Paper corrects and expands stochastic Lie systems theory.
problem Stochastic Lie systems and their properties.
method Corrected stochastic Lie theorem, introduced new stochastic Lie systems.
result Stochastic Lie systems can differ significantly between Stratonovich and Itô approaches.
We consider stochastic versions of Euler--Arnold equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden. For the Euler equation on a compact manifold (possibly with smooth boundary) we establish local existence and uniqueness of a strong solution (in the stochastic sense) in spaces…
Generative models for complex stochastic dynamics using adversarial learning.
problem Data-driven modeling of multistep stochastic dynamics.
method Adversarial learning with GANs and MMD for stable model classes.
result Stable generative models for long-time prediction and stochastic systems.
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 approach proves convergence of SA and SGD with weaker conditions.
problem Proving convergence of SA and SGD with relaxed noise conditions.
method Introduces GSLLN to decouple function and noise properties.
result Derives sufficient conditions for convergence of SA and SGD.
Stochastic Q-learning tackles large action spaces with reduced computation.
problem Effective decision-making in complex environments with large discrete action spaces.
method Stochastic value-based RL approaches that consider a sublinear number of actions in each iteration.
result Stochastic Q-learning achieves near-optimal returns with significantly reduced computation time.
The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.
problem Pricing options under non-Markovian stochastic volatility models is challenging due to the dependence on historical paths.
method Reformulate the asset dynamics as a rough stochastic differential equation and represent rough paths via signatures. Apply standard analytical tools to solve the transformed equation.
result The deep signature approach provides a theoretically grounded and computationally efficient framework for option pricing.
Paper develops efficient methods for estimating Hessian inverses in stochastic optimization.
problem Estimating the inverse Hessian for convex function minimization.
method Robbins-Monro procedure for recursive estimation of the inverse Hessian.
result Develops universal stochastic Newton methods with improved efficiency.
Stochastic approach improves neural network training for kinetic simulations.
problem Training neural networks under physical constraints in kinetic fusion simulations.
method Stochastic augmented Lagrangian approach using pyTorch.
result Higher model prediction accuracy achieved compared to fixed penalty method.
Toolbox for stochastic Euler equations using Ebin-Marsden theory.
problem Applying geometric framework to stochastic PDEs.
method Combining infinite-dimensional geometry and stochastic analysis.
result Local well-posedness of maximal solutions for incompressible Euler equation with noise.
Improves posterior approximation speed for Dirichlet process mixture models.
problem Inefficiency of stochastic variational inference in large datasets.
method Uses stochastic gradient ascent with adaptive stepsize optimization.
result Adaptive stepsize improves speed and performance of posterior approximation.
New approach solves utility maximization problems using Delta family.
problem Utility maximization in stochastic control problems.
method Directly solving DP equation with Delta function representation.
result Explicit series representation of value function.
Novel framework discovers SPDEs from limited data.
problem Discovering SPDEs from limited data.
method Combines stochastic calculus, variational Bayes, and sparse learning.
result Accurately identifies SPDEs from limited data.
New approach handles stochastic and partially-observable environments using discrete autoencoders and Monte Carlo tree search.
problem Challenges in planning for stochastic and partially-observable environments.
method Uses discrete autoencoders and a stochastic variant of Monte Carlo tree search.
result Significantly outperforms MuZero on stochastic chess and scales to DeepMind Lab.
We develop a scalable method for Bayesian neural networks with stochastic differential equations.
problem Uncertainty quantification in deep neural networks.
method Gradient-based stochastic variational inference in continuous-depth Bayesian neural networks.
result Gradient estimator with zero variance as the approximation improves.
New issue found in value-based reinforcement learning for stochastic environments.
problem Value-based reinforcement learning struggles with stochastic state transitions.
method Demonstrated using a multiobjective Markov Decision Process (MOMDP).
result Approaches may converge to Pareto-dominated solutions instead of optimal ones.
Stochastic gradient descent outperforms traditional force-directed methods.
problem Improving graph layout quality and efficiency.
method Applying stochastic gradient descent for stress minimization.
result Stochastic gradient descent is simpler and more robust than traditional methods.
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
Deep learning solves complex stochastic control with jumps.
problem Solving high-dimensional stochastic control tasks with jumps.
method Model-based approach using two neural networks, iteratively trained with objectives derived from the Hamilton-Jacobi-Bellman equation.
result Demonstrates effectiveness in solving complex high-dimensional stochastic control tasks.
This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the practical relevance of the plain stochastic gradient approach and that drastic improvem…
Two new Frank-Wolfe algorithms improve convergence for constrained optimization.
problem Solving optimization problems with structured constraints in machine learning.
method Two new variants of the Frank-Wolfe (FW) method for stochastic finite-sum minimization.
result Best convergence guarantees for convex and non-convex objective functions.
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
problem Discovering explicit governing equations of stochastic dynamical systems with Lévy noise from data.
method ESSR approach using genetic programming, sparse regression, and nonlocal Kramers-Moyal formulas.
result The approach effectively extracts non-Gaussian stochastic dynamical systems from sample path data.
Develops a new method for financial term structure modeling.
problem Analyzing financial term structures with discontinuities.
method Cylindrical stochastic integration approach.
result Establishes a Heath-Jarrow-Morton framework.
