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Optimization algorithm
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate
Gradient_descent
Optimization algorithm
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e
Stochastic_gradient_descent
Decentralized machine learning
dataset and then used to make one step of the gradient descent. Federated stochastic gradient descent is the analog of this algorithm to the federated
Federated_learning
Mathematical optimization algorithm
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose
Conjugate_gradient_method
Machine learning technique
introduced the view of boosting algorithms as iterative functional gradient descent algorithms. That is, algorithms that optimize a cost function over
Gradient_boosting
Transforms equations for numerical solution
grids. If used in gradient descent methods, random preconditioning can be viewed as an implementation of stochastic gradient descent and can lead to faster
Preconditioner
Inequality from distance to a zero of a real analytic function
condition C in ), is commonly used to prove linear convergence of gradient descent algorithms. This section is based on Karimi, Nutini & Schmidt (2016)
Łojasiewicz_inequality
Optimization algorithm for artificial neural networks
model parameters in the negative direction of the gradient, such as by stochastic gradient descent, or as an intermediate step in a more complicated optimizer
Backpropagation
Mathematical optimization method
Armijo–Goldstein condition. Backtracking line search is typically used for gradient descent (GD), but it can also be used in other contexts. For example, it can
Backtracking_line_search
Type of kernel induced by artificial neural networks
methods: gradient descent in the infinite-width limit is fully equivalent to kernel gradient descent with the NTK. As a result, using gradient descent to minimize
Neural_tangent_kernel
Multivariate derivative (mathematics)
intelligence, where it is used to minimize a function by gradient descent. In coordinate-free terms, the gradient of a function f ( r ) {\displaystyle f(\mathbf
Gradient
Method of machine learning
out-of-core versions of machine learning algorithms, for example, stochastic gradient descent. When combined with backpropagation, this is currently the de facto
Online_machine_learning
Structuring text as input to generative artificial intelligence
searched directly by gradient descent to maximize the log-likelihood on outputs. An earlier result uses the same idea of gradient descent search, but is designed
Prompt_engineering
Machine learning model training problem
In machine learning, the vanishing gradient problem is the problem of greatly diverging gradient magnitudes between earlier and later layers encountered
Vanishing_gradient_problem
Machine learning technique for privacy-preserving training
Differentially private stochastic gradient descent (DP-SGD) is an algorithmic technique for learning and a refined analysis of privacy costs within the
Differentially private stochastic gradient descent
Differentially_private_stochastic_gradient_descent
Set of methods for supervised statistical learning
traditional gradient descent (or SGD) methods can be adapted, where instead of taking a step in the direction of the function's gradient, a step is taken
Support_vector_machine
Theorem of probability theory
This form has applications in Stein variational gradient descent and Stein variational policy gradient. The univariate probability density function for
Stein's_lemma
Intelligence of machines
problem. It begins with some form of guess and refines it incrementally. Gradient descent is a type of local search that optimizes a set of numerical parameters
Artificial_intelligence
Method for finding stationary points of a function
{\displaystyle \mu } and small Hessian, the iterations will behave like gradient descent with step size 1 / μ {\displaystyle 1/\mu } . This results in slower
Newton's method in optimization
Newton's_method_in_optimization
Iterative method used to solve a linear system of equations
semi-definite matrix, so it has no negative eigenvalues. A step of gradient descent is x ( k + 1 ) = x ( k ) − t ∇ F ( x ( k ) ) = x ( k ) − t ( A x (
Modified_Richardson_iteration
Method in machine learning
overfitting when training a model with an iterative method, such as gradient descent. Such methods update the model to make it better fit the training data
Early_stopping
Microsoft open source gradient boosting framework for machine learning
LightGBM, short for Light Gradient-Boosting Machine, is a free and open-source distributed gradient-boosting framework for machine learning, originally
LightGBM
Class of artificial neural network
continuous time. A major problem with gradient descent for standard RNN architectures is that error gradients vanish exponentially quickly with the size
Recurrent_neural_network
Russian mathematician
contribution is an accelerated version of gradient descent that converges considerably faster than ordinary gradient descent (commonly referred as Nesterov momentum
Yurii_Nesterov
Form of artificial intelligence
with conventional deep learning techniques that use backpropagation (gradient descent on a neural network) with a fixed topology. Many neuroevolution algorithms
Neuroevolution
Concept in mathematics
