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This is a natural modification of FTL that is used to stabilise the FTL solutions and obtain better regret bounds.

A regularisation function Quadratically regularised FTRL algorithms lead to lazily projected gradient algorithms as described above.

Some simple online convex optimisation algorithms are: The simplest learning rule to try is to select (at the current step) the hypothesis that has the least loss over all past rounds.

This algorithm is called Follow the leader, and is simply given round .

In computer science, online machine learning is a method of machine learning in which data becomes available in a sequential order and is used to update our best predictor for future data at each step, as opposed to batch learning techniques which generate the best predictor by learning on the entire training data set at once.

Online learning is a common technique used in areas of machine learning where it is computationally infeasible to train over the entire dataset, requiring the need of out-of-core algorithms.

It is also used in situations where it is necessary for the algorithm to dynamically adapt to new patterns in the data, or when the data itself is generated as a function of time, e.g. Online learning algorithms may be prone to catastrophic interference.

This discussion is restricted to the case of the square loss, though it can be extended to any convex loss.

For example, in online classification, the prediction domain and the loss functions are not convex.

In such scenarios, two simple techniques for convexification are used: randomisation and surrogate loss functions.

Mini-batch techniques are used with repeated passing over the training data to obtain optimized out-of-core versions of machine learning algorithms, for e.g. When combined with backpropagation, this is currently the de facto training method for training artificial neural networks.

The simple example of linear least squares is used to explain a variety of ideas in online learning.

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