Meta-Learning for Adaptive Control with Automated Mirror Descent
Sunbochen Tang, Haoyuan Sun, Navid Azizan
TL;DR
This work tackles adaptive control under disturbances that are linearly parameterized by unknown parameters, proposing a meta-learning framework to jointly learn nonlinear features and the mirror-descent (MD) potential. By embedding the MD adaptation law within a bi-level, multi-task meta-learning setup, the method automatically selects the Bregman divergence (via the $\ell_p$-norm family with parameter $p$) and learns feature representations $\hat{Y}(q,\dot{q};\theta_Y)$, yielding improved real-time tracking under uncertainty. Theoretical guarantees establish stability up to a bounded tracking error that vanishes when the feature approximation is exact, and numerical experiments on a planar quadrotor show significant performance gains and better generalization to out-of-distribution wind disturbances. The approach advances adaptive control by leveraging data-driven meta-optimization to tailor the geometry of the parameter space and the learned features for improved control performance in uncertain, nonlinear environments.
Abstract
Adaptive control achieves concurrent parameter learning and stable control under uncertainties that are linearly parameterized with known nonlinear features. Nonetheless, it is often difficult to obtain such nonlinear features. To address this difficulty, recent progress has been made in integrating meta-learning with adaptive control to learn such nonlinear features from data. However, these meta-learning-based control methods rely on classical adaptation laws using gradient descent, which is confined to the Euclidean geometry. In this paper, we propose a novel method that combines meta-learning and adaptation laws based on mirror descent, a popular generalization of gradient descent, which takes advantage of the potentially non-Euclidean geometry of the parameter space. In our approach, meta-learning not only learns the nonlinear features but also searches for a suitable mirror-descent potential function that optimizes control performance. Through numerical simulations, we demonstrate the effectiveness of the proposed method in learning efficient representations and real-time tracking control performance under uncertain dynamics.