# sGPO: Trading Inference FLOPs for Training Efficiency in RLVR

arXiv: https://arxiv.org/abs/2606.08854 · HTML: https://mlsanity.com/paper/2606.08854/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [Learning How Hard to Think: Input-Adaptive Allocation of LM Computation](https://mlsanity.com/paper/2410.04707/) (2024)
- [VCRL: Variance-based Curriculum Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2509.19803/) (2025)
- [Improving Sampling Efficiency in RLVR through Adaptive Rollout and Response Reuse](https://mlsanity.com/paper/2509.25808/) (2025)
- [Learning Like Humans: Advancing LLM Reasoning Capabilities via Adaptive Difficulty Curriculum Learning and Expert-Guided Self-Reformulation](https://mlsanity.com/paper/2505.08364/) (2025)
- [Adaptive Rollout Allocation for Online Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.01601/) (2026)
- [Group Distributionally Robust Optimization-Driven Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2601.19280/) (2026)
- [CoBA-RL: Capability-Oriented Budget Allocation for Reinforcement Learning in LLMs](https://mlsanity.com/paper/2602.03048/) (2026)
- [TACLer: Tailored Curriculum Reinforcement Learning for Efficient Reasoning](https://mlsanity.com/paper/2601.21711/) (2026)

## Built on by (most cited first, 3 of 3)

- [ThinkPrior: Zero-Rollout Difficulty Priors for Cold-Start Prompt Selection in RLVR](https://mlsanity.com/paper/2609.09075/) (2026)
- [PAIR: Pairwise-Aware Inclusion Reweighting for Adaptive Rollout Allocation in RLVR](https://mlsanity.com/paper/2608.11368/) (2026)
- [When KL Regularization Misfires in Group Policy Optimization](https://mlsanity.com/paper/2610.12161/) (2026)

## Abstract (arXiv)

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.