Instruction-Conditioned Exploration for Reinforcement Learning with Self-Distillation to an Unconditioned Policy

Sparse reward reinforcement learning (RL) has become a standard tool for improving LLM reasoning, but its success depends critically on the coverage present in the base model. In practice, models are often primed for RL through \emph{mid-training} on curated reasoning traces that teach useful primitive skills such as decomposition, verification, or self-correction. Although effective, this strategy requires manually specifying what the model should learn, and it remains unclear whether such primitive coverage is enough for much harder problems, which require combining these skills into broader solution strategies. We study a more automated approach: \emph{RL-based mid-training} using large corpora of human-written question-answer data. Rather than treating reference solutions as targets to imitate, our method, ExpRL, uses them as \emph{reward scaffolds}: references are hidden from the policy and used only to construct problem-specific grading rubrics for judging on-policy reasoning traces. The policy samples from the original problem prompt, while an LLM judge compares the sampled reasoning trace against the reference solution and assigns outcome-level or process-level dense rewards. This lets ExpRL reinforce partial progress, useful intermediate reductions, and productive reasoning behaviors that sparse final-answer rewards often fail to upweight. On challenging math reasoning tasks, ExpRL yields stronger RL priming than SFT, sparse-reward GRPO, and self-distillation, and provides a better initialization for subsequent sparse-reward RL. Additional mixed-domain experiments further suggest that ExpRL can extend beyond the original math-only setting.

Reinforcement learning (RL) promises to expand the capabilities of language models, but it is unclear if current RL techniques promote the discovery of novel behaviors, or simply sharpen those already present in the base model. In this paper, we investigate the value of deliberate exploration -- explicitly incentivizing the model to discover novel and diverse behaviors -- and aim to understand how the knowledge in pre-trained models can guide this search. Our main finding is that exploration with a simple, principled, representation-based bonus derived from the pre-trained language model's hidden states significantly improves diversity and pass@k rates -- both for post-training, and in a novel inference-time scaling setting we introduce. For inference-time, exploration with representation-based diversity improves efficiency, consistently improving pass@k rates across a variety of models and reasoning tasks. For example, for Qwen-2.5-14b-Instruct we obtain over 50% improvement in verifier efficiency on almost all tasks. For post-training, we show that integrating this exploration strategy into an RL pipeline improves reasoning performance over that of the initial model and over standard RL post-training. For example, on AIME 2024, our post-trained Qwen-2.5-7b-Instruct's pass@80 matches the pass@256 of GRPO on the same model, demonstrating a 3x improvement in test-time sample efficiency. Overall, our findings suggest that deliberate exploration -- with the right notion of diversity -- is a practical path toward discovery of new behaviors beyond sharpening.

Existing reinforcement learning methods for LLM reasoning implicitly assume that the policy generating training trajectories should coincide with the one producing inference responses. We argue that this is a misleading inductive bias: the optimization-optimal trajectory distribution favors informative gradients, whereas the inference-optimal response distribution emphasizes accuracy and consistency. Forcing both into a single policy entangles their gradients and suppresses exploration. We propose R$^2$PO (Residual Rollout Policy Optimization), which attaches a lightweight Residual Rollout-Head atop the policy to decouple training trajectories from inference responses, diversifying rollouts during training while keeping inference generation intact. Experiments show that R$^2$PO consistently outperforms baselines, with average accuracy gains of 3.4% on MATH-500 and 1.3% on APPS, alongside more diverse rollouts and reduced length bias. Our code is available at https://github.com/RRPO-ARR/Code.