How do you host deep learning side projects?

I've been working on a deep learning side project that needs GPU acceleration at inference time. My inference requests are very bursted, however, so I don't need a box to be lying around while waiting for requests. I can stand to wait for a small interval (<1min) before getting results back. Most of the options I'm seeing either assume full batch processing or persistent hosted boxes that lie around in between requests. Is there anything like heroku dynos that can spin up to process a GPU compute request and then spin back down? What do you use for deep learning side projects?