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Subgoaling Relaxation-based Heuristics for Numeric Planning with Infinite Actions

Ángel Aso-Mollar, Diego Aineto, Enrico Scala, Eva Onaindia

TL;DR

This work tackles numeric planning with control parameters that create infinite action spaces by identifying a tractable fragment, controllable simple numeric problems, and introducing an optimistic compilation that transforms them into simple numeric tasks. This compilation is proven to be safe pruning under the subgoaling relaxation, enabling the use of classical numeric heuristics to estimate goal distance in otherwise intractable infinite-action domains. To manage compilation blowup, the authors introduce a signature-based reduction that preserves the relaxation while dramatically reducing the number of actions. Empirical results show the compilation-based heuristics outperform domain-independent baselines across multiple domains, validating the practical viability of applying subgoaling heuristics in control-variable numeric planning, with some domain-specific caveats related to over- and under-estimation balance.

Abstract

Numeric planning with control parameters extends the standard numeric planning model by introducing action parameters as free numeric variables that must be instantiated during planning. This results in a potentially infinite number of applicable actions in a state. In this setting, off-the-shelf numeric heuristics that leverage the action structure are not feasible. In this paper, we identify a tractable subset of these problems--namely, controllable, simple numeric problems--and propose an optimistic compilation approach that transforms them into simple numeric tasks. To do so, we abstract control-dependent expressions into bounded constant effects and relaxed preconditions. The proposed compilation makes it possible to effectively use subgoaling heuristics to estimate goal distance in numeric planning problems involving control parameters. Our results demonstrate that this approach is an effective and computationally feasible way of applying traditional numeric heuristics to settings with an infinite number of possible actions, pushing the boundaries of the current state of the art.

Subgoaling Relaxation-based Heuristics for Numeric Planning with Infinite Actions

TL;DR

This work tackles numeric planning with control parameters that create infinite action spaces by identifying a tractable fragment, controllable simple numeric problems, and introducing an optimistic compilation that transforms them into simple numeric tasks. This compilation is proven to be safe pruning under the subgoaling relaxation, enabling the use of classical numeric heuristics to estimate goal distance in otherwise intractable infinite-action domains. To manage compilation blowup, the authors introduce a signature-based reduction that preserves the relaxation while dramatically reducing the number of actions. Empirical results show the compilation-based heuristics outperform domain-independent baselines across multiple domains, validating the practical viability of applying subgoaling heuristics in control-variable numeric planning, with some domain-specific caveats related to over- and under-estimation balance.

Abstract

Numeric planning with control parameters extends the standard numeric planning model by introducing action parameters as free numeric variables that must be instantiated during planning. This results in a potentially infinite number of applicable actions in a state. In this setting, off-the-shelf numeric heuristics that leverage the action structure are not feasible. In this paper, we identify a tractable subset of these problems--namely, controllable, simple numeric problems--and propose an optimistic compilation approach that transforms them into simple numeric tasks. To do so, we abstract control-dependent expressions into bounded constant effects and relaxed preconditions. The proposed compilation makes it possible to effectively use subgoaling heuristics to estimate goal distance in numeric planning problems involving control parameters. Our results demonstrate that this approach is an effective and computationally feasible way of applying traditional numeric heuristics to settings with an infinite number of possible actions, pushing the boundaries of the current state of the art.
Paper Structure (18 sections, 4 theorems, 8 equations, 2 figures, 2 tables, 1 algorithm)

This paper contains 18 sections, 4 theorems, 8 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Numeric planning with control variables
  4. Searching with Delayed Partial EXpansions
  5. Subgoaling relaxation for numeric planning
  6. Controllable simple numeric problems
  7. Optimistic compilation
  8. Base case.
  9. Inductive step.
  10. Reducing the complexity of the optimistic compilation
  11. Extracting more information from subgoaling heuristics
  12. Experiments
  13. DPEX instantiation
  14. Baselines.
  15. Domains.
  16. ...and 3 more sections

Key Result

Theorem 1

Given $\mathcal{P} = (F, X, U, A, s_0, G)$ a controllable-simple numeric planning problem, $\mathcal{P}_O$ is a simple numeric planning problem.

Figures (2)

  • Figure 1: The inclusion of control variables introduces a shift in the decision space of numeric planning problems.
  • Figure 2: Comparison of the runs of $h^{add}_\Sigma$ or $h^{mrp}_\Sigma$ heuristic versus baselines in terms of plan length, time and number of (partial) expansions, for the best case between the 5 runs.

Theorems & Definitions (19)

  • Definition 1: Controllable numeric condition
  • Definition 2: Controllable numeric assignments
  • Definition 3: Numeric planning problem with control variables
  • Definition 4: Controllable simple numeric conditions
  • Example 1
  • Definition 5: Closed arithmetic of intervals
  • Definition 6: Optimistic compilation
  • Example 2
  • Theorem 1
  • proof
  • ...and 9 more