# Predicate Invention for Bilevel Planning

arXiv: https://arxiv.org/abs/2203.09634 · HTML: https://mlsanity.com/paper/2203.09634/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 60 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Integrated Task and Motion Planning](https://mlsanity.com/paper/2010.01083/) (2020)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [Online Bayesian Goal Inference for Boundedly-Rational Planning Agents](https://mlsanity.com/paper/2006.07532/) (2020)
- [Near Optimal Behavior via Approximate State Abstraction](https://mlsanity.com/paper/1701.04113/) (2017)
- [Online Replanning in Belief Space for Partially Observable Task and Motion Problems](https://mlsanity.com/paper/1911.04577/) (2019)
- [Classical Planning in Deep Latent Space: Bridging the Subsymbolic-Symbolic Boundary](https://mlsanity.com/paper/1705.00154/) (2017)
- [Learning Symbolic Operators for Task and Motion Planning](https://mlsanity.com/paper/2103.00589/) (2021)
- [Learning compositional models of robot skills for task and motion planning](https://mlsanity.com/paper/2006.06444/) (2020)
- [Learning Neuro-Symbolic Relational Transition Models for Bilevel Planning](https://mlsanity.com/paper/2105.14074/) (2021)
- [Learning First-Order Symbolic Representations for Planning from the Structure of the State Space](https://mlsanity.com/paper/1909.05546/) (2019)
- [Discovering State and Action Abstractions for Generalized Task and Motion Planning](https://mlsanity.com/paper/2109.11082/) (2021)
- [Generalized Lazy Search for Robot Motion Planning: Interleaving Search and Edge Evaluation via Event-based Toggles](https://mlsanity.com/paper/1904.02795/) (2019)
- [Learning Quickly to Plan Quickly Using Modular Meta-Learning](https://mlsanity.com/paper/1809.07878/) (2018)
- [Extended Tree Search for Robot Task and Motion Planning](https://mlsanity.com/paper/2103.05456/) (2021)
- [Learning Neural-Symbolic Descriptive Planning Models via Cube-Space Priors: The Voyage Home (to STRIPS)](https://mlsanity.com/paper/2004.12850/) (2020)

## Built on by (most cited first, 30 of 49)

- [Generalized Planning in PDDL Domains with Pretrained Large Language Models](https://mlsanity.com/paper/2305.11014/) (2023)
- [LLM3:Large Language Model-based Task and Motion Planning with Motion Failure Reasoning](https://mlsanity.com/paper/2403.11552/) (2024)
- [VisualPredicator: Learning Abstract World Models with Neuro-Symbolic Predicates for Robot Planning](https://mlsanity.com/paper/2410.23156/) (2024)
- [LEAGUE: Guided Skill Learning and Abstraction for Long-Horizon Manipulation](https://mlsanity.com/paper/2210.12631/) (2022)
- [Practice Makes Perfect: Planning to Learn Skill Parameter Policies](https://mlsanity.com/paper/2402.15025/) (2024)
- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Learning Efficient Abstract Planning Models that Choose What to Predict](https://mlsanity.com/paper/2208.07737/) (2022)
- [Embodied Lifelong Learning for Task and Motion Planning](https://mlsanity.com/paper/2307.06870/) (2023)
- [Partially Observable Task and Motion Planning with Uncertainty and Risk Awareness](https://mlsanity.com/paper/2403.10454/) (2024)
- [Leveraging Environment Interaction for Automated PDDL Translation and Planning with Large Language Models](https://mlsanity.com/paper/2407.12979/) (2024)
- [Learning Compositional Behaviors from Demonstration and Language](https://mlsanity.com/paper/2505.21981/) (2025)
- [Synthesizing world models for bilevel planning](https://mlsanity.com/paper/2503.20124/) (2025)
- [From Pixels to Predicates: Learning Symbolic World Models via Pretrained Vision-Language Models](https://mlsanity.com/paper/2501.00296/) (2024)
- [Open-World Task and Motion Planning via Vision-Language Model Generated Constraints](https://mlsanity.com/paper/2411.08253/) (2024)
- [ExoPredicator: Learning Abstract Models of Dynamic Worlds for Robot Planning](https://mlsanity.com/paper/2509.26255/) (2025)
- [Embodied Active Learning of Relational State Abstractions for Bilevel Planning](https://mlsanity.com/paper/2303.04912/) (2023)
- [Meta-Learning Parameterized Skills](https://mlsanity.com/paper/2206.03597/) (2022)
- [Language Models For Generalised PDDL Planning: Synthesising Sound and Programmatic Policies](https://mlsanity.com/paper/2508.18507/) (2025)
- [Hybrid Diffusion for Simultaneous Symbolic and Continuous Planning](https://mlsanity.com/paper/2509.21983/) (2025)
- [Generalisation Through Negation and Predicate Invention](https://mlsanity.com/paper/2301.07629/) (2023)
- [Graph Learning for Numeric Planning](https://mlsanity.com/paper/2410.24080/) (2024)
- [Neuro-Symbolic Imitation Learning: Discovering Symbolic Abstractions for Skill Learning](https://mlsanity.com/paper/2503.21406/) (2025)
- [Discovering Predictive Relational Object Symbols with Symbolic Attentive Layers](https://mlsanity.com/paper/2309.00889/) (2023)
- [RoboMP2: A Robotic Multimodal Perception-Planning Framework with Multimodal Large Language Models](https://mlsanity.com/paper/2404.04929/) (2024)
- [SLAP: Shortcut Learning for Abstract Planning](https://mlsanity.com/paper/2511.01107/) (2025)
- [Kintsugi: Learning Policies by Repairing Executable Knowledge Bases](https://mlsanity.com/paper/2605.09487/) (2026)
- [CLIMB: Language-Guided Continual Learning for Task Planning with Iterative Model Building](https://mlsanity.com/paper/2410.13756/) (2024)
- [Few-Shot Neuro-Symbolic Imitation Learning for Long-Horizon Planning and Acting](https://mlsanity.com/paper/2508.21501/) (2025)
- [Learning logic programs by discovering higher-order abstractions](https://mlsanity.com/paper/2308.08334/) (2023)
- [Learning to Bridge the Gap: Efficient Novelty Recovery with Planning and Reinforcement Learning](https://mlsanity.com/paper/2409.19226/) (2024)

## Abstract (arXiv)

Efficient planning in continuous state and action spaces is fundamentally hard, even when the transition model is deterministic and known. One way to alleviate this challenge is to perform bilevel planning with abstractions, where a high-level search for abstract plans is used to guide planning in the original transition space. Previous work has shown that when state abstractions in the form of symbolic predicates are hand-designed, operators and samplers for bilevel planning can be learned from demonstrations. In this work, we propose an algorithm for learning predicates from demonstrations, eliminating the need for manually specified state abstractions. Our key idea is to learn predicates by optimizing a surrogate objective that is tractable but faithful to our real efficient-planning objective. We use this surrogate objective in a hill-climbing search over predicate sets drawn from a grammar. Experimentally, we show across four robotic planning environments that our learned abstractions are able to quickly solve held-out tasks, outperforming six baselines. Code: https://tinyurl.com/predicators-release