SALT: When More Rollouts Don't Help in Group-Based Policy Optimization and How to Make Them Matter

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, computational limits often rule out very large groups, so training proceeds with finite rollout sets that can reinforce only the correct behavior they expose. At practical group sizes, updates can miss rare-correct trajectories while still containing mixed rewards, concentrating probability on more common sampled solutions. We derive the probability of such prompt-local tail-miss events as a function of group size, showing non-monotonic behavior, and in the categorical abstraction characterize how unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware scaling coefficient, inspired by Focal loss, that down-weights updates on high-success sampled groups. Empirically, categorical simulation illustrates the same effect in the categorical setting, Maze provides a single-solution test, and LLM experiments include a representative GRPO group-size sweep together with fixed-$N$ transfer across GRPO, DAPO, and CISPO. On Qwen2.5-7B at $N{=}8$, our method improves average math pass@256 from 64.1 $\rightarrow$ 70.3 (GRPO), 69.3 $\rightarrow$ 72.5 (DAPO), and 73.2 $\rightarrow$ 76.8 (CISPO); OOD pass@256 also improves in all three cases, without increasing group size or computational cost.

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).

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.