Stochastic Optimization

Stochastic Gradient Descent is an iterative optimization technique that uses minibatches of data to form an expectation of the gradient, rather than the full gradient using all available data. That is for weights $w$ and a loss function $L$ we have:

$$w_{t+1} = w_{t} - \eta\hat{\nabla}_{w}{L(w_{t})}$$

Where $\eta$ is a learning rate. SGD reduces redundancy compared to batch gradient descent - which recomputes gradients for similar examples before each parameter update - so it is usually much faster.

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