Lazy loaded image10.1 Why GRPO training loss starts at 0

To understand why it starts with zero, let’s review the GRPO loss functions. As mentioned in GRPO Loss Analysis, the loss of GRPO is formulated as follows:
Usually, we model the generation process as a single-step MDP and use the outcome reward model (ORM) for learning, so the state is the prompt and the action is the output . In this case, we basically only perform one exploration step per iteration (this is a standard implementation of GRPO, referring to open-r1 and VLM-R1). Therefore,
Then, the in the loss function becomes:
Let’s simplify as . Consequently,
We know that because we are using ORM, and the is a normalized reward, so its expectation across generations is actually zero. Therefore, the loss function can be simplified as
Now, the remaining term is only depending on the current policy and the reference policy . Since these two are initially equal (both the policy and reference models are initialized from the SFT model), the would be zero. This is why the loss starts at zero. As the training goes on, the policy model will be updated and diverge from the reference model, so the loss increases.
The loss will converge to a proper level, where the current policy model is far enough from the reference model to generate more pleasing responses and simultaneously not too far to avoid performance degradation and generating unexpected/unwanted outcomes.
Reference: https://github.com/huggingface/open-r1/issues/239#issuecomment-2646297851, where the is the objective to maximize during training; it’s equivalent to the to minimize during training.
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