About data cleansing, to what extent should we do our work? As far as I know, when we deal with 'big data'. It is common we deal with more than 10 years' customers data. Quality issue is always there. 

What I am thinking about, to what extend we should deal with the data quality issues? A robust algorithm should tolerate with the data quality issues but if we do better data cleansing work we get outcome confidently.

So how to balance this? 

Somebody please give some ideas!

Thanks.
This is a question that is very dependent upon the data in question. Assuming that you can train your models in a reasonable time, I would start by not cleaning the data at all, and seeing how well your model performs, and then cleaning it a bit and redoing the experiment and so on.
This is because it is possible to overclean your data, essentially removing variations in the data which are actually useful to your modelling.
The amount of cleaning that you apply is yet another meta-variable in your model.