Fix BootstrapFinetune example in index doc and add basic tests for bootstrap_finetune.

[Hangzhi]

Why

Followup for #8395 since to make the example is not runnable after the ChainOfThoughtWithHint fix.

By running the example code in https://dspy.ai/#__tabbed_3_3

Attribution error would be thrown.

dspy/dspy/teleprompt/bootstrap_finetune.py", line 89, in compile
    logger.info(f"Using {len(train_data)} data points for fine-tuning the model: {pred.lm.model}")
                                                                                  ^^^^^^^^^^^^^
AttributeError: 'NoneType' object has no attribute 'model'

What

1. Add the .set_lm(lm) for the example code.
2. Add basic tests for BootstrapFinetune module and better error handling in BootstrapFinetune
3. Link a full tutorial in the BootstrapFinetune index example.

After

I can get the result as below with the example code by adding .set_lm.

2025/06/26 10:07:42 INFO dspy.teleprompt.bootstrap_finetune: Updating the student program with the fine-tuned LMs...
2025/06/26 10:07:42 INFO dspy.teleprompt.bootstrap_finetune: BootstrapFinetune has finished compiling the student program
Prediction(
    reasoning='A pending cash withdrawal refers to a cash withdrawal transaction that has been initiated but is still being processed and has not been completed yet.',
    label='pending_cash_withdrawal'
)

[chenmoneygithub]

@dilarasoylu Do you remember the context for us always requiring the pred.lm to be set?

dspy/dspy/teleprompt/bootstrap_finetune.py

Line 69 in 734eff2

all_predictors_have_lms(student)

[dilarasoylu]

@dilarasoylu Do you remember the context for us always requiring the pred.lm to be set?

dspy/dspy/teleprompt/bootstrap_finetune.py

Line 69 in 734eff2

all_predictors_have_lms(student)

Oh, yes, we always want to ensure that predictor level LMs are set for the finetune optimizers, otherwise we might end up modifying a globally set LM as part of the finetune process, which might be confusing for the users. We use the 'set_lm(...)' method on the program to be finetuned before calling any optimizer that modifies the weights in order to ensure that predictor level LMs are set.

[Hangzhi]

@chenmoneygithub @dilarasoylu
Thanks for the suggestions. I updated the example code and set_lm works.

[Hangzhi]

@chenmoneygithub let me know if there are better way refer to another doc page.

[okhat]

@Hangzhi This looks great to me, and I was about to merge. But why are we catching all exceptions from the teacher? I think the original behavior should have been to let it be handled by dspy.settings.max_errors essentially (through dspy.Evaluate). This allows more fine-grained control and alerts the user if the program seems broken.

[Hangzhi]

@okhat That makes sense. Thanks for the clarification.
I removed the call exception catching logic.