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Closed-Loop Long-Horizon Robotic Planning via Equilibrium Sequence Modeling
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Proposes equilibrium sequence modeling, which trains an LLM self-refining planner via deep-equilibrium fixed-point supervised learning, plus nested equilibrium solving with environment or world-model feedback for closed-loop long-horizon robot planning on VirtualHome-Env.
Problem
LLM agents make planning errors and cannot plan ahead or correct outputs well for closed-loop long-horizon robotic task planning; self-refinement training typically needs backprop through many steps or RL with verifiers.
Approach
Formulate iterative self-refinement as a fixed-point (deep equilibrium) problem; use the implicit function theorem with the inverse Jacobian dropped (A≈I) so training reduces to standard supervised finetuning on (equilibrium plan, ground truth) pairs; nest an inner equilibrium loop over plan refinement inside an outer loop of environment or world-model feedback, reusing previous equilibria.
Key results
- With up to 10 corrections on novel scene and task split, the method reaches 56.45% SR and 76.63% GCR vs. 43.55% SR / 65.18% GCR for SELF-REFINE (Llama 3 8B).
- Without correction, on the novel scene split it achieves 65.26% SR vs. 51.58% for Tree-Planner (N=25) with the same Llama 3 8B backbone, while Tree-Planner is better in the no-feedback novel scene and task setting in some metrics.
- Fixed-point convergence takes about 3 iterations on average (mean 3.02) vs. 6.70 for original Llama-3-8B.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| equilibrium sequence modeling (self-refining planner) vs. supervised finetuning, no correction setting | Finetuned Llama 3 8B planner · VirtualHome-Env Novel Scene | SR: 41.05 -> 65.26 | Helped |
| equilibrium sequence modeling with up to 10 corrections vs. SELF-REFINE | Finetuned Llama 3 8B planner · VirtualHome-Env Novel Scene and Task | SR: 43.55 -> 56.45 | Helped |
| adding environmental feedback (up to 10 corrections) to the equilibrium planner (ablation) | Equilibrium planner · VirtualHome-Env Novel Scene and Task | SR: 40.32 -> 56.45 | Helped |
| adding world model internal feedback to the equilibrium planner (ablation) | Equilibrium planner · VirtualHome-Env Novel Scene | SR: 49.47 -> 65.26 (no env feedback) | Helped |
| adding world model internal feedback without environment feedback (ablation) | Equilibrium planner · VirtualHome-Env Novel Scene and Task | GCR: 59.98 -> 65.40 | Helped |
| adding noise to environmental feedback (5% to 20%) (ablation) | Equilibrium planner · VirtualHome-Env Novel Scene and Task | SR: 56.45 at 0% -> 50.00 to 53.23 at 10-20% | No clear effect |
| Tree-Planner (N=25/50) vs. equilibrium planner without feedback | Equilibrium planner · VirtualHome-Env Novel Scene and Task | SR: 38.71/38.71 (Tree-Planner) vs 40.32 - ours is competitive; paper says ours is inferior to Tree-Planner in no-feedback se | Hurt |
| reusing previous equilibrium solution as starting point and dynamic inner loops | Equilibrium planner · VirtualHome-Env inference efficiency | inference time (hours): 16h vs 24h for Tree-Planner | Helped |
Surprising findings
- Without any environment feedback, the method is inferior to Tree-Planner in the no-feedback setting, which the authors attribute to Tree-Planner generating 25-50 candidate plans.
- Internal world-model feedback alone does not enable successful replanning, though it reduces environment interactions before convergence.
Limitations
- Training is slower than baselines due to equilibrium solving for synthesizing training pairs.
- Performance drops relative to Tree-Planner in the no-feedback setting.
- Relies on a dataset partition of VirtualHome-Env since prior works did not release their splits; comparisons with GPT-3.5 baselines are for reference only due to differing setups.
Experimental setup
Datasets: VirtualHome-Env
Benchmarks: VirtualHome-Env ALFRED
Metrics: executability success rate goal conditions recall TFLOPS fixed-point iterations
Baselines: Tree-Planner SELF-REFINE Supervised finetuned Llama 3 8B ProgPrompt Zero-shot Planner Local Replan Global Replan
Builds on: deep equilibrium models SELF-REFINE Tree-Planner one-step gradient
Closest papers by meaning
- Plan-Seq-Learn: Language Model Guided RL for Solving Long Horizon Robotics Tasks (ICLR 2024 · similarity 0.89)
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- Long-Horizon Planning for Multi-Agent Robots in Partially Observable Environments (NeurIPS 2024 · similarity 0.87)
- Embodied Task Planning via Graph-Informed Action Generation with Large Language Models (ICML 2026 · similarity 0.87)
- Hierarchical Planning for Complex Tasks with Knowledge Graph-RAG and Symbolic Verification (ICML 2025 · similarity 0.86)
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