Real time updating of training data and classification model

Question

Setup: I have a couple of binary classification models based on Logistic Regression and Gradient Boosted Trees. Currently I train the model offline and use it to predict the class of incoming data.

Problem: One of my features is order_count i.e. number of purchases made by the user. So if the order_count of a user changes (i.e. he/she purchases new products) it will not be reflected in my classification model until I retrain it. There are 1000s of such dynamically changing features.

Current solution: One option is to retrain the model say every day or every week with the updated dataset.

Question: Is there any alternative to this method of retraining at regular intervals? Is there a way to update the model with the modified training samples in real time? For example, the moment a user purchases a new product, the model should re-train itself based on this updated data in real time. Or is there some completely different approach that people use in such a situation?

Answer 1

Instead of retraining the model, it is best to use a procedure such as stochastic gradient descent (SGD), in which the true gradient $Q(\mathbf{w})$ is approximated by the gradient at a single new sample and the intermediate solution $\mathbf{w}$ is updated accordingly: $$\mathbf{w} \leftarrow \mathbf{w} - \alpha \nabla Q_i(\mathbf{w}),$$ where $\alpha$ is the step size aka learning rate. A large step size implies a higher weight to the gradient of the new sample $Q_i(\mathbf{w})$. Usually, the step size remains fixed and is treated as a hyperparameter.

Increasing the step size will automatically emphasize new instances in an online setting. You can think of this as overfitting the new data to some extent. To be clear: you do not have to increase the step size over iterations, just use a larger value of $\alpha$ than you typically would in a standard context.

You can do the same idea in a minibatch sense, instead of for a single example