It's lambda - basically the amount of regularization (simplification or 'overfit penalty') to impose. Usually chosen by cross-validation - try every lambda between say 0 and 10 in 0.5 increments and choose lambda that gives the model the lowest error cross validation measure...
OP's point (and it's valid) is that the author covers the regularization term but does not explain the task aside from the following throwaway line:
> "The goal is to find the model that minimzes (sp) this loss function."
Unless we're overloading the word "model" -- which is only going to confuse your intended audience -- this statement is incorrect. We're actually searching for the parameterization \alpha of the model that minimizes the loss function.