as gradient descent and multiplicative weights. Mirror descent was originally proposed by Nemirovski and Yudin in 1983. In gradient descent with the sequence
Mirror_descent
Technique used in stochastic gradient variational inference
computation of gradients through random variables, enabling the optimization of parametric probability models using stochastic gradient descent, and the variance
Reparameterization_trick
Type of feedforward neural network
reported the first multilayered neural network trained by stochastic gradient descent, was able to classify non-linearily separable pattern classes. Amari's
Multilayer_perceptron
Algorithm used to solve non-linear least squares problems
interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in many cases
Levenberg–Marquardt_algorithm
Object detection system
with the highest IoU with the ground truth bounding boxes is used for gradient descent. Concretely, let j {\displaystyle j} be that predicted bounding box
You_Only_Look_Once
Gradient descent learning rule in machine learning
In machine learning, the delta rule is a gradient descent learning rule for updating the weights of the inputs to artificial neurons in a single-layer
Delta_rule
the gradient of the function at the current point. Examples of gradient methods are the gradient descent and the conjugate gradient. Gradient descent Stochastic
Gradient_method
Computer optimization methods
Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies
Proximal gradient methods for learning
Proximal_gradient_methods_for_learning
Adaptive boosting based classification algorithm
_{i}\phi (i,y,f)=\sum _{i}\ln \left(1+e^{-y_{i}f(x_{i})}\right).} In the gradient descent analogy, the output of the classifier for each training point is considered
AdaBoost
Technique for the generative modeling of a continuous probability distribution
walker) and gradient descent down the potential well. The randomness is necessary: if the particles were to undergo only gradient descent, then they will
Diffusion_model
Computational model used in machine learning
first deep learning multilayer perceptron (MLP) trained by stochastic gradient descent was published in 1967 by Shun'ichi Amari. In computer experiments conducted
Neural network (machine learning)
Neural_network_(machine_learning)
Technique to make a model more generalizable and transferable
including stochastic gradient descent for training deep neural networks, and ensemble methods (such as random forests and gradient boosted trees). In explicit
Regularization_(mathematics)
Optimization and sampling technique
Stochastic gradient Langevin dynamics (SGLD) is an optimization and sampling technique composed of characteristics from Stochastic gradient descent, a Robbins–Monro
Stochastic gradient Langevin dynamics
Stochastic_gradient_Langevin_dynamics
3D reconstruction technique
between the predicted image and the original image can be minimized with gradient descent over multiple viewpoints, encouraging the MLP to develop a coherent
Neural_radiance_field
Model-free reinforcement learning algorithm
}\left(s_{t}\right)-{\hat {R}}_{t}\right)^{2}} typically via some gradient descent algorithm. Like all policy gradient methods, PPO is used for training an RL agent whose
Proximal_policy_optimization
Evolutionary algorithm
search steps is increased. Both updates can be interpreted as a natural gradient descent. Also, in consequence, the CMA conducts an iterated principal components
CMA-ES
Class of reinforcement learning algorithms
Policy gradient methods are a class of reinforcement learning algorithms and a sub-class of policy optimization methods. Unlike value-based methods which
Policy_gradient_method
Deep learning method
possible neural network functions. The standard strategy of using gradient descent to find the equilibrium often does not work for GAN, and often the
Generative adversarial network
Generative_adversarial_network
Computer vision framework
in the negative gradient of the point with controlled step size γ {\displaystyle \gamma } to find local minima. This gradient-descent minimization can
Active_contour_model
Machine learning technique
function are trained by minimizing some loss function, generally via gradient descent. There is much freedom in choosing the precise form of experts, the
Mixture_of_experts
Mathematical term
In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. It is commonly denoted by the letter m
Slope
landscape correspond to regions of high data density. QC then uses gradient descent to move each data point 'downhill' in the landscape, causing points
Quantum_clustering
Algorithm for finding a local minimum of a function
Davidon–Fletcher–Powell Symmetric rank-one (SR1) Other methods Conjugate gradient Gauss–Newton Gradient Mirror Levenberg–Marquardt Powell's dog leg method Truncated
Powell's_method
Recurrent neural network architecture
type of recurrent neural network (RNN) aimed at mitigating the vanishing gradient problem commonly encountered by traditional RNNs. Its relative insensitivity
Long_short-term_memory
Machine learning technique
used only during training, and not outside of training. The PPO uses gradient descent on the following clipped surrogate advantage: L PPO ( ϕ ) := E x ∼
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
Research field that lies at the intersection of machine learning and computer security
