[docs] document how to use a custom objective function via the C API

[parsiad]

Follow-up to #6393.

Clarifies that objective=custom must be provided via parameters in the C API if you want to use a custom objective function and provide gradients/hessians manually.

[parsiad]

@microsoft-github-policy-service agree

[jameslamb]

Thanks for this!

I've updated the title and added a PR description. In the future when you contribute here, please do provide a PR description briefly describing what the PR does and how it improves the project, including links to any other relevant information. This helps maintainers to understand how what the goal is (to provide useful feedback) and helps other people finding the PR in the future (e.g. from search engines or release notes).

After applying the suggestions I left, please run the script we use to automatically generate parameter documentation and the corresponding C++ code.

python ./helpers/parameter_generator.py

[jameslamb]

Thanks very much! I just pushed commits to get this up to date with the latest changes in this repo (now that we've fixed continuous integration), and to split up 2 lines of documentation.

I also changed this from your phrasing:

must be passed through parameters explicitly

to this

must be passed through parameters explicitly in the C API

So that users of the R and Python packages don't get confused and think they need to pass "objective": "custom" (they do not).

👋🏻 Come back and contribute any time!