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Learning Symbolic Operators for Task and Motion Planning

Tom Silver, Rohan Chitnis, Joshua Tenenbaum, Leslie Pack Kaelbling, Tomas Lozano-Perez

arXiv:2103.00589v2cs.ROcs.AIcs.LG

TL;DR

TAMP must coordinate continuous motions with task-level plan feasibility, but its symbolic operators are usually domain-specific. This paper learns probabilistic operators from transition data and finds that LOFT matches oracle performance across three domains with enough data, outperforming learning-based baselines in data efficiency.

  • Problem

    TAMP operators guide symbolic search, but popular systems hand-specify them for each domain, motivating domain-independent operator learning.

    Source: §I · p. 1

  • Method

    LOFT learns probabilistic operators from transition data through lifted effect clustering, precondition learning, and parameter estimation.

    Source: B. Learning Probabilistic Operators · p. 4

  • Results

    With enough data, LOFT achieves oracle performance in all three domains and is more data-efficient than learning-based baselines; in Painting, no baseline solves a problem within 10 seconds.

    Source: B. Results and Discussion · p. 7

  • Takeaways & Limitations

    Operators provide guidance for efficient TAMP planning, and that guidance improves with more data, though planning remains possible without operators.

    Source: C. Planning with Learned Operators · p. 5

    The method assumes predicates are given, a severe limitation because their quality determines the quality of the abstraction.

    Source: §VII · p. 8

Abstract

from arXiv · show

Robotic planning problems in hybrid state and action spaces can be solved by integrated task and motion planners (TAMP) that handle the complex interaction between motion-level decisions and task-level plan feasibility. TAMP approaches rely on domain-specific symbolic operators to guide the task-level search, making planning efficient. In this work, we formalize and study the problem of operator learning for TAMP. Central to this study is the view that operators define a lossy abstraction of the transition model of a domain. We then propose a bottom-up relational learning method for operator learning and show how the learned operators can be used for planning in a TAMP system. Experimentally, we provide results in three domains, including long-horizon robotic planning tasks. We find our approach to substantially outperform several baselines, including three graph neural network-based model-free approaches from the recent literature. Video: https://youtu.be/iVfpX9BpBRo Code: https://git.io/JCT0g

I. INTRODUCTION

TAMP must coordinate discrete task choices with continuous motions, yet its symbolic operators are typically hand-specified for each domain. This work formalizes learning those operators and evaluates a relational approach across three domains.

I. INTRODUCTION

  • TAMP must coordinate low-level geometric choices with high-level plan feasibility, while popular systems rely on hand-specified operators for each domain.The paper aims to develop a domain-independent operator-learning algorithm.Source: §I · p. 1
  • Symbolic operators can prune plans that cannot reach a goal, support bilevel optimization, and enable heuristics that speed symbolic search.These benefits motivate learning operators rather than dispensing with them.Source: §I · p. 1
  • The paper formalizes operator learning for TAMP and proposes a bottom-up relational learning method.The setting includes a simulator, hybrid controllers and samplers, continuous object states, and predicates defining a lossy abstraction.Source: §I · p. 1
  • Experiments span three domains, including long-horizon robotic planning, and compare the approach with several baselines.The paper includes three graph neural network-based model-free approaches among the baselines.Source: §I · p. 1

A. Task and Motion Planning (TAMP)

The paper situates operator learning within TAMP, where learned symbolic operators guide planning over a lossy abstraction. Its problem setting assumes provided predicates, controllers, samplers, and transition data.

