# Gradient-Based Mixed Planning with Symbolic and Numeric Action Parameters

arXiv: https://arxiv.org/abs/2110.10007 · HTML: https://mlsanity.com/paper/2110.10007/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 59 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 9 of 9)

- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [Plan-And-Write: Towards Better Automatic Storytelling](https://mlsanity.com/paper/1811.05701/) (2018)
- [Learning Continuous Control Policies by Stochastic Value Gradients](https://mlsanity.com/paper/1510.09142/) (2015)
- [Learning Plannable Representations with Causal InfoGAN](https://mlsanity.com/paper/1807.09341/) (2018)
- [Controllable Neural Story Plot Generation via Reward Shaping](https://mlsanity.com/paper/1809.10736/) (2018)
- [Size Independent Neural Transfer for RDDL Planning](https://mlsanity.com/paper/1902.03081/) (2019)
- [Transfer of Deep Reactive Policies for MDP Planning](https://mlsanity.com/paper/1810.11488/) (2018)
- [COLIN: Planning with Continuous Linear Numeric Change](https://mlsanity.com/paper/1401.5857/) (2014)
- [Scalable Planning with Tensorflow for Hybrid Nonlinear Domains](https://mlsanity.com/paper/1704.07511/) (2017)

## Built on by (most cited first, 6 of 6)

- [Planning with Logical Graph-based Language Model for Instruction Generation](https://mlsanity.com/paper/2308.13782/) (2023)
- [Learning Visual Planning Models from Partially Observed Images](https://mlsanity.com/paper/2211.15666/) (2022)
- [On the Roles of LLMs in Planning: Embedding LLMs into Planning Graphs](https://mlsanity.com/paper/2403.00783/) (2024)
- [LaPlaSS: Latent Space Planning for Stochastic Systems](https://mlsanity.com/paper/2404.07063/) (2024)
- [A Hierarchical Temporal Planning-Based Approach for Dynamic Hoist Scheduling Problems](https://mlsanity.com/paper/2212.05412/) (2022)
- [XRoute Environment: A Novel Reinforcement Learning Environment for Routing](https://mlsanity.com/paper/2305.13823/) (2023)

## Abstract (arXiv)

Dealing with planning problems with both logical relations and numeric changes in real-world dynamic environments is challenging. Existing numeric planning systems for the problem often discretize numeric variables or impose convex constraints on numeric variables, which harms the performance when solving problems. In this paper, we propose a novel algorithm framework to solve numeric planning problems mixed with logical relations and numeric changes based on gradient descent. We cast the numeric planning with logical relations and numeric changes as an optimization problem. Specifically, we extend syntax to allow parameters of action models to be either objects or real-valued numbers, which enhances the ability to model real-world numeric effects. Based on the extended modeling language, we propose a gradient-based framework to simultaneously optimize numeric parameters and compute appropriate actions to form candidate plans. The gradient-based framework is composed of an algorithmic heuristic module based on propositional operations to select actions and generate constraints for gradient descent, an algorithmic transition module to update states to next ones, and a loss module to compute loss. We repeatedly minimize loss by updating numeric parameters and compute candidate plans until it converges into a valid plan for the planning problem. In the empirical study, we exhibit that our algorithm framework is both effective and efficient in solving planning problems mixed with logical relations and numeric changes, especially when the problems contain obstacles and non-linear numeric effects.