Reinforcement learning with verifiable rewards (RLVR) is bottlenecked by rollout generation, yet many sampled prompts produce saturated groups (all responses correct or all incorrect) whose zero reward variance yields no policy-gradient signal. Existing remedies either oversample a larger candidate pool and discard saturated prompts (dynamic sampling), paying heavy extra rollouts, or predict prompt difficulty before sampling, which is fragile under a shifting policy. We observe that a group's effectiveness is usually decided early, within the first few of its rollouts, so spending a full group on an already-decided prompt is wasteful. We cast per-step rollout collection as a budget-constrained sequential allocation (optimal stopping) problem and introduce SARA (Sequential Adaptive Rollout Allocation). SARA maintains a Beta posterior over each prompt's success rate, evaluates a closed-form predictor of group effectiveness, and applies a two-threshold, SPRT-style rule that commits effective groups, abandons saturated ones after a short probe, and reallocates the freed budget to fresh prompts, without any extra prediction rollouts. We prove abandonment reliability, expected rollout savings, fixed-budget yield dominance, and a link between effective-group yield and the GRPO gradient norm. On mathematical reasoning and planning with 1.5B/3B models on a single GPU, SARA matches DPS (both below the DS oracle) while using 22% fewer rollouts than DS; composing SARA with DPS yields the best accuracy, slightly above DS, at 67% fewer rollouts (near-uniform cost).
Reinforcement Learning from Human Feedback (RLHF) for Large Language Models increasingly relies on critic-free methods as a practical alternative to actor--critic training. Despite their simplicity, existing critic-free approaches propagate a trajectory-level learning signal uniformly across all tokens in a trajectory. This requires full-trajectory policy updates for every rollout, leading to substantial optimization cost for long reasoning traces, even though intermediate prefixes often contain enough information to largely determine the final outcome. We propose Prefix-Sampling Proximal Policy Optimization (PS-PPO), a compute-efficient critic-free method for RLHF that exploits this temporal redundancy. PS-PPO introduces a prompt-conditioned cutoff distribution and samples a cutoff timestep for each trajectory. During the update pass, PS-PPO backpropagates only through the sampled prefix of each trajectory and applies an importance-weighting correction so that the resulting truncated gradient estimator remains unbiased with respect to the full-trajectory objective. Experiments on mathematical reasoning and RLHF benchmarks show that PS-PPO achieves large reductions in training compute and peak GPU memory, while maintaining accuracy comparable to strong critic-free baselines.
Shivchander Sudalairaj, Kai Xu, Akash Srivastava +1cs.LG cs.AI cs.CL stat.ML
Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.
Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for reasoning in language models, with GRPO as its primary example. However, GRPO requires continuous online rollout generation, making it computationally expensive and difficult to scale. While Direct Preference Optimization (DPO) offers a stable and efficient offline alternative, it is typically expected to underperform w.r.t. online RL methods such as GRPO when trained on rollouts from a cold supervised fine-tuned (SFT) policy. We introduce G2D (GRPO to DPO)}, a three-stage pipeline that performs a short GRPO warm-up, constructs a static preference dataset, and fine-tunes a model offline with DPO. Across a set of values of the number of online steps (K) in GRPO on Qwen2.5-7B and Llama-3.1-8B, we find that offline DPO with moderate warm-up matches or outperforms GRPO at substantially lower compute cost in our setting. On Qwen2.5-7B, G2D at K=150 achieves 62.4% on MATH-500, outperforming GRPO (51.6%) by 10.8% at ~4x lower compute. On Llama-3.1-8B, G2D at K=500 achieves 49.4%, surpassing GRPO in our experimental setting. We show that performance is not governed by the number of preference pairs, which does not vary much w.r.t. K, but by their informativeness. Moderate warm-up produces rollouts with calibrated uncertainty, yielding stronger contrastive signal, while excessive warm-up leads to overconfident policies and less informative data. Our results recast the offline-online gap in RLVR as primarily a data informativeness problem, and identify short online RL warm-up with appropriate difficulty calibration of the fine-tuning dataset as a compute-efficient alternative to online RL.