💻 computer science

Bilevel Planning with Learned Symbolic Abstractions from Interaction Data

This paper proposes a bilevel neuro-symbolic framework that combines learned probabilistic symbolic rules for rapid high-level planning with learned continuous effect models for low-level verification, enabling robots to efficiently generate and validate plans in complex environments by effectively bridging discrete abstractions and continuous dynamics.

Original authors: Fatih Dogangun, Burcu Kilic, Serdar Bahar, Emre Ugur

Published 2026-03-10

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CC BY 4.0

Original authors: Fatih Dogangun, Burcu Kilic, Serdar Bahar, Emre Ugur

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are teaching a robot to tidy up a messy room full of toys. The robot has two ways of thinking: The Big Picture (symbolic) and The Fine Details (continuous).

This paper describes a new "brain" for robots that uses both ways of thinking together, like a team of a Strategic General and a Precision Engineer.

The Problem: Why Robots Get Stuck

Robots live in a world of continuous movement (millimeters, angles, forces). If a robot tries to calculate every possible move in this complex world, it gets overwhelmed—like trying to count every grain of sand on a beach to decide which path to walk.

To solve this, scientists usually teach robots to use symbols (like "Block A is on Block B"). This is fast and easy, like using a map with just city names. But maps are imperfect. A map might say "Drive to the park," but it doesn't know there's a giant pothole or a fallen tree blocking the road. If the robot follows the map blindly, it crashes.

The Solution: A Two-Level Team

The authors built a system that works in two levels, switching between the "Map" and the "Real World" as needed.

Level 1: The Strategic General (Symbolic Planning)

This is the fast, high-level thinker.

How it works: It learns from the robot's own playtime. The robot bumps into things, picks them up, and drops them. The robot's brain watches this and learns simple rules: "If I pick up the red block, it usually ends up on the blue block."
The Upgrade: Previous robots only learned the most likely outcome (e.g., "Red block goes on Blue block"). This new system learns the probabilities. It knows, "90% of the time, the red block goes on the blue one, but 10% of the time, it might slide off."
The Analogy: Imagine a chess player who doesn't just plan the best move, but also considers the "what if" scenarios where the opponent makes a weird move. This makes the plan more robust.

The Safety Check: The Inspector

Before the robot actually moves, the system runs a Simulation.

It takes the "General's" plan and runs it through a Precision Engineer (a second, highly accurate AI model).
The Analogy: Think of this like a flight simulator. The pilot (General) says, "We are going to fly to Paris." The simulator (Engineer) checks the weather, fuel, and engine physics. If the simulator says, "No, we will crash into a mountain," the plan is rejected before the robot moves a muscle.
This step catches plans that look good on the map but fail in reality.

Level 2: The Precision Engineer (Continuous Search)

If the General's plan fails the safety check, or if the problem is too complex for a simple map, the system switches to Level 2.

How it works: This is the "brute force" method. Instead of using simple symbols, it calculates the exact physics of every single move in real-time.
The Trade-off: This is very accurate but very slow and expensive to compute. It's like calculating the trajectory of every single leaf in the wind to find a path.
The Strategy: The robot only uses this heavy-duty method when the fast, symbolic method fails. It's like calling a specialist surgeon only when a general practitioner can't fix the problem.

What They Found

The researchers tested this on a robot arm moving blocks of different sizes.

Better than just a Map: The new system solved more problems than robots that only used the "General" (symbolic) approach.
Better than just the Engineer: It was almost as good as robots that only used the slow, heavy-duty "Engineer" method, but it was much faster because it solved most problems using the quick "General" method.
The Safety Net Works: The "Inspector" successfully stopped the robot from trying plans that would fail, saving time and preventing crashes.

The Bottom Line

This paper presents a robot brain that is fast because it uses simple rules, smart because it understands probabilities (chances of things going wrong), and safe because it double-checks its plans with a physics simulator before acting. It only slows down to do the heavy math when absolutely necessary, making it a very efficient way for robots to learn and act in the real world.

Technical Summary: Bilevel Planning with Learned Symbolic Abstractions from Interaction Data

Problem Definition

Robotic agents operating in continuous environments face a fundamental trade-off: reasoning directly in high-dimensional continuous state spaces is computationally intractable due to the infinite or vast number of possible solutions, while purely symbolic reasoning often fails because it discards critical geometric and dynamic information, leading to execution failures. Existing methods that learn symbolic abstractions from unsupervised robot exploration typically rely on deterministic domains, lack mechanisms to verify if a symbolic plan will succeed in the continuous world, and offer no fallback when the abstraction is insufficient. This paper addresses the need for a planning framework that combines the efficiency of high-level symbolic reasoning with the precision of continuous dynamics verification.

Methodology

The authors propose a bilevel neuro-symbolic planning framework that operates through two distinct levels, supported by a dual-model architecture trained on unsupervised interaction data.

