A Stochastic Approximation Method

1951/09/01 by Herbert Robbins, Sutton Monro · 637 citations
Decision Sciences · #Optimal Experimental Design Methods

paper · pdf · doi:10.1214/aoms/1177729586

Abstract

Let M(x) denote the expected value at level x of the response to a certain experiment. M(x) is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = θ of the equation M(x) = α, where α is a given constant. We give a method for making successive experiments at levels x₁,x₂,⋯ in such a way that x_n will tend to θ in probability.

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• Stochastic Approximator of Motor Threshold (SAMT) for transcranial magnetic stimulation: Online software and its performance in clinical studies
• Variance Reduction for Evolution Strategies via Structured Control Variates
• Dual Control for Approximate Bayesian Reinforcement Learning
• Practical Quasi-Newton Methods for Training Deep Neural Networks
• Conditional Generative Modeling via Learning the Latent Space
• A Variant of Gradient Descent Algorithm Based on Gradient Averaging
• Asymptotic study of stochastic adaptive algorithm in non-convex\n landscape
• Characterization of Excess Risk for Locally Strongly Convex Population Risk
• Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit
• Integrating Stacked Intelligent Metasurfaces and Power Control for Dynamic Edge Inference via Over-The-Air Neural Networks
• Decentralized Control via Dynamic Stochastic Prices: The Independent System Operator Problem
• Differentiable Light Transport with Gaussian Surfels via Adapted Radiosity for Efficient Relighting and Geometry Reconstruction
• Antithetic variates in higher dimensions
• A consensus-based global optimization method for high dimensional machine learning problems
• Pathfinder: Parallel quasi-Newton variational inference
• Development of Deep Learning Optimizers: Approaches, Concepts, and Update Rules
• Faster On-Device Training Using New Federated Momentum Algorithm
• Zero-inflation in the Multivariate Poisson Lognormal Family
• Randomized Block Coordinate Descent for Online and Stochastic Optimization
• Graph Coloring for Multi-Task Learning
• The Root Finding Problem Revisited: Beyond the Robbins-Monro procedure
• Towards Robust Visual Continual Learning with Multi-Prototype Supervision
• Consciousness as a Functor
• VGG-TSwinformer: Transformer-based deep learning model for early Alzheimer’s disease prediction
• DIVEBATCH: Accelerating Model Training Through Gradient-Diversity Aware Batch Size Adaptation
• Bounding the expected run-time of nonconvex optimization with early stopping
• Almost sure convergence of dropout algorithms for neural networks
• Supervised and Unsupervised Deep Learning Applied to the Majority Vote Model
• Progressive Identification of True Labels for Partial-Label Learning
• Online Learning to Sample
• Dissecting Federated-Graph Aggregation under Domain Shift: Importance-Aware Aggregation via Empirical Analysis
• On Tackling High-Dimensional Nonconvex Stochastic Optimization via Stochastic First-Order Methods with Non-smooth Proximal Terms and Variance Reduction
• The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
• On the Convergence of SARAH and Beyond
• On the Convergence of Decentralized Adaptive Gradient Methods
• Accelerated Gradient Methods with Biased Gradient Estimates: Risk Sensitivity, High-Probability Guarantees, and Large Deviation Bounds
• Scaling Gaussian Processes with Derivative Information Using Variational Inference
• Extragradient method with variance reduction for stochastic variational inequalities
• Item Response Theory -- A Statistical Framework for Educational and Psychological Measurement
• A Unified Theory of SGD: Variance Reduction, Sampling, Quantization and\n Coordinate Descent
• Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programming
• On Empirical Comparisons of Optimizers for Deep Learning
• Learning Dependency-Based Compositional Semantics
• Artificial Neural Networks for Neuroscientists: A Primer
• A Multi-Batch L-BFGS Method for Machine Learning
• Revisiting the Polyak step size
• Optimal Subsampling for Data Streams with Measurement Constrained Categorical Responses
• Stochastic Neural Network with Kronecker Flow
• SVRG for Policy Evaluation with Fewer Gradient Evaluations
