# Neuro-Symbolic Learning for Long-Horizon Task Planning Under Complex Logical Constraints

arXiv: https://arxiv.org/abs/2606.06877 · HTML: https://mlsanity.com/paper/2606.06877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 79 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Builds on (most cited first, 30 of 37)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Integrated Task and Motion Planning](https://mlsanity.com/paper/2010.01083/) (2020)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Hydra: A Real-time Spatial Perception System for 3D Scene Graph Construction and Optimization](https://mlsanity.com/paper/2201.13360/) (2022)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [PDDLStream: Integrating Symbolic Planners and Blackbox Samplers via Optimistic Adaptive Planning](https://mlsanity.com/paper/1802.08705/) (2018)
- [Reducing the Barrier to Entry of Complex Robotic Software: a MoveIt! Case Study](https://mlsanity.com/paper/1404.3785/) (2014)
- [The LAMA Planner: Guiding Cost-Based Anytime Planning with Landmarks](https://mlsanity.com/paper/1401.3839/) (2014)
- [Foundations of Spatial Perception for Robotics: Hierarchical Representations and Real-time Systems](https://mlsanity.com/paper/2305.07154/) (2023)
- [Learning Neuro-Symbolic Skills for Bilevel Planning](https://mlsanity.com/paper/2206.10680/) (2022)
- [Predicate Invention for Bilevel Planning](https://mlsanity.com/paper/2203.09634/) (2022)
- [Learning Neuro-Symbolic Relational Transition Models for Bilevel Planning](https://mlsanity.com/paper/2105.14074/) (2021)
- [Planning with Learned Object Importance in Large Problem Instances using Graph Neural Networks](https://mlsanity.com/paper/2009.05613/) (2020)
- [Bisimulation Makes Analogies in Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2204.13060/) (2022)
- [iPlanner: Imperative Path Planning](https://mlsanity.com/paper/2302.11434/) (2023)
- [PyPose: A Library for Robot Learning with Physics-based Optimization](https://mlsanity.com/paper/2209.15428/) (2022)
- [Practice Makes Perfect: Planning to Learn Skill Parameter Policies](https://mlsanity.com/paper/2402.15025/) (2024)
- [Learning Efficient Abstract Planning Models that Choose What to Predict](https://mlsanity.com/paper/2208.07737/) (2022)
- [Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy](https://mlsanity.com/paper/2406.16087/) (2024)
- [iSLAM: Imperative SLAM](https://mlsanity.com/paper/2306.07894/) (2023)
- [WildDet3D: Scaling Promptable 3D Detection in the Wild](https://mlsanity.com/paper/2604.08626/) (2026)
- [RD-VIO: Robust Visual-Inertial Odometry for Mobile Augmented Reality in Dynamic Environments](https://mlsanity.com/paper/2310.15072/) (2023)
- [Embodied Active Learning of Relational State Abstractions for Bilevel Planning](https://mlsanity.com/paper/2303.04912/) (2023)
- [Bilevel Learning for Bilevel Planning](https://mlsanity.com/paper/2502.08697/) (2025)
- [Cellular-enabled Collaborative Robots Planning and Operations for Search-and-Rescue Scenarios](https://mlsanity.com/paper/2403.09177/) (2024)
- [iA*: Imperative Learning-based A* Search for Path Planning](https://mlsanity.com/paper/2403.15870/) (2024)

## Abstract (arXiv)

Task planning often suffers from severe efficiency bottlenecks when robots must reason over long-horizon action sequences under complex logical constraints, including object affordances, spatial relationships, and sequential action dependencies. Recent neuro-symbolic methods improve planning efficiency by learning object-importance scores to prune task-irrelevant objects, but they typically rely on fixed offline supervision generated from full search spaces. This creates a train-test mismatch: at deployment, the planner operates in pruned search spaces induced by the model's own imperfect predictions, leading to exposure bias and degraded planning performance. To address this challenge, we formulate object-importance learning for task planning as an imperative learning-based bilevel optimization problem. The upper level optimizes a neural scorer, while the lower level solves a symbolic planning problem in the score-pruned search space. To stabilize this learning process, we introduce a 3R strategy into the lower-level planning, using parallel Repair, Restart, and Rollback recovery to provide reliable and adaptive feedback for upper-level learning. Experiments on three challenging benchmarks demonstrate state-of-the-art performance, including an 80.04% reduction in failure rate and a 57.14% reduction in planning time. We further validate the framework on a quadruped-based mobile manipulator in simulation and the real world, demonstrating its potential for efficient and deployable neuro-symbolic task planning.