Does TPE (from Optuna) takes account of the number of trials?
If I reduce n_trials, does TPE explore faster (and less precisely)?

No.

... is interupting optuna at 500 with n_step=1000 the same as using n_trials = 500 and waiting until the end.

Yes.
This is because TPE (from Optuna) is not aware of the number of remaining (or total) trials.
I am using TPE sampler from optuna to optimize hyperparameters for Deep Learning vision models.
I was wondering if optuna adapt search depending of the number of trials.
If I train for 1000 trials and stop at 500, I can see that many parameters were not tried by the algorithm.
If I reduce n_trials, does TPE explore faster (and less precisely) ?
In other terms, is interupting optuna at 500 with n_step=1000 the same as using n_trials = 500 and waiting until the end.
I only have basic understanding of how TPE works.
Thanks.