[R-package] expose start_iteration to dump/save/lgb.model.dt.tree

[mayer79]

Fixes #6397

Contributes to #6380

[jameslamb]

Thanks for this! Now that CI seems to be working again, let's continue with this. I left some initial suggestions and questions for your consideration, but overall I'm very supportive of this addition to the R package's API.

[mayer79]

@jameslamb Increadible review, thank you so much for your dedication!

Some comments:

1. Now, the user sees 1-based start_iteration. The conversion to 0-based is done before calling the R wrappers of the C_API. We could also move the 0-basing into the R wrappers.
2. The new argument start_iteration has moved to the end of all argument lists, also those of the R wrappers of the C++ code.
3. I have left the weak unit test of $save_model_to_string() because I don't know how to parse the content of the string.
4. Also the unit test of lgb.save() is untouched because serializing and deserializing loses the tree index. At least I have this in mind from when I tried to improve the test. Maybe you have a good idea how to make this better?

[jameslamb]

Thanks so much!

Thanks for working with me on the unit tests. I'm really happy that this PR is going to add so much better coverage of an under-tested part of the library.

I left one more set of small suggestions, and then I think this is ready to merge 🎉

[mayer79]

Thanks so much!

Thanks for working with me on the unit tests. I'm really happy that this PR is going to add so much better coverage of an under-tested part of the library.

I left one more set of small suggestions, and then I think this is ready to merge 🎉

Perfect! Should we reformulate the docstrings of all affected functions?

[jameslamb]

yes please

[mayer79]

yes please

done.

[jameslamb]

Thanks very much!

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