SPADE: Self-Play in Adaptive Synthetic Executable Environments
On the map: Synthetic data and self-improvement for LLMs → Self-evolving LLM agents
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.
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.
Builds on
107 of 141 references.
Closest ancestors · 6
Same direction, newest first
- 2026G-Zero: Self-Play for Open-Ended Generation from Zero Data11 May
- 2026Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Data24 Feb
- 2026Self-Play Only Evolves When Self-Synthetic Pipeline Ensures Learnable Information Gain10 Feb
- 2026Endless Terminals: Scaling RL Environments for Terminal Agents23 Jan
- 2025Toward Training Superintelligent Software Agents through Self-Play SWE-RL21 Dec
- 2025Bootstrapping Task Spaces for Self-Improvement4 Sep
Other references · 101
- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
- 2019Sentence-BERT: Sentence Embeddings using Siamese BERT-Networkscited by 9,170
- 2022ReAct: Synergizing Reasoning and Acting in Language Modelscited by 8,695
- 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
- 2023Reflexion: Language Agents with Verbal Reinforcement Learningcited by 4,276
- 2023GPQA: A Graduate-Level Google-Proof Q&A Benchmarkcited by 2,879
- 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scalecited by 2,810
- 2024LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Codecited by 2,004
- 2016OpenAI Gymcited by 1,736
- 2024OpenAI o1 System Cardcited by 1,244
- 2019Dota 2 with Large Scale Deep Reinforcement Learningcited by 1,103
- 2025τ2-Bench: Evaluating Conversational Agents in a Dual-Control Environmentcited by 627
38 more
- 2024Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Modelscited by 557
- 2015Illuminating search spaces by mapping elitescited by 425
- 2018AI safety via debatecited by 400
- 2024DataComp-LM: In search of the next generation of training sets for language modelscited by 398
- 2025RAGEN: Understanding Self-Evolution in LLM Agents via Multi-Turn Reinforcement Learningcited by 386
- 2023Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Modelscited by 349
- 2025Absolute Zero: Reinforced Self-play Reasoning with Zero Datacited by 344
- 2022The Vendi Score: A Diversity Evaluation Metric for Machine Learningcited by 311
- 2025R-Zero: Self-Evolving Reasoning LLM from Zero Datacited by 228
- 2022Will we run out of data? Limits of LLM scaling based on human-generated datacited by 195
- 2026GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimizationcited by 193
- 2019Paired Open-Ended Trailblazer (POET): Endlessly Generating Increasingly Complex and Diverse Learning Environments and Their Solutionscited by 192
- 2017Intrinsic Motivation and Automatic Curricula via Asymmetric Self-Playcited by 141
- 2025Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)cited by 141
- 2026MemRL: Self-Evolving Agents via Runtime Reinforcement Learning on Episodic Memorycited by 129
- 2025Self-Evolving Curriculum for LLM Reasoningcited by 112
- 2025Verbalized Sampling: How to Mitigate Mode Collapse and Unlock LLM Diversitycited by 105
- 2025SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learningcited by 100
- 2019AI-GAs: AI-generating algorithms, an alternate paradigm for producing general artificial intelligencecited by 86
- 2024Prover-Verifier Games improve legibility of LLM outputscited by 85
- 2025Agent Learning via Early Experiencecited by 85
- 2025SPICE: Self-Play In Corpus Environments Improves Reasoningcited by 83
- 2024Open-Endedness is Essential for Artificial Superhuman Intelligencecited by 80
- 2025ReMA: Learning to Meta-think for LLMs with Multi-Agent Reinforcement Learningcited by 79
- 2024OMNI-EPIC: Open-endedness via Models of human Notions of Interestingness with Environments Programmed in Codecited by 74
- 2024Self-play with Execution Feedback: Improving Instruction-following Capabilities of Large Language Modelscited by 73
- 2025ACEBench: Who Wins the Match Point in Tool Usage?cited by 71
- 2023OMNI: Open-endedness via Models of human Notions of Interestingnesscited by 70
- 2025Can Large Reasoning Models Self-Train?cited by 68
- 2026Agent World Model: Infinity Synthetic Environments for Agentic Reinforcement Learningcited by 66
- 2025AgentRL: Scaling Agentic Reinforcement Learning with a Multi-Turn, Multi-Task Frameworkcited by 62
- 2025Self-Challenging Language Model Agentscited by 59
- 2025MegaScience: Pushing the Frontiers of Post-Training Datasets for Science Reasoningcited by 59
- 2025Simulating Environments with Reasoning Models for Agent Trainingcited by 57
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- 2025Towards General Agentic Intelligence via Environment Scalingcited by 54
- 2026Agent-World: Scaling Real-World Environment Synthesis for Evolving General Agent Intelligencecited by 54
- 2026EvoCUA: Evolving Computer Use Agents via Learning from Scalable Synthetic Experiencecited by 53
50 most cited of 101 All 101 (JSON)
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Citing papers per year: 2026: 12.
12 papers.
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- 2026Multi-LLM Collaborative Alignment via Stackelberg Gamescited by 0
- 2026Learning to Simulate Individuals from Macro Social Signalscited by 0
- 2026DAEDALUS: Bootstrapping Agent Memory from Self-Generated Taskscited by 0
- 2026Collaborative Learning and Reasoning over Model Slicescited by 0
- 2026AutoEnvScaling: Automating the Data Flywheel with Terminal Agentscited by 0
- 2026Recursive Environment Scaling for General Long-Horizon Agentscited by 0
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- 2026Player-1: Learning to Play from Synthetic Experience14 Oct 2026
- 2026Recursive Environment Scaling for General Long-Horizon Agents12 Oct 2026
- 2026AutoEnvScaling: Automating the Data Flywheel with Terminal Agents9 Oct 2026
- 2026Collaborative Learning and Reasoning over Model Slices9 Oct 2026
- 2026DAEDALUS: Bootstrapping Agent Memory from Self-Generated Tasks6 Oct 2026
- 2026Learning to Simulate Individuals from Macro Social Signals5 Oct 2026
- 2026Multi-LLM Collaborative Alignment via Stackelberg Games30 Sep 2026
- 2026Frontier Learning: Training LLM Reasoners at the Edge of Capability28 Sep 2026
- 2026Self-Play Search Distillation for Large Language Model Reasoning25 Sep 2026
- 2026Recursive self-improvement of AI research agents22 Sep 2026
- 2026FrogNano: Training a 4B Coding Agent via Online Task Synthesis7 Sep 2026
- 2026EnvHarness: Awakening Static Worlds for Agent Learning20 Aug 2026
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