Issue encountered

The response_format parameter was not passed to litellm API calls in the JudgeLM class, even though it was available as an instance variable and used in other backends (OpenAI/TGI). This prevented structured output formats (e.g., JSON) when using the litellm backend.

Solution/Feature

Add "response_format": self.response_format to the kwargs dictionary when calling litellm.completion() in the __call_litellm method, matching the pattern used in the __call_api method for OpenAI/TGI backends.

Possible alternatives

1. Make response_format backend-specific via configuration, but this adds complexity and breaks consistency.
2. Handle response_format only in backends that support it, but this reduces feature parity.
3. Remove response_format support entirely, but this removes a useful feature.

The chosen solution maintains consistency across backends and enables structured output formats with litellm.