• Convergence Rate in Nonlinear Two-Time-Scale Stochastic Approximation with State (Time)-Dependence
• A Proximal Stochastic Gradient Method with Adaptive Step Size and Variance Reduction for Convex Composite Optimization
• Momentum-based variance-reduced proximal stochastic gradient method for composite nonconvex stochastic optimization
• Asymptotic distribution and convergence rates of stochastic algorithms\n for entropic optimal transportation between probability measures
• Heart Disease Prediction: A Comparative Study of Optimisers Performance in Deep Neural Networks
• Federated Optimization: Distributed Machine Learning for On-Device Intelligence
• Statistical Measures For Defining Curriculum Scoring Function
• Prescribe-then-Select: Adaptive Policy Selection for Contextual Stochastic Optimization
• SVN-ICP: Uncertainty Estimation of ICP-based LiDAR Odometry using Stein Variational Newton
• Online Robust and Adaptive Learning from Data Streams
• Stochastic Sign Descent Methods: New Algorithms and Better Theory
• Breaking the Conventional Forward-Backward Tie in Neural Networks: Activation Functions
• Stochastic Polyak Step-size for SGD: An Adaptive Learning Rate for Fast\n Convergence
• Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods
• History-Gradient Aided Batch Size Adaptation for Variance Reduced\n Algorithms
• Deep Learning for Markov Chains: Lyapunov Functions, Poisson's Equation, and Stationary Distributions
• An Interactive Framework for Finding the Optimal Trade-off in Differential Privacy
• A Study of Gradient Variance in Deep Learning
• Starting Small -- Learning with Adaptive Sample Sizes
• Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function
• Explicit Mean-Square Error Bounds for Monte-Carlo and Linear Stochastic Approximation
• Shuffling Heuristic in Variational Inequalities: Establishing New Convergence Guarantees
• Deep Gamblers: Learning to Abstain with Portfolio Theory
• An Overview of Lead and Accompaniment Separation in Music
• Learning Convex Optimization Control Policies
• EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings
• Network Implosion: Effective Model Compression for ResNets via Static Layer Pruning and Retraining
• Stochastic versus Deterministic in Stochastic Gradient Descent
• Learning Latent Space Energy-Based Prior Model
• GENO -- GENeric Optimization for Classical Machine Learning
• Understanding the Effects of Data Parallelism and Sparsity on Neural\n Network Training
• A Framework for Evaluating Gradient Leakage Attacks in Federated Learning
• Principled Design of Translation, Scale, and Rotation Invariant Variation Operators for Metaheuristics
• Online Sinkhorn: Optimal Transport distances from sample streams
• Convergence and Stability of the Stochastic Proximal Point Algorithm\n with Momentum
• GradES: Significantly Faster Training in Transformers with Gradient-Based Early Stopping
• Elastic Consistency: A General Consistency Model for Distributed Stochastic Gradient Descent
• Globally aware optimization with resurgence
• Proximal Backpropagation
• Distributed stochastic gradient tracking methods with momentum acceleration for non-convex optimization
• Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance
• Multiplicative noise and heavy tails in stochastic optimization
• A Contour Stochastic Gradient Langevin Dynamics Algorithm for Simulations of Multi-modal Distributions
• Accelerated, Optimal, and Parallel: Some Results on Model-Based Stochastic Optimization
• CNN with large memory layers
• Solutions for Mitotic Figure Detection and Atypical Classification in MIDOG 2025
• Extreme MRI: Large-Scale Volumetric Dynamic Imaging from Continuous Non-Gated Acquisitions
• Stochastic Online Feedback Optimization for Networks of Non-Compliant Agents
• Convergence of regularized agent-state-based Q-learning in POMDPs
• Calibrating generalized predictive distributions
• Revisit Stochastic Gradient Descent for Strongly Convex Objectives: Tight Uniform-in-Time Bounds
• A Twin Neural Model for Uplift
• The Impact of Neural Network Overparameterization on Gradient Confusion\n and Stochastic Gradient Descent
• Combined Stochastic and Robust Optimization for Electric Autonomous Mobility-on-Demand with Nested Benders Decomposition
• Federated Consistency- and Complementarity-aware Consensus-enhanced Recommendation
