# SPO++: Stream-Aligned Policy Optimization for Asynchronous Agentic RL

arXiv: https://arxiv.org/abs/2608.24870 · HTML: https://mlsanity.com/paper/2608.24870/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 23 of its 25 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 23 of 23)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret](https://mlsanity.com/paper/2503.01491/) (2025)
- [Single-Rollout Asynchronous Optimization for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.07508/) (2026)
- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [Single-stream Policy Optimization](https://mlsanity.com/paper/2509.13232/) (2025)
- [A-3PO: Accelerating Asynchronous LLM Training with Staleness-aware Proximal Policy Approximation](https://mlsanity.com/paper/2512.06547/) (2025)
- [Stable and Efficient Single-Rollout RL for Multimodal Reasoning](https://mlsanity.com/paper/2512.18215/) (2025)
- [V0: A Generalist Value Model for Any Policy at State Zero](https://mlsanity.com/paper/2602.03584/) (2026)
- [V0.5: Generalist Value Model as a Prior for Sparse RL Rollouts](https://mlsanity.com/paper/2603.10848/) (2026)
- [Missing Old Logits in Asynchronous Agentic RL: Semantic Mismatch and Repair Methods for Off-Policy Correction](https://mlsanity.com/paper/2605.12070/) (2026)
- [Stale but Stable: Staleness-Adaptive Trust Regions for Stabilizing Asynchronous Reinforcement Learning](https://mlsanity.com/paper/2607.18722/) (2026)
- [VIMPO: Value-Implicit Policy Optimization for LLMs](https://mlsanity.com/paper/2606.20008/) (2026)
- [Balanced Aggregation: Understanding and Fixing Aggregation Bias in GRPO](https://mlsanity.com/paper/2605.04077/) (2026)
- [SAPO: Single-Rollout Autoregressive Policy Optimization for Agentic Reinforcement Learning](https://mlsanity.com/paper/2608.19842/) (2026)
- [SRPO: Self-Reflective Policy Optimization for Long-Horizon Reasoning](https://mlsanity.com/paper/2608.23493/) (2026)
- [BASIS: Batchwise Advantage Estimation from Single-Rollout Information Sharing for LLM Reasoning](https://mlsanity.com/paper/2605.27293/) (2026)
- [Reusing Rollouts under Policy Lag: Prefix-Normalized Policy Optimization for LLM Reinforcement Learning](https://mlsanity.com/paper/2608.01418/) (2026)

## Built on by (most cited first, 2 of 2)

- [QwenGyre: An Elastic Reinforcement Learning Framework for Training xLong-Horizon Agents](https://mlsanity.com/paper/2609.33848/) (2026)
- [Long-Horizon RL Needs Muon](https://mlsanity.com/paper/2610.20256/) (2026)

## Abstract (arXiv)

Group-relative reinforcement learning waits for sibling rollouts of the same prompt, which is costly for long and variable tool-use trajectories. Single-stream Policy Optimization (SPO) removes this dependency with a persistent prompt-level value estimate, but its recipe whitens one advantage per trajectory before optimizing a token-mean actor loss. We show that trajectory centering generally does not center the token-weighted quantity consumed by the actor, and fix the mismatch by standardizing terminal-outcome advantages under the action-token measure. We additionally organize prompt evidence by the policy event that generated it rather than learner receipt order. Across matched runs on ALFWorld at two model scales and on Math-TIR, SPO++ improves online learning efficiency over SPO. A paired ablation identifies action-token-measure normalization as the strongest tested component.