1. Dual-Model Architecture

The framework utilizes two specialized neural network models derived from an encoder-decoder architecture trained to predict action effects:

Symbolic Model ( $M_{sym}$ ): Uses a Gumbel-Sigmoid activation function in its bottleneck layers. This model is designed to discover discrete unary object symbols and relational symbols (e.g., "on," "next to") to generate symbolic operators for high-level planning.
Dynamics Model ( $M_{dyn}$ ): Uses a standard Sigmoid activation function in its bottleneck layers. While sharing the same architecture, this model is optimized for accurate continuous effect prediction, serving as a forward dynamics model for verification and low-level search.

2. Learning Process

The system learns from a dataset of interaction samples $(X, a, X')$ , where $X$ represents the continuous state (object positions and types) and $a$ represents parameterized pick-place skills.

Symbol Discovery: The Symbolic Model maps continuous states to discrete symbols. Relational symbols are computed using a self-attention mechanism adapted with Gumbel-Sigmoid to allow differentiable learning of discrete symbols.
Operator Extraction: Continuous transitions are converted into symbolic datasets. Operators are defined as sets of preconditions and effects based on the most frequent post-action states observed in the data.
Probabilistic Domain Construction: Instead of deterministic operators, the framework constructs a PPDDL (Probabilistic PDDL) domain. Each operator includes a probability distribution over possible symbolic effects based on their empirical frequency, capturing the stochasticity of real-world interactions.

3. The Bilevel Planning Algorithm

The planning process proceeds in two levels:

Level 1: Probabilistic Symbolic Planning with Verification
- The system generates an ensemble of $N$ PDDL domains by sampling effects from the learned probabilistic distributions.
- A classical AI planner (Fast-Downward) searches for plans in these domains.
- Continuous Verification: Candidate symbolic plans are ranked by probability. The Dynamics Model ( $M_{dyn}$ ) is used as a forward simulator to predict the continuous outcome of each candidate plan. If the predicted final state is within a tolerance threshold ( $\tau_{verify}$ ) of the goal, the plan is accepted.
Level 2: Continuous Forward Search Fallback
- If no symbolic plan passes verification, the system invokes a weighted $A^*$ search in the continuous state space.
- This search uses the Dynamics Model for state transitions and a heuristic based on Euclidean distance to the goal.
- To ensure tractability, the search employs heuristic action pruning, generating only goal-oriented actions (e.g., moving misplaced objects toward their target positions) rather than exploring the full action space.

Key Contributions

Bilevel Framework: A novel architecture that integrates probabilistic symbolic planning at the high level with continuous forward search as a fallback, bridging the gap between abstract reasoning and continuous dynamics.
Dual-Model Scheme: The introduction of two specialized models—one for discrete symbol discovery and another for precise continuous effect prediction—demonstrating that a single model cannot optimally serve both purposes.
Verification Mechanism: A method that utilizes the continuous dynamics model to verify symbolic plans before execution, effectively filtering out plans that are symbolically valid but dynamically infeasible.
Probabilistic Operator Learning: Moving beyond deterministic domains to learn operators with stochastic effects, allowing the planner to explore less probable but potentially successful paths.

Experimental Results

The framework was evaluated on multi-object manipulation tasks in a simulated tabletop environment with 2 to 4 objects and action sequences of length 1 to 5.

Model Validation: The Dynamics Model achieved a lower mean effect prediction error (1.96 cm) compared to the Symbolic Model (3.33 cm), validating the need for separate models for continuous prediction.
Probabilistic vs. Deterministic: The probabilistic planner significantly outperformed the deterministic baseline (e.g., 73.0% vs. 64.67% success rate for 1-step tasks), demonstrating that considering the full distribution of outcomes improves robustness.
Verification Performance: The continuous plan verifier achieved a mean accuracy of 0.91 and an F1 score of 0.90. Verified plans had a 94.5% success rate, while unverified plans had an 87.3% failure rate, confirming the mechanism's reliability in filtering failed plans.
Overall Performance: The proposed Bilevel Planner achieved planning success rates statistically comparable to full Continuous Forward Search ( $p=0.71$ ). However, it solved the majority of problems using efficient symbolic reasoning, resorting to the computationally expensive continuous search only when necessary.

Significance

The paper claims that this approach successfully mitigates the limitations of purely symbolic planning (loss of geometric detail) and purely continuous planning (computational intractability). By combining the efficiency of symbolic reasoning with the precision of learned continuous dynamics, the framework offers a robust solution for robotic manipulation. It demonstrates that agents can achieve high-level planning performance comparable to exhaustive continuous search while maintaining computational efficiency, provided they can verify symbolic plans against learned physical dynamics. The work highlights the importance of probabilistic modeling and verification in making learned symbolic abstractions reliable for real-world execution.