no means an exhaustive list). Gradient-based evasion attack Fast Gradient Sign Method (FGSM) Projected Gradient Descent (PGD) Carlini and Wagner (C&W)
Adversarial_machine_learning
Mathematical algorithm
coordinate descent algorithm Conjugate gradient – Mathematical optimization algorithmPages displaying short descriptions of redirect targets Gradient descent –
Coordinate_descent
French mathematician and computer scientist
machine learning and data compression. His work presents stochastic gradient descent as a fundamental learning algorithm. He is also one of the main creators
Léon_Bottou
Type of neural network which utilizes recursion
nodes in the tree. Typically, stochastic gradient descent (SGD) is used to train the network. The gradient is computed using backpropagation through
Recursive_neural_network
Filling in missing entries of a matrix
X , Y ) {\displaystyle G(X,Y)} is some regularization function by gradient descent with line search. Initialize X , Y {\displaystyle X,\;Y} at X 0 , Y
Matrix_completion
Method of improving artificial neural network
problem achieves a linear convergence rate in gradient descent, which is faster than the regular gradient descent with only sub-linear convergence. Denote
Batch_normalization
Deep learning generative model to encode data representation
for simplicity. In such a case, the variance can be optimized with gradient descent. To optimize this model, one needs to know two terms: the "reconstruction
Variational_autoencoder
Computer vision framework
Gradient vector flow (GVF), a computer vision framework introduced by Chenyang Xu and Jerry L. Prince, is the vector field that is produced by a process
Gradient_vector_flow
Statistical algorithm
(difference between the desired and the actual signal). It is a stochastic gradient descent method in that the filter is only adapted based on the error at the
Least_mean_squares_filter
Method used to normalize the range of independent variables
final distance. Another reason why feature scaling is applied is that gradient descent converges much faster with feature scaling than without it. It's also
Feature_scaling
Game-playing artificial intelligence
Reinforcement learning Supervised learning Unsupervised learning Gradient descent Stochastic gradient descent Local search (Texel tuning) Graph and tree search algorithms
MuZero
Method of estimating the parameters of a statistical model, given observations
\left({\widehat {\theta }}_{r};\mathbf {y} \right)} Gradient descent method requires to calculate the gradient at the r-th iteration, but no need to calculate
Maximum_likelihood_estimation
Type of feedforward neural network
first CNN utilizing weight sharing in combination with a training by gradient descent, using backpropagation. Thus, while also using a pyramidal structure
Convolutional_neural_network
Type of artificial neural network
{E}}(n)={\frac {1}{2}}\sum _{{\text{output node }}j}e_{j}^{2}(n).} Using gradient descent, the change in each weight w i j {\displaystyle w_{ij}} is Δ w j i
Feedforward_neural_network
Concept in mathematics
its gradient ∇ x f {\displaystyle \nabla _{x}f} indicates the direction of maximum increase. One simply starts in the opposite (steepest descent) direction:
Nonlinear conjugate gradient method
Nonlinear_conjugate_gradient_method
Representation learning method
stuck at local minima. One can also apply a widespread stochastic gradient descent method with iterative projection to solve this problem. The idea of
Sparse_dictionary_learning
Game-playing artificial intelligence
Reinforcement learning Supervised learning Unsupervised learning Gradient descent Stochastic gradient descent Local search (Texel tuning) Graph and tree search algorithms
AlphaZero
Branch of machine learning
The first deep learning multilayer perceptron trained by stochastic gradient descent was published in 1967 by Shun'ichi Amari. In computer experiments conducted
Deep_learning
System for rating game players
{if}}~{\mathsf {B}}~{\textrm {wins}},\end{cases}}} and, using the stochastic gradient descent the log loss is minimized as follows: R A ← R A − η d ℓ d R A {\displaystyle
Elo_rating_system
Tasks in machine learning
method, for example using optimization methods such as gradient descent or stochastic gradient descent. In practice, the training data set often consists
Training, validation, and test data sets
Training,_validation,_and_test_data_sets
2017 research paper by Google
weights" or "dynamic links" (1981). A slow neural network learns by gradient descent to generate keys and values for computing the weight changes of the
Attention_Is_All_You_Need
Mathematical optimization function
continuously differentiable. Indeed, many proximal gradient methods can be interpreted as a gradient descent method over M f {\displaystyle M_{f}} . The Moreau
Moreau_envelope
Gradient boosting machine learning library
XGBoost works as Newton–Raphson in function space unlike gradient boosting that works as gradient descent in function space, a second order Taylor approximation
XGBoost
Technique in statistics
developing of information-geometric optimization methods (mirror descent and natural gradient descent). The standard references in the field are Shun’ichi Amari
Information_geometry
Optimization algorithm
differs from gradient descent methods, which adjust all of the values in x {\displaystyle \mathbf {x} } at each iteration according to the gradient of the hill