A. Task and Motion Planning (TAMP)

  • TAMP combines AI task planning and robotic motion planning for continuous robotic planning problems, but popular systems rely on hand-defined planning models.The paper targets this hand-specification limitation.Source: A. Task and Motion Planning (TAMP) · p. 2

B. Learning for Task and Motion Planning

  • Learning for TAMP includes sampler learning and symbolic search guidance; this work assumes samplers are given and focuses on learning operators.Related model-free approaches address symbolic guidance by sampling low-level transitions or learning a recurrent Q-function.Source: B. Learning for Task and Motion Planning · p. 2

C. Learning Symbolic Operators

  • Unlike prior symbolic operator learning, this work treats TAMP operators as a lossy abstraction that guides candidate plans for a low-level optimizer.The operators are a means to guide the overall planning procedure, not the entire planning model.Source: C. Learning Symbolic Operators · p. 2

III. PROBLEM SETTING

  • The setting assumes typed-object continuous states, hybrid controllers with samplers, a deterministic simulator, and provided discrete predicates that parse states into symbolic states.Offline transitions from related planning problems supply the learning data.Source: §III · p. 2

IV. TASK AND MOTION PLANNING WITH OPERATORS

Symbolic operators guide search over plan skeletons, which are refined by assigning continuous parameters. Because the abstraction is lossy and refinement can fail, planning alternates symbolic search with low-level backtracking.

IV. TASK AND MOTION PLANNING WITH OPERATORS

  • A symbolic operator combines a controller, typed object parameters, preconditions, and effects, but does not model continuous action parameters.Operators predict from discrete controller parameters and symbolic state alone.Source: §IV · p. 3
  • A plan skeleton is a sequence of action templates with continuous parameters unassigned; a symbolic goal-achieving skeleton is not guaranteed to refine into an environment-valid plan.The lack of a guarantee follows from the lossy predicate-induced abstraction.Source: §IV · p. 3
  • Search-then-sample TAMP alternates symbolic search for skeletons with low-level optimization for continuous arguments.The high-level search uses A* with hAdd, and the low-level process backtracks over sampler calls before requesting another skeleton.Source: §IV · p. 3
  • Operators prune refinement by rejecting plan prefixes whose parsed symbolic transitions disagree with the operators’ expected transitions.The sampler arguments for the inconsistent action are resampled.Source: §IV · p. 3
  • The described planner is not probabilistically complete: a valid skeleton may be missed when refinement fails within its sampler-call limit, because failed skeletons are not revisited.The authors selected this approach for relative simplicity and strong empirical performance.Source: §IV · p. 3

V. LEARNING SYMBOLIC OPERATORS FOR TAMP

LOFT learns probabilistic operators to account for lossiness in symbolic abstraction, then applies them in TAMP planning. The approach comprises effect clustering, precondition learning, and parameter estimation.

V. LEARNING SYMBOLIC OPERATORS FOR TAMP

  • LOFT learns probabilistic operators to account for the lossiness induced by symbolic abstraction.The section presents this as the motivation for probabilistic operators.Source: §V · p. 3
  • The operator-learning algorithm has three stages: lifted effect clustering, precondition learning, and parameter estimation.The paper identifies this as its efficient learning algorithm from transition data.Source: §V · p. 3
  • The learned probabilistic operators are used for task and motion planning.The section frames their use as part of the LOFT pipeline.Source: §V · p. 3

A. Probabilistic Operators as Symbolic Transition Models

The paper treats symbolic operators as a probabilistic transition model because the symbolic abstraction is lossy. Learned probabilistic operators are converted into deterministic operators for planning.

A. Probabilistic Operators as Symbolic Transition Models

  • Lossiness in the symbolic abstraction means a deterministic operator cannot accurately model symbolic transitions; probabilistic operators instead describe P(s_t+1 | s_t, a_t).The probabilistic operators represent a distribution over effect sets rather than one effect set.Source: A. Probabilistic Operators as Symbolic… · p. 3
  • Probabilities are used to filter rare outcomes before being discarded, so their precise semantics are not needed for the stated planning purpose.Source: A. Probabilistic Operators as Symbolic… · p. 3
  • The learning pipeline clusters transition data by lifted effects, learns preconditions, instantiates operators, and estimates their effect probabilities.Figure 2 depicts learned probabilistic operators being determinized and used to generate high-level plan skeletons for new TAMP instances.Source: A. Probabilistic Operators as Symbolic… · p. 4, Figure 2 · p. 4

B. Learning Probabilistic Operators

The method learns probabilistic operators from symbolic transitions, separating effect clustering, precondition learning, and probability estimation. Its approximate precondition search is the computationally hard step.

