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Stochastic optimization (SO) are optimization methods that generate and use random variables. For stochastic optimization problems, the objective functions or constraints are random. Stochastic optimization also include methods with random iterates .
In 1997, the practical performance benefits from vectorization achievable with such small batches were first explored, [13] paving the way for efficient optimization in machine learning. As of 2023, this mini-batch approach remains the norm for training neural networks, balancing the benefits of stochastic gradient descent with gradient descent .
SGLD can be applied to the optimization of non-convex objective functions, shown here to be a sum of Gaussians. Stochastic gradient Langevin dynamics (SGLD) is an optimization and sampling technique composed of characteristics from Stochastic gradient descent, a Robbins–Monro optimization algorithm, and Langevin dynamics, a mathematical extension of molecular dynamics models.
This includes, for example, early stopping, using a robust loss function, and discarding outliers. Implicit regularization is essentially ubiquitous in modern machine learning approaches, including stochastic gradient descent for training deep neural networks, and ensemble methods (such as random forests and gradient boosted trees).
Recently, stochastic approximations have found extensive applications in the fields of statistics and machine learning, especially in settings with big data. These applications range from stochastic optimization methods and algorithms, to online forms of the EM algorithm , reinforcement learning via temporal differences , and deep learning ...
scikit-learn – A machine learning library for Python which includes Gaussian process regression and classification; SAMBO Optimization library for Python supports sequential optimization driven by Gaussian process regressor from scikit-learn.
In machine learning, ... Dynamic programming is the approach to solve the stochastic optimization problem with stochastic, randomness, and unknown model parameters ...
Here the surrogate is tuned to mimic the underlying model as closely as needed over the complete design space. Such surrogates are a useful, cheap way to gain insight into the global behavior of the system. Optimization can still occur as a post-processing step, although with no update procedure (see above), the optimum found cannot be validated.