# Combining Local Symmetry Exploitation and Reinforcement Learning for Optimised Probabilistic Inference -- A Work In Progress

arXiv: https://arxiv.org/abs/2503.08786 · HTML: https://mlsanity.com/paper/2503.08786/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

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

- [Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference](https://mlsanity.com/paper/1401.1247/) (2014)
- [Duality of Graphical Models and Tensor Networks](https://mlsanity.com/paper/1710.01437/) (2017)
- [Causal Inference Using Tractable Circuits](https://mlsanity.com/paper/2202.02891/) (2022)
- [An Advance on Variable Elimination with Applications to Tensor-Based Computation](https://mlsanity.com/paper/2002.09320/) (2020)
- [Tensor Variable Elimination for Plated Factor Graphs](https://mlsanity.com/paper/1902.03210/) (2019)
- [Optimizing Tensor Network Contraction Using Reinforcement Learning](https://mlsanity.com/paper/2204.09052/) (2022)
- [State-Space Abstractions for Probabilistic Inference: A Systematic Review](https://mlsanity.com/paper/1804.06748/) (2018)
- [Generating and Sampling Orbits for Lifted Probabilistic Inference](https://mlsanity.com/paper/1903.04672/) (2019)
- [Variable Elimination in the Fourier Domain](https://mlsanity.com/paper/1508.04032/) (2015)

## Abstract (arXiv)

Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of random variables. Most recently, a reinforcement learning approach has been proposed to find efficient contraction orders in tensor networks. Due to the duality between graphical models and tensor networks, we adapt this approach to probabilistic inference in graphical models. Furthermore, we incorporate structure exploitation into the process of finding an optimal order. Currently, the agent's cost function is formulated in terms of intermediate result sizes which are exponential in the number of indices (i.e., random variables). We show that leveraging specific structures during inference allows for introducing compact encodings of intermediate results which can be significantly smaller. By considering the compact encoding sizes for the cost function instead, we enable the agent to explore more efficient contraction orders. The structure we consider in this work is the presence of local symmetries (i.e., symmetries within a model's factors).