sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
New method uses backward SDEs for deep learning uncertainty.
problem Uncertainty quantification in deep learning models.
method Probabilistic machine learning with stochastic neural networks and stochastic optimal control.
result Effectiveness validated through numerical experiments.
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic approximation theorems typically possess assumptions which are difficult to communicate an…
Paper improves learning rates for SGD and NAG.
problem Generalization performance of stochastic optimization algorithms.
method Establishes new learning rates for SGD and NAG.
result Improved guarantees in some settings or comparable rates under weaker assumptions.
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.
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.
New method learns stochastic process representations without exact reconstruction.
problem Learning exact representations of high-dimensional noisy stochastic processes.
method CReSP framework for contrastive learning of stochastic processes.
result Effective for learning representations of various stochastic processes.
Stochasticity is key for machine learning's robustness and generalizability.
problem Machine learning's need for robustness and generalizability.
method Review of ML literature and biological intelligence.
result Stochasticity is a critical ingredient for intelligent systems in ML.
Proposes SPFB method for optimizing partition functions in stochastic learning.
problem Optimizing partition functions in stochastic learning settings.
method Stochastic Gradient Bound (SPFB) method based on upper-bounding the partition function with a quadratic surrogate.
result Sub-linear convergence rate of SPFB method and efficient training of deep learning models.
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.
Paper examines the structure of stochastic gradients in deep learning.
problem Exploring the structure and heavy tails of stochastic gradients in deep learning.
method Conducted formal statistical tests on stochastic gradients and gradient noise.
result Stochastic gradients and gradient noise do not exhibit power-law heavy tails, but their covariance spectra do.
SALSA automatically adjusts learning rates in stochastic gradient methods.
problem Automatic adjustment of learning rates in stochastic gradient methods.
method SALSA uses a line-search procedure to gradually increase the learning rate, then a statistical test to decrease it.
result SALSA matches the performance of best hand-tuned learning rate schedules in deep learning tasks.
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.
GenFormer uses deep learning to generate complex stochastic data.
problem Creating synthetic stochastic data that matches real-world statistical properties.
method Transformer-based deep learning model that maps Markov state sequences to time series values.
result GenFormer preserves target marginal distributions and other statistical properties in multivariate spatio-temporal data.
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.
Study on test risk dynamics in learning theory with stochastic gradient flow.
problem Understanding test risk in stochastic gradient flow dynamics.
method Path integral formulation for small learning rates, explicit computation for weak features.
result Explicit corrections due to stochastic term in dynamics, good agreement with simulations.
Overview of non-stochastic-gradient SA algorithms in signal processing and ML.
problem Dealing with large data sets and uncertainties in signal processing and machine learning.
method General framework of SA algorithms using Lyapunov functions.
result Unified convergence properties of non-stochastic-gradient algorithms.
New learnability criteria for non-iid processes equivalent to online learning.
problem Statistical learning under non-iid stochastic processes is underdeveloped.
method Defined two learnability notions and showed their equivalence to online learning.
result Learnability criteria for non-iid processes are equivalent to online learning.
This work learns effective dynamics from short-term data of stochastic systems.
problem Learning effective dynamics from short-term data of stochastic systems.
method Proposes a novel algorithm using a neural network (Auto-SDE) to learn invariant slow manifold from data.
result Validated through numerical experiments to be accurate, stable, and effective.
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.
Analyzes non-Markovian environments in stochastic approximation.
problem Understanding learning mechanisms in non-ergodic, non-Markovian settings.
method Analytic framework for transformer learning and continual learning.
result Proposes a new approach to transformer and continual learning.
VSDN models sporadic time series with neural SDEs.
problem Modeling irregular and sparse time series data.
method Variational Bayesian method and neural SDEs.
result VSDNs outperform state-of-the-art models in prediction and interpolation.
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.
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive gradient) methods are the two main techniques to improve the slow convergence of \text…
NOVAS uses adaptive stochastic search for non-convex optimization in deep networks.
problem Non-convex optimization challenges in deep neural networks.
method Adaptive stochastic search for non-convex optimization.
result NOVAS outperforms existing alternatives in a structured prediction task.
LASG improves communication efficiency in distributed learning.
problem Efficiently communicating gradients in distributed machine learning.
method Develops a new stochastic gradient descent approach, LASG, that predicts and selects significant communication rounds.
result Achieves communication savings by an order of magnitude in federated learning.
New model solves complex SDEs with high-dimensional spatial and stochastic spaces.
problem Solving SDEs with high-dimensional spatial and stochastic spaces.
method Physics-informed deep generative model (sPI-GeM) combining PI-BasisNet and PI-GeM.
result Scalable solution for high-dimensional SDE problems.
