The poisson loss function is used for regression when modeling count data. Use for data follows the poisson distribution. Ex: churn of customers next week. The loss takes the form of:
where ŷ is the predicted expected value.
Minimizing the Poisson loss is equivalent of maximizing the likelihood of the data under the assumption that the target comes from a Poisson distribution, conditioned on the input.
When to use Poisson loss function
Use the Poisson loss when you believe that the target value comes from a Poisson distribution and want to model the rate parameter conditioned on some input. Examples of this are the number of customers that will enter a store on a given day, the number of emails that will arrive within the next hour, or how many customers that will churn next week.
In this video Calle explains how to use the Poisson loss.