
method Post-integrated inference method using surrogate control outcomes to account for latent heterogeneity.
result The method provides consistent and efficient estimators under minimal assumptions and potential misspecifications.
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.