# SPADE: Self-Play in Adaptive Synthetic Executable Environments

arXiv: https://arxiv.org/abs/2608.19197 · HTML: https://mlsanity.com/paper/2608.19197/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Self-evolving LLM agents, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 107 of its 141 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-evolving LLM agents](https://mlsanity.com/synth/self-evolving-llm-agents/)

## Builds on (most cited first, 30 of 107)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [τ2-Bench: Evaluating Conversational Agents in a Dual-Control Environment](https://mlsanity.com/paper/2506.07982/) (2025)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [RAGEN: Understanding Self-Evolution in LLM Agents via Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2504.20073/) (2025)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Will we run out of data? Limits of LLM scaling based on human-generated data](https://mlsanity.com/paper/2211.04325/) (2022)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [Paired Open-Ended Trailblazer (POET): Endlessly Generating Increasingly Complex and Diverse Learning Environments and Their Solutions](https://mlsanity.com/paper/1901.01753/) (2019)
- [Intrinsic Motivation and Automatic Curricula via Asymmetric Self-Play](https://mlsanity.com/paper/1703.05407/) (2017)
- [Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)](https://mlsanity.com/paper/2510.22954/) (2025)
- [MemRL: Self-Evolving Agents via Runtime Reinforcement Learning on Episodic Memory](https://mlsanity.com/paper/2601.03192/) (2026)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Verbalized Sampling: How to Mitigate Mode Collapse and Unlock LLM Diversity](https://mlsanity.com/paper/2510.01171/) (2025)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)

## Built on by (most cited first, 12 of 12)

- [EnvHarness: Awakening Static Worlds for Agent Learning](https://mlsanity.com/paper/2608.19880/) (2026)
- [Recursive self-improvement of AI research agents](https://mlsanity.com/paper/2609.26457/) (2026)
- [FrogNano: Training a 4B Coding Agent via Online Task Synthesis](https://mlsanity.com/paper/2609.07925/) (2026)
- [Self-Play Search Distillation for Large Language Model Reasoning](https://mlsanity.com/paper/2609.30936/) (2026)
- [Frontier Learning: Training LLM Reasoners at the Edge of Capability](https://mlsanity.com/paper/2609.35426/) (2026)
- [Multi-LLM Collaborative Alignment via Stackelberg Games](https://mlsanity.com/paper/2609.39076/) (2026)
- [Learning to Simulate Individuals from Macro Social Signals](https://mlsanity.com/paper/2610.07062/) (2026)
- [DAEDALUS: Bootstrapping Agent Memory from Self-Generated Tasks](https://mlsanity.com/paper/2610.08048/) (2026)
- [Collaborative Learning and Reasoning over Model Slices](https://mlsanity.com/paper/2610.12927/) (2026)
- [AutoEnvScaling: Automating the Data Flywheel with Terminal Agents](https://mlsanity.com/paper/2610.14163/) (2026)
- [Recursive Environment Scaling for General Long-Horizon Agents](https://mlsanity.com/paper/2610.16397/) (2026)
- [Player-1: Learning to Play from Synthetic Experience](https://mlsanity.com/paper/2610.20584/) (2026)

## Abstract (arXiv)

Continuous self-improvement requires an ever-expanding pool of self-generated, diverse, adaptive goals. For language agents, existing training environment pools (hand-curated, statically synthesized, or frozen-verifier) keep the goal distribution fixed as the learner scales. We introduce SPADE (Self-Play in Adaptive Synthetic Executable Environments), a self-play RL framework in which a single LLM plays two roles: an Environment Designer that writes complete, long-horizon training environments as executable code with an OpenAI Gym-style reset()/step() interface, and a Reasoning Agent that learns to act in them. Each is a stateful, multi-turn environment (state transitions, reward functions, and verification code), so one interface spans reasoning problems and multi-step agentic tool use. The Reasoning Agent's regret is estimated using the gap between its reward with and without privileged hints; in optimizing this regret signal the Environment Designer learns to target environments at the edge of the agent's capabilities while keeping them feasible. Through extensive experimentation, we find several components critical to success: grounding the Environment Designer on documents sampled from a large pretraining corpus, and giving it an accumulated environment memory. Scaling to 30B-parameter models, SPADE improves over the strongest fixed-environment baseline by +5.3 on average across eight held-out math, science, code, and reasoning benchmarks, and lifts the tool-use setting by +5.7 on BFCL-v4 multi-turn and +13.9 on ACEBench-Agent; on the games setting, the margin over the strongest baseline grows with model scale. By making environment design itself a learnable component, SPADE takes a concrete step toward open-ended self-improvement.