Training is quite expensive computationally, but inference needn't be. We have many models that can run on a smartphone, after all.
However, you can do some limited training on the smartphone by leveraging pre-trained models. Usually the internal representation at the very end of the network can be used as an input to train a simpler algorithm on top of it.
But all of the above depends on what actually needs to be done, which you have not specified. Classical, non-deep, ML models could easily be trained on a smartphone provided the datasets can fit.
The keyword for you to seek would be "edge AI", if that helps.