# Meta Learning MPC using Finite-Dimensional Gaussian Process Approximations

arXiv: https://arxiv.org/abs/2008.05984 · HTML: https://mlsanity.com/paper/2008.05984/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2020.

## Built on by (most cited first, 8 of 8)

- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Optimizing Closed-Loop Performance with Data from Similar Systems: A Bayesian Meta-Learning Approach](https://mlsanity.com/paper/2211.00077/) (2022)
- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [From Shadow to Light: Toward Safe and Efficient Policy Learning Across MPC, DeePC, RL, and LLM Agents](https://mlsanity.com/paper/2510.04076/) (2025)
- [Shallow Representation is Deep: Learning Uncertainty-aware and Worst-case Random Feature Dynamics](https://mlsanity.com/paper/2106.13066/) (2021)
- [META-SMGO-Delta: similarity as a prior in black-box optimization](https://mlsanity.com/paper/2305.00438/) (2023)
- [Efficient Automatic Tuning for Data-driven Model Predictive Control via Meta-Learning](https://mlsanity.com/paper/2404.00232/) (2024)

## Abstract (arXiv)

Data availability has dramatically increased in recent years, driving model-based control methods to exploit learning techniques for improving the system description, and thus control performance. Two key factors that hinder the practical applicability of learning methods in control are their high computational complexity and limited generalization capabilities to unseen conditions. Meta-learning is a powerful tool that enables efficient learning across a finite set of related tasks, easing adaptation to new unseen tasks. This paper makes use of a meta-learning approach for adaptive model predictive control, by learning a system model that leverages data from previous related tasks, while enabling fast fine-tuning to the current task during closed-loop operation. The dynamics is modeled via Gaussian process regression and, building on the Karhunen-Lo`eve expansion, can be approximately reformulated as a finite linear combination of kernel eigenfunctions. Using data collected over a set of tasks, the eigenfunction hyperparameters are optimized in a meta-training phase by maximizing a variational bound for the log-marginal likelihood. During meta-testing, the eigenfunctions are fixed, so that only the linear parameters are adapted to the new unseen task in an online adaptive fashion via Bayesian linear regression, providing a simple and efficient inference scheme. Simulation results are provided for autonomous racing with miniature race cars adapting to unseen road conditions.