Ask HN: cloud data storage cheaper than AWS S3?

I'm working on a new neural network based project, which means I'll need to access and store more data than I can keep on my hard drives.

While I'm familiar with AWS S3 from my day job, I was wondering what other alternatives are out there that may be cheaper (or even free)?

I'm also aware of dropbox, google docs, etc., but ideally I'd like to have programmatic access via an API.