Should I update my regularisation L1 and L2 regularisation parameters in online setting? I have been working on online learning for a few weeks now, especially with Vowpal Wabbit and logistic regression. My understanding of the online learning algorithms and the problem is alright but I can't get my head straight about the regularisation issue. 

In a standard machine learning problem, one uses a validation dataset in order to tune regularisations parameters for L1 and L2. But how do you choose those regularisation parameters in an online setting? Do you just fix them from start, or should I update them while training occurs?
As you say @Alexis, cross-validation is the standard way of selecting a model (or its parameters) in offline learning (especially when previous knowledge in not available). For online training, one usually incorporates some sort of (automatic) compensation for the model parameters that adjust them at the same time that training takes place (the alternative being to cross-validate on some gather data or equivalently to pre-optimize your parameters). Check also this answer as well as, for example, this paper (it shows that this issue is a very active research area)!