B. Learning Probabilistic Operators

  • Low-level transition data are parsed into symbolic transitions, partitioned by controller, and processed through lifted effect clustering, precondition learning, and parameter estimation.The dataset also includes goals, although they are irrelevant to learning a transition model.Source: B. Learning Probabilistic Operators · p. 4
  • Transitions are clustered when their ground effects match under a bijective object mapping, yielding lifted effect sets with placeholder variables.The passage says this unification check is linear in the effect-set sizes.Source: B. Learning Probabilistic Operators · p. 4
  • Preconditions are learned by greedy outer search and best-first predicate removal, scoring true positives against false positives with β = 10 in all experiments.Candidate preconditions are formed by lifting prior states; the score rewards transitions explained by the effect cluster and penalizes false positives.Source: B. Learning Probabilistic Operators · pp. 4–5
  • Precondition learning is the computationally hard step, and its outer and inner searches approximate the best sets under the score function.The inner-search limit was 100 iterations in all experiments; complexity also depends on data, controller count, and the largest state’s predicate count.Source: B. Learning Probabilistic Operators · p. 5
  • For each operator, effect probabilities are estimated by dividing transitions producing an effect by those satisfying its lifted preconditions.Matching precondition sets across lifted effects are combined to initialize probabilistic operators.Source: B. Learning Probabilistic Operators · p. 5
  • Against LNDR, the method is reported faster and more effective in these domains, with the difference attributed to separating effect clustering, precondition learning, and parameter estimation.Source: B. Learning Probabilistic Operators · p. 5

C. Planning with Learned Operators

The paper uses learned probabilistic operators to guide TAMP planning by converting them into deterministic operators. Planning remains possible without operators, but exhaustive plan-skeleton search is less efficient guidance.

C. Planning with Learned Operators

  • A learned operator’s effects may not form a proper probability distribution when one transition matches multiple preconditions, but probabilities are only used to filter low-probability effects.The paper says this technicality can be ignored for its planning purpose.Source: C. Planning with Learned Operators · p. 5
  • Probabilistic operators are determinized by creating one deterministic operator per effect set, after filtering effects below the pmin probability threshold.Source: C. Planning with Learned Operators · p. 5
  • Without learned operators, the planner can still search all plan skeletons in increasing length, making operators guidance for efficient TAMP rather than a prerequisite.Source: C. Planning with Learned Operators · p. 5
  • The stated aim is to demonstrate learning the operators underpinning TAMP; preliminary LOFT use with another TAMP system was set aside for speed advantages.Source: C. Planning with Learned Operators · p. 5

A. Experimental Setup

Experiments evaluate LOFT in Cover, Blocks, and long-horizon Painting tasks, using shared transition data and comparisons with learned and oracle planning approaches.

