Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML
  Approach for the Model-free LQR
Leonardo F. Toso Donglin Zhan James Anderson Han Wang
We investigate the problem of learning Linear Quadratic Regulators (LQR) in a
multi-task, heterogeneous, and model-free setting. We characterize the
stability and personalization guarantees of a Policy Gradient-based (PG)
Model-Agnostic Meta-Learning (MAML) (Finn et al., 2017) approach for the LQR
problem under different task-heterogeneity settings. We show that the MAML-LQR
approach produces a stabilizing controller close to each task-specific optimal
controller up to a task-heterogeneity bias for both model-based and model-free
settings. Moreover, in the model-based setting, we show that this controller is
achieved with a linear convergence rate, which improves upon sub-linear rates
presented in existing MAML-LQR work. In contrast to existing MAML-LQR results,
our theoretical guarantees demonstrate that the learned controller can
efficiently adapt to unseen LQR tasks.