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

2026-07-09

AI Summary

This work addresses the limitations of existing distributed solvers in multi-robot or cross-session large-scale geometric optimization, which rely on hand-tuned parameters and struggle to generalize across arbitrary matrix Lie groups. To overcome this, we propose DeepCORD, a novel framework that introduces learning-based mechanisms into distributed Lie group factor graph optimization for the first time. DeepCORD employs a differentiable unfolded parallel Riemannian optimizer combined with self-supervised learning to dynamically adjust solver parameters according to varying optimization stages and communication conditions. The approach supports both synchronous and asynchronous communication and is applicable to general matrix Lie groups such as SE(3) and SL(4), achieving adaptive optimization without requiring labeled data. Experiments on real-world pose graph and submap alignment tasks demonstrate that DeepCORD consistently attains significantly lower objective values than state-of-the-art distributed methods across most benchmarks.

Abstract

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.

Problem

• distributed optimization
• factor graph
• matrix Lie groups
• adaptive solvers
• robotic perception

Innovation

• learning-augmented optimization
• distributed factor graphs
• matrix Lie groups
• Riemannian optimization
• adaptive solvers