A. Experimental Setup

  • Cover tests picking and placing colored blocks along a line to cover matching targets, with allowed regions requiring advance consideration of future placement.Evaluation uses 30 randomly generated problems per seed, with average optimal plan length 3.Source: A. Experimental Setup · p. 5
  • Blocks evaluates assembling tabletop blocks into towers, including continuous placement choices that affect the feasibility of later plan steps.Evaluation uses 10 randomly generated problems per seed, with average optimal plan length 8.Source: A. Experimental Setup · pp. 5–6
  • Painting requires objects to be washed, dried, and painted before placement, and a grasp choice can affect placement feasibility up to four timesteps later.Evaluation uses 30 randomly generated problems per seed, with average optimal plan length 31.Source: A. Experimental Setup · p. 6
  • Comparisons include LOFT with LNDR substituted for operator learning, Q-function GNN baselines with and without low-level state input, and a recurrent GNN plan-skeleton predictor.Source: A. Experimental Setup · p. 6
  • Additional comparisons include a raw GNN policy, planning without operators, and an oracle planner using hand-written operators.The no-operator baseline tries to optimize every possible plan skeleton; the oracle is described as an upper bound for LOFT.Source: A. Experimental Setup · p. 6
  • Training data come from oracle demonstrations on 20 smaller problems per domain, augmented with random-action transitions from demonstrated states.The learning-based methods receive the same dataset; transition counts are 126 for Cover, 152 for Blocks, and 2819 for Painting.Source: A. Experimental Setup · pp. 6–7
  • Across all three domains, LOFT reaches better planning performance than other approaches with less data, measured as the percent of planning problems solved within timeout (1 second for Cover; 10 seconds for Blocks and Painting).Each plotted point is a mean over 5 seeds; dotted lines indicate the non-learning approaches B5 and Oracle.Source: Figure 4 · p. 7

B. Results and Discussion

LOFT reaches oracle planning performance with enough data in all three domains and is more data-efficient than learning-based baselines. The results also expose how learned-operator quality, sampler use, and heuristic choice affect planning performance.

Results and Discussion

  • With enough data, LOFT reaches oracle performance in all three domains, is more data-efficient than learning-based baselines, and solves Painting problems when none of those baselines solve one within 10 seconds.The authors attribute LOFT’s data efficiency to needing less data on average to learn probabilistic operators than neural networks need for training.Source: B. Results and Discussion · p. 7
  • LNDR often performs worse because it can get stuck in local minima; LOFT’s decoupled effect clustering avoids repeatedly reconsidering learned effect sets.In Painting, LNDR consistently uses one operator with Holding rather than separate HoldingSide and HoldingTop operators.Source: B. Results and Discussion · p. 7
  • Adding low-level state input can make model-free learning harder, while LOFT’s reliance on predicates may limit it when those predicates are inadequate for useful operators.The authors suggest a learned Q-function could instead serve as a heuristic in LOFT’s high-level A* search.Source: B. Results and Discussion · p. 7
  • B4 performs especially poorly across domains because its raw GNN policy does not use the samplers, suggesting direct policy learning without hand-written samplers is challenging in many TAMP domains.Source: B. Results and Discussion · p. 7
  • With enough data LOFT outperforms planning without operators, but in Blocks it performs slightly worse with little data, likely because poor operators provide misleading guidance.Source: B. Results and Discussion · p. 7
  • With up to three predicates withheld, LOFT remains the only non-oracle approach to solve any Painting problems, but performance deteriorates quickly as hAdd is sensitive to missing preconditions or effects.Replacing hAdd with a blind heuristic yields significantly worse results, especially in harder domains.Source: B. Results and Discussion · p. 7, Table II · p. 8
  • LOFT trains orders of magnitude faster than GNN baselines and one order of magnitude faster than B0, while B5 is excluded from the training-time comparison because it is not learning-based.Training times are means with standard deviations over five seeds.Source: B. Results and Discussion · p. 7, Table I · p. 8

VII. CONCLUSION

The learned operators guide high-level symbolic search in hybrid robotic planning, and experiments on long-horizon tasks show strength against several baselines. The approach assumes given predicates, whose quality determines the quality of the abstraction.

VII. CONCLUSION

  • Learned operators guide high-level symbolic search, making planning efficient in hybrid robotic planning problems.Experiments on long-horizon planning problems demonstrate strength compared with several baselines, including graph neural network-based model-free approaches.Source: §VII · p. 8
  • The approach assumes predicates are given, and their quality determines the quality of the abstraction.The authors identify learning what makes a good predicate as a future research direction.Source: §VII · p. 8
  • Learning the hybrid controllers, which are currently given, is another future research direction.Source: §VII · p. 8
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