A new method for high-dimensional RBDO using stochastic emulators.
problem Efficient RBDO in high-dimensional settings.
method Unified stochastic representation, stochastic emulators, deterministic mapping.
result Significant computational gains in high-dimensional settings.
New method optimizes sensor placement for stochastic systems efficiently.
problem Optimizing sensor placements for black-box stochastic systems with computational constraints.
method Trains a joint energy-based model on simulation data to learn parameter and solution distributions, allowing efficient sensor placement.
result Demonstrates lower computational cost and more informative sensor locations compared to conventional approaches.
Develops a new method to discover stochastic systems with non-Gaussian noise.
problem Discovering governing laws from complex systems with non-Gaussian noise.
method Theoretical framework and numerical algorithm to extract stochastic differential equations with Gaussian and non-Gaussian noise.
result Demonstrated the efficacy and accuracy of the approach on various systems.
Unified approach to stochastic Volterra systems' deviations.
problem Large and moderate deviations for stochastic Volterra systems.
method Weak convergence approach by Budhijara, Dupuis and Ellis.
result Unified treatment of deviations for a broad class of stochastic Volterra equations.
Deep learning model approximates stochastic responses.
problem Approximating stochastic responses using neural networks.
method Generative neural network with conditional maximum mean discrepancy (CMMD) loss.
result Excellent performance on benchmark problems.
An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within a specified interval. The complete algorithm---which dynamically chooses whethe…
The paper solves investment problems with uncertain factors using game theory.
problem Optimal forward investment in an incomplete market with model uncertainty.
method Combining stochastic differential games and ergodic BSDE approach.
result Representation of robust forward performance processes in factor form.
In this note, we extend an evolutionary stochastic portfolio optimization framework to include probabilistic constraints. Both the stochastic programming-based modeling environment as well as the evolutionary optimization environment are ideally suited for an integration of various types of probabilistic constraints. W…
PALS extends PAL for optimizing stochastic simulators efficiently.
problem Optimizing stochastic simulators with high output variance and expensive evaluations.
method Bayesian optimization with probabilistic models, extending PAL for stochastic settings.
result PALS outperforms other methods in optimizing stochastic simulators.
Deep neural networks have dramatically achieved great success on a variety of challenging tasks. However, most successful DNNs have an extremely complex structure, leading to extensive research on model compression.As a significant area of progress in model compression, traditional gradual pruning approaches involve an…
We introduce a fully stochastic gradient based approach to Bayesian optimal experimental design (BOED). Our approach utilizes variational lower bounds on the expected information gain (EIG) of an experiment that can be simultaneously optimized with respect to both the variational and design parameters. This allows the …
Stochastic models analyze traffic network performance.
problem Evaluate traffic system performance.
method Stochastic cell transmission models, preference functionals, Gaussian process regression.
result Illustrated in two case studies.
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaim, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of a…
A new stochastic method handles ensemble creation with cost constraints.
problem Creating ensembles under cost limitations in decision-making.
method Introducing a novel stochastic approach to solve the knapsack problem.
result The approach efficiently incorporates ensemble accuracy and cost constraints.
Develops a GMM method to estimate roughness in stochastic volatility models.
problem Estimating roughness in stochastic volatility models with fractional Brownian motion.
method GMM approach for log-normal models with integrated variance and noisy realized variance.
result Consistent and asymptotically normal parameter estimator with bias correction.
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory shows these optimization methods can converge by using an unbiased gradient estimat…
Investor optimizes worst-case portfolio in uncertain markets.
problem Optimizing investment in markets with potential crashes.
method Enhanced martingale approach via BSDEs and PDEs.
result Characterized indifference optimal strategies for various models.
New approach uses SGLD to minimize CVaR for portfolio weights.
problem Minimizing CVaR for portfolio weights with complete theoretical guarantees.
method Stochastic Gradient Langevin Dynamics (SGLD) with discontinuous updating.
result Theoretical guarantees for convergence in Wasserstein distances for convex and non-convex functions.
This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equat…
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.
New method assesses financial and cyber risks under uncertainty.
problem Uncertainty in risk assessment for financial and cyber systems.
method Combines stochastic approximation and distorted mix method to compute worst case average value at risk.
result Efficient algorithm for tail uncertainty in multivariate distributions.
New EI strategies using OWA and SSD for excess return.
problem Selecting EI portfolios that stochastically dominate a benchmark.
method Proposes a new OWA-based EI model and introduces a new SSD criterion.
result OWA-based EI portfolios stochastically dominate a benchmark and generate excess return.
The paper solves TIC LQ control problems using stochastic differential games.
problem Time-inconsistent linear-quadratic stochastic control problems.
method Stochastic differential games, spike variation approach.
result Achieves Nash equilibrium for TIC problems, demonstrating impact of ambiguity aversion.
Paper introduces multitask neural networks for efficient stochastic control problems.
problem Infeasibility of simulating state variables in some stochastic control problems.
method Multitask neural networks with dynamic task balancing.
result Multitask neural networks outperform state-of-the-art approaches in derivatives pricing problems.
We consider the problem of multi-class classification and a stochastic opti- mization approach to it. We derive risk bounds for stochastic mirror descent algorithm and provide examples of set geometries that make the use of the algorithm efficient in terms of error in k.