• A Model-agnostic Strategy to Mitigate Embedding Degradation in Personalized Federated Recommendation
• Backprop with Approximate Activations for Memory-efficient Network Training
• Renewable Quantile Regression with Heterogeneous Streaming Datasets
• Implicit particle filters for data assimilation
• GRADSTOP: Early Stopping of Gradient Descent via Posterior Sampling
• Learning with springs and sticks
• Dissipativity Theory for Accelerating Stochastic Variance Reduction: A Unified Analysis of SVRG and Katyusha Using Semidefinite Programs
• A Neural Network-Based On-device Learning Anomaly Detector for Edge Devices
• Variational Wasserstein Barycenters with c-Cyclical Monotonicity
• The Emergence of Compositional Languages for Numeric Concepts Through Iterated Learning in Neural Agents
• Optimal Auction Design for the Gradual Procurement of Strategic Service\n Provider Agents
• Universal Reinforcement Learning in Coalgebras: Asynchronous Stochastic Computation via Conduction
• Natural Compression for Distributed Deep Learning
• Information Directed Sampling for Sparse Linear Bandits
• Network formation in the interbank money market: An application of the actor-oriented model
• Explainable Learning Rate Regimes for Stochastic Optimization
• Beyond the Mean: Fisher-Orthogonal Projection for Natural Gradient Descent in Large Batch Training
• Learning dynamical systems with particle stochastic approximation EM
• Optimization problems for machine learning: A survey
• Stochastic Gradient Hamiltonian Monte Carlo with Variance Reduction for Bayesian Inference
• An Iterative Bayesian Robbins--Monro Sequence
• The Discrete Infinite Logistic Normal Distribution
• Enabling scalable stochastic gradient-based inference for Gaussian\n processes by employing the Unbiased LInear System SolvEr (ULISSE)
• Search of RRATs on declinations from +42^∘ to +55^∘ with a neural network
• Graph Neural Diffusion via Generalized Opinion Dynamics
• Contrastive Weight Regularization for Large Minibatch SGD
• SPAN: A Stochastic Projected Approximate Newton Method
• Belief Flows of Robust Online Learning
• A learning-driven automatic planning framework for proton PBS treatments of H&N cancers
• Hybrid Stochastic-Deterministic Minibatch Proximal Gradient: Less-Than-Single-Pass Optimization with Nearly Optimal Generalization
• Condition Number Analysis of Logistic Regression, and its Implications\n for Standard First-Order Solution Methods
• On the mean field limit of the Random Batch Method for interacting particle systems
• WeatherPrompt: Multi-modality Representation Learning for All-Weather Drone Visual Geo-Localization
• Natural Analysts in Adaptive Data Analysis
• How much progress have we made in neural network training? A New Evaluation Protocol for Benchmarking Optimizers
• Audio-Visual Speech Enhancement: Architectural Design and Deployment Strategies
• \(X\)-evolve: Solution space evolution powered by large language models
• Online Convex Optimization with Heavy Tails: Old Algorithms, New Regrets, and Applications
• Sample-Efficient Reinforcement Learning for Linearly-Parameterized MDPs with a Generative Model
• Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators
• Adaptive Weight Decay for Deep Neural Networks
• High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation
• Adaptive Batch Size and Learning Rate Scheduler for Stochastic Gradient Descent Based on Minimization of Stochastic First-order Oracle Complexity
• Generalized Inner Loop Meta-Learning
• ULU: A Unified Activation Function
• Compressed Decentralized Momentum Stochastic Gradient Methods for Nonconvex Optimization
• No Masks Needed: Explainable AI for Deriving Segmentation from Classification
• Neural Network Training via Stochastic Alternating Minimization with Trainable Step Sizes
• CSG: A stochastic gradient method for a wide class of optimization\n problems appearing in a machine learning or data-driven context
• QuantNet: Learning to Quantize by Learning within Fully Differentiable Framework
• Accelerating SGDM via Learning Rate and Batch Size Schedules: A Lyapunov-Based Analysis
• Breaking the Top-K Barrier: Advancing Top-K Ranking Metrics Optimization in Recommender Systems
• SGD for Structured Nonconvex Functions: Learning Rates, Minibatching and\n Interpolation
• Computationally efficient Gauss-Newton reinforcement learning for model predictive control
