ThinkPrior: Zero-Rollout Difficulty Priors for Cold-Start Prompt Selection in RLVR
ThinkPrior builds zero-rollout difficulty priors via an offline verifier-anchored pass, halving silent groups in RLVR and cutting wasted rollouts on Qwen2.5-Math-7B.
In GRPO-based RLVR, groups where all rollouts are correct or all are wrong yield zero advantages and consume about 39% of a run's rollouts under uniform sampling. ThinkPrior initializes a Beta posterior from an external anchor pass's verifier-scored pass rate, selecting prompts by expected learnability before any target-policy rollout, without changing the loss or optimizer. On Qwen2.5-Math-7B across sixteen seeds it more than halves early silent groups and cuts wasted rollouts through step 30 by nearly a fifth, with no detected final-accuracy difference. The ThinkPrior+DAPO composition reduces generated rollouts by 10.6% at an equal 3,840-rollout update budget.
- Zero-advantage silent groups waste 39% of rollouts under uniform sampling
- Beta posterior initialized offline; no loss or optimizer change
- Early silent groups more than halved across sixteen seeds
- ThinkPrior+DAPO cuts generated rollouts 10.6% at equal update budget
Full article213 words · extracted from arxiv.org · click to collapse
In reinforcement learning with verifiable rewards (RLVR) trained with group relative policy optimization (GRPO), the KL-free reward-advantage term studied here depends on within-group reward variation. If all rollouts in a group are correct or all are wrong, their group-relative advantages are identically zero; these zero-advantage silent groups provide no reward-advantage gradient, yet uniform sampling spends 39% of a run's rollouts on them. History-based prompt selection must first spend target-policy rollouts to estimate difficulty, creating a cold start with rollout waste; ThinkPrior instead uses an external anchor in one offline pass to construct a zero-rollout difficulty prior before the first target-policy rollout. The verifier-scored anchor pass rate supplies an external-anchor initialization for a Beta posterior; ThinkPrior selects by expected learnability and then updates from training outcomes, changing neither the loss nor the optimizer. On Qwen2.5-Math-7B across sixteen seeds, ThinkPrior more than halves early silent groups and cuts wasted rollouts through step 30 by nearly a fifth, while we detect no difference in final accuracy. On this 250-prompt pool the fixed-budget result is a reallocation rather than a net saving. The measured ThinkPrior+DAPO composition reduces generated rollouts by 10.6% while both arms retain the same 3840-rollout update budget. The prior requires no target-policy rollout before the first selection, but the posterior thereafter uses target-policy outcomes.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.09075