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On Computing Plans with Uniform Action Costs

Alberto Pozanco, Daniel Borrajo, Manuela Veloso

TL;DR

This work addresses planning with uniform action costs by framing a two-objective problem that lexicographically optimizes total plan cost $c(\pi)$ and dispersion $d(\pi)$ of action costs under three dispersion metrics. It introduces three grounded compilations (Number of Different Costs, Delta, Range) that extend STRIPS tasks with bookkeeping propositions and actions to enforce uniformity, controlled by a weight $\omega_d$, and demonstrates their compatibility with standard planners. Through extensive experiments on 387 problems across 19 domains, including novel finance and navigation benchmarks, the authors show that uniform plans can be generated with practical overhead, and that standard cost-optimal plans often exhibit suboptimal dispersion for uniformity objectives. The results highlight trade-offs between scalability and dispersion fidelity and point to future work in satisficing solutions and alternative notions of uniformity beyond action-cost dispersion.

Abstract

In many real-world planning applications, agents might be interested in finding plans whose actions have costs that are as uniform as possible. Such plans provide agents with a sense of stability and predictability, which are key features when humans are the agents executing plans suggested by planning tools. This paper adapts three uniformity metrics to automated planning, and introduce planning-based compilations that allow to lexicographically optimize sum of action costs and action costs uniformity. Experimental results both in well-known and novel planning benchmarks show that the reformulated tasks can be effectively solved in practice to generate uniform plans.

On Computing Plans with Uniform Action Costs

TL;DR

This work addresses planning with uniform action costs by framing a two-objective problem that lexicographically optimizes total plan cost and dispersion of action costs under three dispersion metrics. It introduces three grounded compilations (Number of Different Costs, Delta, Range) that extend STRIPS tasks with bookkeeping propositions and actions to enforce uniformity, controlled by a weight , and demonstrates their compatibility with standard planners. Through extensive experiments on 387 problems across 19 domains, including novel finance and navigation benchmarks, the authors show that uniform plans can be generated with practical overhead, and that standard cost-optimal plans often exhibit suboptimal dispersion for uniformity objectives. The results highlight trade-offs between scalability and dispersion fidelity and point to future work in satisficing solutions and alternative notions of uniformity beyond action-cost dispersion.

Abstract

In many real-world planning applications, agents might be interested in finding plans whose actions have costs that are as uniform as possible. Such plans provide agents with a sense of stability and predictability, which are key features when humans are the agents executing plans suggested by planning tools. This paper adapts three uniformity metrics to automated planning, and introduce planning-based compilations that allow to lexicographically optimize sum of action costs and action costs uniformity. Experimental results both in well-known and novel planning benchmarks show that the reformulated tasks can be effectively solved in practice to generate uniform plans.
Paper Structure (18 sections, 2 theorems, 11 equations, 5 figures, 3 tables)

This paper contains 18 sections, 2 theorems, 11 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Uniformest Cost-Optimal Planning Problem
  4. Dispersion Metrics
  5. Computing Plans with Uniform Action Costs
  6. Compilation 1: Number of Different Action Costs
  7. Compilation 2: Delta
  8. Compilation 3: Range
  9. Evaluation
  10. Experimental Setting
  11. Benchmark.
  12. Approaches.
  13. Reproducibility.
  14. Results
  15. Coverage and Execution Time Overhead.
  16. ...and 3 more sections

Key Result

Proposition 1

If $\Pi$ is solvable, $\Pi_\#$ is also solvable.

Figures (5)

  • Figure 1: Navigation task where a driver wants to reach location $G$. The color of each cell depicts the cost (travel time) of traversing the cell.
  • Figure 2: Distribution of the execution time overhead factor $\frac{T(X)}{T(\Pi)}$ for each approach $X$. Black dots represent the average.
  • Figure 3: Distribution of the dispersion suboptimality ratio $\frac{d(\pi)}{d(\pi_{d})}$ for each dispersion metric $d$.
  • Figure 4: Cost ($y$) and number of different action costs ($x$) of the plans that solve $\Pi$, $\Pi_{\#}^{c,d}$, and $\Pi_{\#}^{d,c}$ tasks in finance.
  • Figure 5: Dispersion suboptimality ratio for each combination of compilation (rows) and dispersion metric (columns). Lighter cells indicate better performance.

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Proposition 1
  • Proposition 2
  • Definition 6
  • Definition 7