# A Differentiable Loss Function for Learning Heuristics in A*

arXiv: https://arxiv.org/abs/2209.05206 · HTML: https://mlsanity.com/paper/2209.05206/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [Imagination-Augmented Agents for Deep Reinforcement Learning](https://mlsanity.com/paper/1707.06203/) (2017)
- [An investigation of model-free planning](https://mlsanity.com/paper/1901.03559/) (2019)
- [Path Planning using Neural A* Search](https://mlsanity.com/paper/2009.07476/) (2020)
- [Learning Domain-Independent Planning Heuristics with Hypergraph Networks](https://mlsanity.com/paper/1911.13101/) (2019)
- [ASNets: Deep Learning for Generalised Planning](https://mlsanity.com/paper/1908.01362/) (2019)
- [Learning Generalized Reactive Policies using Deep Neural Networks](https://mlsanity.com/paper/1708.07280/) (2017)
- [Learning Heuristic Search via Imitation](https://mlsanity.com/paper/1707.03034/) (2017)
- [Learning to Search with MCTSnets](https://mlsanity.com/paper/1802.04697/) (2018)
- [Solving Hard AI Planning Instances Using Curriculum-Driven Deep Reinforcement Learning](https://mlsanity.com/paper/2006.02689/) (2020)
- [Neuro-algorithmic Policies enable Fast Combinatorial Generalization](https://mlsanity.com/paper/2102.07456/) (2021)
- [Heuristic Search Planning with Deep Neural Networks using Imitation, Attention and Curriculum Learning](https://mlsanity.com/paper/2112.01918/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning Admissible Heuristics for A*: Theory and Practice](https://mlsanity.com/paper/2509.22626/) (2025)
- [DAA*: Deep Angular A Star for Image-based Path Planning](https://mlsanity.com/paper/2507.09305/) (2025)

## Abstract (arXiv)

Optimization of heuristic functions for the A* algorithm, realized by deep neural networks, is usually done by minimizing square root loss of estimate of the cost to goal values. This paper argues that this does not necessarily lead to a faster search of A* algorithm since its execution relies on relative values instead of absolute ones. As a mitigation, we propose a L* loss, which upper-bounds the number of excessively expanded states inside the A* search. The L* loss, when used in the optimization of state-of-the-art deep neural networks for automated planning in maze domains like Sokoban and maze with teleports, significantly improves the fraction of solved problems, the quality of founded plans, and reduces the number of expanded states to approximately 50%