Expected behavior

• trial.report() accepts nan
• Return value of multi-objective study accepts nan
• Multi-objective study mark trials as FAILED when one or more return values are nan.

Bugs

1. trial.report fails when the value is nan when combined with MySQL backend.
2. Multi-objective trial also fails on report with nan value when combined with MySQL backend.
3. Multi-objective study internally depends on trial.report and thus error occurs when one or more return value is nan.
4. With in-memory db, multi-objective study registers trials with nan return value as COMPLETED trial.

Notes

I think whether trial.report should accept nan or not requires discussion.

Environment

• Optuna version: 2.3.0
• Python version: 3.8
• OS: macOS Catalina
• PyMySQL version: 0.10.1

Error messages, stack traces, or logs

(When called trial.report with nan value w/ MySQL backend.)

ProgrammingError: (pymysql.err.ProgrammingError) nan can not be used with MySQL
[SQL: INSERT INTO trial_values (trial_id, step, value) VALUES (%(trial_id)s, %(step)s, %(value)s)]
[parameters: {'trial_id': 34849, 'step': 1, 'value': nan}]
(Background on this error at: http://sqlalche.me/e/13/f405)

Steps to reproduce

1. trial.report(float(np.nan), 1)

Additional context (optional)

Single-objective study accepts nan as the return value and marks it as failed. This is achieved in the following.

With in-memory db, trial.report accepts nan.