Right now the updates occur daily, we're planning on building a bit more intelligence into the update cadence over time (e.g. once we see we have a stat sig read on how the price change impacted conversion).
Retailers don't approve the discount changes, but they do provide guardrails like maximum discount value to avoid us carving into their margins too much. They can also log in and review / update discounts at any time in our app.
We've been open to working with customers on a trial basis also. This price is mostly based on industry comps for other optimization tools.