Consider introducing type hints and mypy

[hvy]

Consider adding type hints to the code and run mypy in the CI (optuna itself has type hints). In addition to the static checking, type hints acts as documentation. The downside is that it will increase maintenance cost.

[hvy]

See also https://github.com/optuna/optuna/issues/2165.

[Crissman]

This is a good idea and would bring the examples in line with the optuna/optuna code. This doesn't need to be done all at once, so we welcome contributors to work on adding type hints and mypy compatibility on a example by example basis.

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