Hill_climbing
Tuning parameter (hyperparameter) in optimization
rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines
Learning_rate
Hypothesis in neuroscience
theory of neuronal dynamics is based on minimising free energy through gradient descent. This corresponds to generalised Bayesian filtering (where ~ denotes
Free_energy_principle
The chain rule, developed by Gottfried Wilhelm Leibniz in 1676, and gradient descent, independently proposed by Augustin-Louis Cauchy in 1847 and Jacques
History of artificial neural networks
History_of_artificial_neural_networks
Study of mathematical algorithms for optimization problems
generalized gradients. Following Boris T. Polyak, subgradient–projection methods are similar to conjugate–gradient methods. Bundle method of descent: An iterative
Mathematical_optimization
Slovak mathematician
learning, known for his work on randomized coordinate descent algorithms, stochastic gradient descent and federated learning. He is currently a Professor
Peter_Richtarik
Type of artificial neural network
gradient descent. In gradient descent training, the weights are adjusted at each time step by moving them in a direction opposite from the gradient of
Radial_basis_function_network
Chess-playing computer made by IBM
Reinforcement learning Supervised learning Unsupervised learning Gradient descent Stochastic gradient descent Local search (Texel tuning) Graph and tree search algorithms
Deep_Blue_(chess_computer)
Software program
activity of looking for animals or other patterns in clouds. Applying gradient descent independently to each pixel of the input produces images in which adjacent
DeepDream
Method of representing a chessboard in software
Reinforcement learning Supervised learning Unsupervised learning Gradient descent Stochastic gradient descent Local search (Texel tuning) Graph and tree search algorithms
0x88
Free and open-source chess engine
Reinforcement learning Supervised learning Unsupervised learning Gradient descent Stochastic gradient descent Local search (Texel tuning) Graph and tree search algorithms
Stockfish_(chess)
Optimization algorithm
should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size
Line_search
Topics referred to by the same term
solving partial differential equations Gradient descent, a first-order optimization algorithm going back to Newton Descents in permutations, a classical permutation
Descent
Computer hardware and software capable of playing chess
(machine learning, neural networks, texel tuning, genetic algorithms, gradient descent, reinforcement learning) Knowledge based (PARADISE, endgame tablebases)
Computer_chess
Overview of and topical guide to deep learning
Artificial neural network Representation learning Feature learning Gradient descent Backpropagation Loss function Optimization Training, validation, and
Outline_of_deep_learning
Chess engine software
Reinforcement learning Supervised learning Unsupervised learning Gradient descent Stochastic gradient descent Local search (Texel tuning) Graph and tree search algorithms
Fruit_(software)
for training support vector machines Stochastic gradient descent – randomized variant of gradient descent for large-scale machine learning Support Vector
List_of_data_science_software
Method of mathematical optimization
differentiable, as is required by classic optimization methods such as gradient descent and quasi-newton methods. DE can therefore also be used on optimization
Differential_evolution
Method for finding largest (or smallest) eigenvalues
{\displaystyle A} by steepest descent using a direction r = A x − λ ( x ) x {\displaystyle r=Ax-\lambda (x)x} of a scaled gradient of a Rayleigh quotient λ
LOBPCG
2018 text-generating language model
64-dimensional states each (for a total of 768). Rather than simple stochastic gradient descent, the Adam optimization algorithm was used; the learning rate was increased
GPT-1
Volume rendering technique
Optimization algorithm: Optimizing the parameters using stochastic gradient descent to minimize a loss function combining L1 loss and D-SSIM, inspired
Gaussian_splatting
Optimization algorithm
to stochastic gradient descent, this can be used to reduce the computational complexity by evaluating the error function and gradient on a randomly drawn
Limited-memory_BFGS
Ensemble learning method
fit into the AnyBoost framework, which shows that boosting performs gradient descent in a function space using a convex cost function. Given images containing
Boosting_(machine_learning)
Numerical approximation algorithm
implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS
Iterative_method
Optimization method
Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so by gradually
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Solving multiple machine learning tasks at the same time
view provide insight about how to build efficient algorithms based on gradient descent optimization (GD), which is particularly important for training deep
Multi-task_learning
GRADIENT DESCENT
GRADIENT DESCENT
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French form of Roman Latin Gratian, GRATIEN means "pleasing, agreeable."
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Surname or Lastname
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