Primal-dual Learning for the Model-free Risk-constrained Linear Quadratic Regulator

• URL: http://arxiv.org/abs/2011.10931v4
• Date: Sun, 30 May 2021 14:11:51 GMT
• Title: Primal-dual Learning for the Model-free Risk-constrained Linear Quadratic Regulator
• Authors: Feiran Zhao, Keyou You
• Abstract summary: Risk-aware control, though with promise to tackle unexpected events, requires a known exact dynamical model. We propose a model framework to learn a risk-aware controller with a focus on the linear system.
• Score: 0.8629912408966145
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Risk-aware control, though with promise to tackle unexpected events, requires a known exact dynamical model. In this work, we propose a model-free framework to learn a risk-aware controller with a focus on the linear system. We formulate it as a discrete-time infinite-horizon LQR problem with a state predictive variance constraint. To solve it, we parameterize the policy with a feedback gain pair and leverage primal-dual methods to optimize it by solely using data. We first study the optimization landscape of the Lagrangian function and establish the strong duality in spite of its non-convex nature. Alongside, we find that the Lagrangian function enjoys an important local gradient dominance property, which is then exploited to develop a convergent random search algorithm to learn the dual function. Furthermore, we propose a primal-dual algorithm with global convergence to learn the optimal policy-multiplier pair. Finally, we validate our results via simulations.

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