# Automatic Induction of Bellman-Error Features for Probabilistic Planning

arXiv: https://arxiv.org/abs/1401.3847 · HTML: https://mlsanity.com/paper/1401.3847/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2014.

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

- [Learning General Optimal Policies with Graph Neural Networks: Expressive Power, Transparency, and Limits](https://mlsanity.com/paper/2109.10129/) (2021)
- [Reinforcement Learning for Classical Planning: Viewing Heuristics as Dense Reward Generators](https://mlsanity.com/paper/2109.14830/) (2021)

## Abstract (arXiv)

Domain-specific features are important in representing problem structure throughout machine learning and decision-theoretic planning. In planning, once state features are provided, domain-independent algorithms such as approximate value iteration can learn weighted combinations of those features that often perform well as heuristic estimates of state value (e.g., distance to the goal). Successful applications in real-world domains often require features crafted by human experts. Here, we propose automatic processes for learning useful domain-specific feature sets with little or no human intervention. Our methods select and add features that describe state-space regions of high inconsistency in the Bellman equation (statewise Bellman error) during approximate value iteration. Our method can be applied using any real-valued-feature hypothesis space and corresponding learning method for selecting features from training sets of state-value pairs. We evaluate the method with hypothesis spaces defined by both relational and propositional feature languages, using nine probabilistic planning domains. We show that approximate value iteration using a relational feature space performs at the state-of-the-art in domain-independent stochastic relational planning. Our method provides the first domain-independent approach that plays Tetris successfully (without human-engineered features).