Learning Adaptive Solvers for Distributed Factor Graph Optimization on Matrix Lie Groups

Summary

Abstract Summary

Modern robotic perception increasingly involves large-scale geometric optimization problems distributed across multiple robots or sessions. However, existing distributed solvers often depend on brittle hand tuning and primarily target rigid body pose graphs. To address this, we present DeepCORD, a learning-augmented framework for distributed factor graph optimization on general matrix Lie groups. By unfolding a parallel and accelerated Riemannian optimizer into differentiable iterations, DeepCORD learns a self-supervised feedback policy that dynamically adapts solver parameters according to the optimization phase and communication status. The resulting method enables adaptive distributed optimization over matrix Lie groups under both synchronous and asynchronous communication regimes. Extensive experiments on real-world $\mathrm{SE}$(3) pose graph optimization and $\mathrm{SL}$(4) projective submap alignment show that our method achieves lower objective values than existing distributed baselines on most benchmarks across realistic operating scenarios.

Key Points

Modern robotic perception increasingly involves large-scale geometric optimization problems distributed across multiple robots or sessions.
However, existing distributed solvers often depend on brittle hand tuning and primarily target rigid body pose graphs.
To address this, we present DeepCORD, a learning-augmented framework for distributed factor graph optimization on general matrix Lie groups.
By unfolding a parallel and accelerated Riemannian optimizer into differentiable iterations, DeepCORD learns a self-supervised feedback policy that dynamically adapts solver parameters according to the optimization phase and communication status.
The resulting method enables adaptive distributed optimization over matrix Lie groups under both synchronous and asynchronous communication regimes.

Problem Formulation

In this work, we consider distributed factor graph optimization problems with pairwise relative measurements between group-valued variables. This class of factor graphs forms the backbone for modern SLAM and 3D reconstruction systems [ 11 , 7 ] . Formally, let $G\subseteq\mathrm{GL}(n)$ be a matrix Lie group with Lie algebra $\mathfrak{g}$.

Let $\mathcal{G}=(\mathcal{V},\mathcal{E})$ represent a connected factor graph, where each node $u\in\mathcal{V}$ represents an optimization variable $X_{u}\in G$.

Problem Formulation — Learning Adaptive Solvers for Distributed Factor Graph Optimization on Matrix Lie Groups — Figure 3: Distributed PGO solved by the proposed method. Each color denotes a different robot.

Proposed Method

DeepCORD arises from unfolding the iterations of CORD [ 45 ] , a state-of-the-art distributed solver, to a learning-augmented framework. In the following, we will review necessary background, discuss the neural network architecture, and then present the self-supervised training approach. Details about the network architecture, feature definitions, and training setup are deferred to the Appendix.

Background: CORD [ 45 ] . CORD applies the Euler–Poincaré equation [ 5 ] to solve distributed optimization over general matrix Lie groups $G$.

Proposed Method — Learning Adaptive Solvers for Distributed Factor Graph Optimization on Matrix Lie Groups — Figure 6: Evolution of the adaptive parameters ($m,d,\Delta t$) predicted by DeepCORD over 100 iterations, illustrated across optimization phases and maximum delays.

Experiments

In this section, we validate DeepCORD on standard PGO over $\mathrm{SE}(3)$ and projective submap alignment over $\mathrm{SL}(4)$. Our experiments demonstrate that DeepCORD achieves the best cost on 11 out of 13 synchronous instances and 10 out of 13 asynchronous instances, and predicts adaptive parameters that generalize to larger datasets and longer optimization iterations. Experiment Setup.

To test generalization, all problems in the experiments are not seen during training.

Sources and Demonstrations

Figures are reproduced from Shin et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.