# Few-Shot Bayesian Imitation Learning with Logical Program Policies

arXiv: https://arxiv.org/abs/1904.06317 · HTML: https://mlsanity.com/paper/1904.06317/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 12 Apr 2019.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

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

- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Overcoming Exploration in Reinforcement Learning with Demonstrations](https://mlsanity.com/paper/1709.10089/) (2017)
- [One-Shot Imitation Learning](https://mlsanity.com/paper/1703.07326/) (2017)
- [One-Shot Visual Imitation Learning via Meta-Learning](https://mlsanity.com/paper/1709.04905/) (2017)
- [Programmatically Interpretable Reinforcement Learning](https://mlsanity.com/paper/1804.02477/) (2018)
- [Neuro-Symbolic Program Synthesis](https://mlsanity.com/paper/1611.01855/) (2016)
- [Leveraging Grammar and Reinforcement Learning for Neural Program Synthesis](https://mlsanity.com/paper/1805.04276/) (2018)
- [Neural Task Programming: Learning to Generalize Across Hierarchical Tasks](https://mlsanity.com/paper/1710.01813/) (2017)
- [Learning to Infer Graphics Programs from Hand-Drawn Images](https://mlsanity.com/paper/1707.09627/) (2017)
- [Neural Task Graphs: Generalizing to Unseen Tasks from a Single Video Demonstration](https://mlsanity.com/paper/1807.03480/) (2018)
- [Schema Networks: Zero-shot Transfer with a Generative Causal Model of Intuitive Physics](https://mlsanity.com/paper/1706.04317/) (2017)
- [DDCO: Discovery of Deep Continuous Options for Robot Learning from Demonstrations](https://mlsanity.com/paper/1710.05421/) (2017)
- [Beyond imitation: Zero-shot task transfer on robots by learning concepts as cognitive programs](https://mlsanity.com/paper/1812.02788/) (2018)

## Built on by (most cited first, 30 of 30)

- [Learning to Synthesize Programs as Interpretable and Generalizable Policies](https://mlsanity.com/paper/2108.13643/) (2021)
- [Leveraging Language to Learn Program Abstractions and Search Heuristics](https://mlsanity.com/paper/2106.11053/) (2021)
- [AGENT: A Benchmark for Core Psychological Reasoning](https://mlsanity.com/paper/2102.12321/) (2021)
- [Generating Code World Models with Large Language Models Guided by Monte Carlo Tree Search](https://mlsanity.com/paper/2405.15383/) (2024)
- [Explainable Deep Reinforcement Learning: State of the Art and Challenges](https://mlsanity.com/paper/2301.09937/) (2023)
- [Hierarchical Programmatic Reinforcement Learning via Learning to Compose Programs](https://mlsanity.com/paper/2301.12950/) (2023)
- [Synthesizing Programmatic Reinforcement Learning Policies with Large Language Model Guided Search](https://mlsanity.com/paper/2405.16450/) (2024)
- [Learning Sketches for Decomposing Planning Problems into Subproblems of Bounded Width: Extended Version](https://mlsanity.com/paper/2203.14852/) (2022)
- [Learning Differentiable Logic Programs for Abstract Visual Reasoning](https://mlsanity.com/paper/2307.00928/) (2023)
- [Learning Neuro-symbolic Programs for Language Guided Robot Manipulation](https://mlsanity.com/paper/2211.06652/) (2022)
- [Efficient Symbolic Policy Learning with Differentiable Symbolic Expression](https://mlsanity.com/paper/2311.02104/) (2023)
- [Learning General Policies from Small Examples Without Supervision](https://mlsanity.com/paper/2101.00692/) (2021)
- [Hierarchical Neural Program Synthesis](https://mlsanity.com/paper/2303.06018/) (2023)
- [Generalized Planning as Heuristic Search: A new planning search-space that leverages pointers over objects](https://mlsanity.com/paper/2301.11087/) (2023)
- [Relational decomposition for program synthesis](https://mlsanity.com/paper/2408.12212/) (2024)
- [Target Languages (vs. Inductive Biases) for Learning to Act and Plan](https://mlsanity.com/paper/2109.07195/) (2021)
- [Learning of Generalizable and Interpretable Knowledge in Grid-Based Reinforcement Learning Environments](https://mlsanity.com/paper/2309.03651/) (2023)
- [From Code to Play: Benchmarking Program Search for Games Using Large Language Models](https://mlsanity.com/paper/2412.04057/) (2024)
- [Stage Conscious Attention Network (SCAN) : A Demonstration-Conditioned Policy for Few-Shot Imitation](https://mlsanity.com/paper/2112.02278/) (2021)
- [KnowPC: Knowledge-Driven Programmatic Reinforcement Learning for Zero-shot Coordination](https://mlsanity.com/paper/2408.04336/) (2024)
- [Supervised Bayesian Specification Inference from Demonstrations](https://mlsanity.com/paper/2107.02912/) (2021)
- [Automatic Discovery and Description of Human Planning Strategies](https://mlsanity.com/paper/2109.14493/) (2021)
- [Unveiling the Decision-Making Process in Reinforcement Learning with Genetic Programming](https://mlsanity.com/paper/2407.14714/) (2024)
- [Learning logic programs by explaining their failures](https://mlsanity.com/paper/2102.12551/) (2021)
- [Guided Sketch-Based Program Induction by Search Gradients](https://mlsanity.com/paper/2402.06990/) (2024)
- [Sketch-Plan-Generalize: Learning and Planning with Neuro-Symbolic Programmatic Representations for Inductive Spatial Concepts](https://mlsanity.com/paper/2404.07774/) (2024)
- [An Empirical Comparison of Cost Functions in Inductive Logic Programming](https://mlsanity.com/paper/2503.07554/) (2025)
- [A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes](https://mlsanity.com/paper/2506.09499/) (2025)
- [Finite Automata Extraction: Low-data World Model Learning as Programs from Gameplay Video](https://mlsanity.com/paper/2508.11836/) (2025)
- [DiPRL: Learning Discrete Programmatic Policies via Architecture Entropy Regularization](https://mlsanity.com/paper/2605.18508/) (2026)

## Abstract (arXiv)

Humans can learn many novel tasks from a very small number (1--5) of demonstrations, in stark contrast to the data requirements of nearly tabula rasa deep learning methods. We propose an expressive class of policies, a strong but general prior, and a learning algorithm that, together, can learn interesting policies from very few examples. We represent policies as logical combinations of programs drawn from a domain-specific language (DSL), define a prior over policies with a probabilistic grammar, and derive an approximate Bayesian inference algorithm to learn policies from demonstrations. In experiments, we study five strategy games played on a 2D grid with one shared DSL. After a few demonstrations of each game, the inferred policies generalize to new game instances that differ substantially from the demonstrations. Our policy learning is 20--1,000x more data efficient than convolutional and fully convolutional policy learning and many orders of magnitude more computationally efficient than vanilla program induction. We argue that the proposed method is an apt choice for tasks that have scarce training data and feature significant, structured variation between task instances.