[RFC] Show progress bar based on `timeout`

Motivation

The current study.optimize shows the progress bar when we specify the number of trials. We can show the progress bar based on the timeout value as well.

Note that before implementing this feature, we need to decide the priority of n_trials and timeout. When we specify both values as not None values, there are two ways to show the progress bar.

Moreover, we need to discuss the case when both None. I suppose not showing the progress bar makes sense when both are None.

Description

• Show progress bar using timeout value.
• Add test by following https://github.com/optuna/optuna/pull/2900

Alternatives (optional)

Additional context (optional)

We might need to support the n_jobs!=1 case depending on https://github.com/optuna/optuna/issues/2957.

[nzw0301]

@toshihikoyanase suggested using only n_trials: the first candidate. A user wants to perform optimisation n_trials times ideally but, to avoid taking too much to perform optimisation, he/she specifies timeout at the same time. Indeed, I saw such a setting in a machine learning paper, so his suggestion is supposed to be natural.

So how about implementing candidate 1 at first? If the optuna community prefers the last candidates to the first one or sends feedback to us, we can change the logic.

Thanks, @toshihikoyanase for your comment.

[xadrianzetx]

Sure, I’ll prioritize n_trials then! Will come back with implementation after the weekend.