• SGD momentum optimizer with step estimation by online parabola model
• Server Averaging for Federated Learning
• Stochastic Reweighted Gradient Descent
• Soft Separation and Distillation: Toward Global Uniformity in Federated Unsupervised Learning
• Training Deep Neural Networks by optimizing over nonlocal paths in\n hyperparameter space
• Neighbor-Sampling Based Momentum Stochastic Methods for Training Graph Neural Networks
• Advancing Welding Defect Detection in Maritime Operations via Adapt-WeldNet and Defect Detection Interpretability Analysis
• EMA Without the Lag: Bias-Corrected Iterate Averaging Schemes
• Stochastic variance reduced multiplicative update for nonnegative matrix factorization
• FADO: A Deterministic Detection/Learning Algorithm
• Popov Mirror-Prox Method for Variational Inequalities
• Formal Bayesian Transfer Learning via the Total Risk Prior
• Investigating the Invertibility of Multimodal Latent Spaces: Limitations of Optimization-Based Methods
• Personalized Dynamic Treatment Regimes in Continuous Time: A Bayesian Approach for Optimizing Clinical Decisions with Timing
• Quantifying the mini-batching error in Bayesian inference for Adaptive Langevin dynamics
• Do We Need Zero Training Loss After Achieving Zero Training Error?
• Explaining Natural Language Processing Classifiers with Occlusion and Language Modeling
• Event-driven contrastive divergence for spiking neuromorphic systems. [europepmc]
• A Unifying Probabilistic View of Associative Learning. [europepmc]
• Midbrain Synchrony to Envelope Structure Supports Behavioral Sensitivity to Single-Formant Vowel-Like Sounds in Noise. [europepmc]
• Cerebellar learning using perturbations. [europepmc]
• RPITER: A Hierarchical Deep Learning Framework for ncRNA⁻Protein Interaction Prediction. [europepmc]
• Deeper Profiles and Cascaded Recurrent and Convolutional Neural Networks for state-of-the-art Protein Secondary Structure Prediction. [europepmc]
• DeepPoseKit, a software toolkit for fast and robust animal pose estimation using deep learning. [europepmc]
• Knowing What You Know in Brain Segmentation Using Bayesian Deep Neural Networks. [europepmc]
• Classification of brain tumor isocitrate dehydrogenase status using MRI and deep learning. [europepmc]
• LRRpredictor-A New LRR Motif Detection Method for Irregular Motifs of Plant NLR Proteins Using an Ensemble of Classifiers. [europepmc]
• Modern Soft-Sensing Modeling Methods for Fermentation Processes. [europepmc]
• A deep learning based framework for the registration of three dimensional multi-modal medical images of the head. [europepmc]
• Practices and Applications of Convolutional Neural Network-Based Computer Vision Systems in Animal Farming: A Review. [europepmc]
• MSU-Net: Multi-Scale U-Net for 2D Medical Image Segmentation. [europepmc]
• EDLMFC: an ensemble deep learning framework with multi-scale features combination for ncRNA-protein interaction prediction. [europepmc]
• Using smart speakers to contactlessly monitor heart rhythms. [europepmc]
• Classification of Diffuse Glioma Subtype from Clinical-Grade Pathological Images Using Deep Transfer Learning. [europepmc]
• AI in drug development: a multidisciplinary perspective. [europepmc]
• Advancements in Oncology with Artificial Intelligence-A Review Article. [europepmc]
• Pre-trained deep learning models for brain MRI image classification. [europepmc]
• Automated Classification of Brain Tumors from Magnetic Resonance Imaging Using Deep Learning. [europepmc]
• Compact optical convolution processing unit based on multimode interference. [europepmc]
• Developmental changes in exploration resemble stochastic optimization. [europepmc]
• Three novel methods for determining motor threshold with transcranial magnetic stimulation outperform conventional procedures. [europepmc]
• Brain Tumor Classification from MRI Using Image Enhancement and Convolutional Neural Network Techniques. [europepmc]

Related

• Stochastic Estimation of the Maximum of a Regression Function
• Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea
• Asymptotic Variance in the Central Limit Theorem for Multilevel Markovian Stochastic Approximation
• Multi-level stochastic approximation algorithms
• General multilevel adaptations for stochastic approximation algorithms