A new stochastic method tackles bi-level optimization problems in deep learning.
problem Bi-level optimization problems in deep learning, including hyperparameter optimization and meta learning.
method Turning a BLO problem into a stochastic optimization, using SGLD MCMC and a recurrent algorithm to compute MC-estimated hypergradient.
result Our method is more robust to suboptimal inner optimization and non-unique inner minima, leading to more reliable solutions.
A machine learning framework predicts self-induced stochastic resonance in neurons.
problem Predicting coherent oscillations in slow-fast excitable systems driven by noise.
method Physics-informed machine learning with a Noise-Augmented State Predictor architecture and Kramers' escape theory constraints.
result Trained PINN accurately predicts spike-train coherence on noise intensity, excitability, and timescale separation.
Unified analysis of stochastic iterative algorithms using Lyapunov functions.
problem Analyzing convergence of stochastic iterative algorithms for fixed-point equations.
method Lyapunov-based techniques for finite-time analysis of stochastic approximation algorithms.
result Unified mean-square convergence guarantees for various algorithms.
New convergence guarantees for learning with unknown nuisance parameters.
problem Learning problems with unknown nuisance parameters.
method Stochastic gradient optimization with Neyman orthogonality and approximately orthogonalized updates.
result Stochastic gradient algorithms can converge under conditions of nuisance parameters.
Paper proves large deviation principle for stochastic approximations.
problem Asymptotic estimates of learning algorithm deviations.
method Weak convergence approach to large deviations.
result Identifies appropriate scaling sequence and new representation for rate function.
SON learns SPDE solutions and uncertainty from noisy data.
problem Uncertainty quantification in SPDEs with unknown model uncertainties.
method Combining DeepONet and SNNs, SON models stochasticity and predicts uncertainty.
result SON accurately captures solution structure and quantifies predictive uncertainty.
Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the noise in stochastic estimates of the gradients. In this paper, we propose a new ad…
Study on stochastic hypergradient computation for machine learning problems.
problem Efficient computation of hypergradients in machine learning models.
method Stochastic approximation schemes for hypergradient computation, focusing on empirical risk minimization.
result Bounds for the mean square error of hypergradient approximation under contraction assumptions.
Paper proposes a reinforcement learning framework for efficient hyper-parameter tuning of stochastic optimization algorithms.
problem Efficient tuning of hyper-parameters for stochastic optimization algorithms.
method Modeling hyper-parameter tuning as a Markov decision process and using policy gradient algorithms.
result The proposed framework significantly reduces the time required for hyper-parameter tuning compared to Bayesian optimization.
Paper establishes convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
problem Analyzing convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
method Novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing length.
result First almost sure convergence rate and maximal concentration bound with exponential tails for contractive stochastic approximation algorithms with Markovian noise.
Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a …
Paper proves deep learning method for stochastic control converges and outperforms existing algorithms.
problem Formulating and solving stochastic control problems using FBSDE and SMP.
method Deep learning algorithm based on SMP, with convergence proof and error bounds.
result Deep SMP-BSDE algorithm converges and outperforms existing methods in high-dimensional stochastic control problems.
Paper tackles active labeling for partial supervision.
problem Accessing stochastic gradients with partial supervision.
method Streaming technique to minimize generalization error.
result Proves minimization of generalization error ratio.
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning scenarios. In this paper, we provide dynamic programming algorithms for the comput…
In reinforcement learning episodes, the rewards and punishments are often non-deterministic, and there are invariably stochastic elements governing the underlying situation. Such stochastic elements are often numerous and cannot be known in advance, and they have a tendency to obscure the underlying rewards and punishm…
Introduces a new stochastic optimization method for deep learning.
problem Minimizing loss functions in deep neural networks.
method Introduces a second-order stochastic Runge-Kutta method and an adaptive SGD-G2.
result The method yields consistent minimization of loss functions and automatically adjusts learning rates.
Unified view of federated learning and distributed RL using local stochastic approximation.
problem Finding the root of an operator composed of local operators in a network of agents with dependent data.
method Local stochastic approximation over a network of agents with Markov process-dependent data.
result Convergence rates of local stochastic approximation for both constant and time-varying step sizes, within a logarithmic factor of independent data.
In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The sto…
A new ML algorithm solves complex economic control problems.
problem Solving high-dimensional, finite-horizon stochastic control problems in economics.
method Deep neural network representation of optimal policy functions with three key features.
result Efficiently solves various economic control problems including recursive utility and growth models.
Paper introduces a new multi-kernel algorithm for better gradient approximation.
problem Improving gradient approximation in high-dimensional problems.
method Develops a multi-kernel passive stochastic gradient algorithm with variance reduction.
result The multi-kernel algorithm performs better in high-dimensional problems.