Bilevel Planning with Learned Symbolic Abstractions from Interaction Data

TL;DR

A bilevel neuro-symbolic framework is proposed in which learned probabilistic symbolic rules generate candidate plans rapidly at the high level, and learned continuous effect models verify these plans and perform forward search when necessary at the low level.

Abstract

Intelligent agents must reason over both continuous dynamics and discrete representations to generate effective plans in complex environments. Previous studies have shown that symbolic abstractions can emerge from neural effect predictors trained with a robot's unsupervised exploration. However, these methods rely on deterministic symbolic domains, lack mechanisms to verify the generated symbolic plans, and operate only at the abstract level, often failing to capture the continuous dynamics of the environment. To overcome these limitations, we propose a bilevel neuro-symbolic framework in which learned probabilistic symbolic rules generate candidate plans rapidly at the high level, and learned continuous effect models verify these plans and perform forward search when necessary at the low level. Our experiments on multi-object manipulation tasks demonstrate that the proposed bilevel method outperforms symbolic-only approaches, reliably identifying failing plans through verification, and achieves planning performance statistically comparable to continuous forward search while resolving most problems via efficient symbolic reasoning.

Figures (7)

• Figure 1: Learning pipeline of the proposed bilevel planning framework. The system learns both a Symbolic Model ($M_{\text{sym}}$) and a Dynamics Model ($M_{\text{dyn}}$) from a transition dataset consisting of interaction samples. The Symbolic Model is used to generate symbols and then find rules to form a symbolic domain $\Phi$, containing probabilistic operators. The Dynamics Model is used for accurate effect prediction, which is then utilized to verify symbolic plans, and explore plans in continuous state space when no verified symbolic plan is present.
• Figure 2: Probabilistic symbolic planning and verification. The PDDL domains, $\mathcal{D}$, are initially sampled from the symbolic domain $\Phi$, and then given to an AI planner alongside a symbolic problem. Then, candidate symbolic plans are passed into the verification step accordingly to their occurrences, and each action is verified in the continuous domain using the Dynamics Model. If the plan passes verification within a tolerance threshold $\tau_{\text{verify}}$, the bilevel algorithm returns that symbolic plan; otherwise, the system invokes a continuous forward search.
• Figure 3: Planning success rate comparison of Symbolic Model and Dynamics Model across both planning levels: Symbolic planning and Continuous Forward Search. Results are averaged over two runs and the number of objects ($n \in {\{2,3,4\}}$).
• Figure 4: The top row shows the states while generating the problem, including the initial and goal states. In the following rows, the sequence of plan verifier predicted states (transparent objects illustrate the predicted positions) and their executions are demonstrated. The middle row presents the most probable plan, which also corresponds to the only symbolic plan if a probabilistic planner is not employed. The Dynamics Model accurately predicted the misalignment of the pink block's placement and classified the plan as an unverified. The bottom row shows the predictions of the verifier and the execution of the next symbolic plan, which has been verified and deemed successful.
• Figure 5: The F1 and Accuracy scores of the verifier for symbolic plans across varying thresholds ($\tau_{verify}$). Results are averaged over 50 problems, and the high-level actions ($k \in {1,2,3,4,5}$) for each number of objects.