i know they have a 10 day training so speed can go up and down a bit.
That's a myth, and applies only to ADSL packages (via BT).
For FTTC, the modem starts out as fast as it possibly can, tempered only by the distance to the cabinet (and the quality of the copper pair), with a ceiling placed by the package you have bought.
One synchronised, DLM monitors the connection. If it needs to intervene in an emergency (because of dire connectivity) it will, but I haven't seen this happen yet. If it needs to intervene because of "middling" errors seen on the line, it will do so after 24-48 hours. Intervention at this point is invariably to slow the speed down or to add interleaving (which tends to slow the line down anyway). I've never seen it increase the speed of a line in these first 48 hours.
For almost all people, that is the end of it. The line will stay this way for a long period.
For some people, this first intervention isn't enough to fix the connection - and the process will continue over the next few days. I've seen this happen on a handful of occasions.
After this, DLM monitors forever. If the line encounters a temporary problem, DLM will again intervene. In this case, it will usually trigger a resync next morning (between 4AM and 8AM). When the temporary problem has gone, DLM will remove (or reduce) the intervention level between 2 and 4 weeks later.
ISPs have no way to interfere or alter this process. The whole DLM process *can* be reset - but only by being regraded (to a new speed package) or when an Openreach engineer attends to investigate a fault.