Abstract
We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the partial gradients of policies, strong guarantees of robust stability can be obtained based on a proposed semidefinite programming feasibility problem. The method is able to certify a large set of stabilizing controllers by exploiting problem-specific structures; furthermore, we analyze and establish its (non)conservatism. Empirical evaluations on two decentralized control tasks, namely multi-flight formation and power system frequency regulation, demonstrate that the reinforcement learning agents can have high performance within the stability-certified parameter space and also exhibit stable learning behaviors in the long run.
Highlights
R EINFORCEMENT learning (RL) aims at guiding an agent to perform a task as efficiently and skillfully as possible through interactions with the environment
We focus on system (16) where an linear time-invariant (LTI) system is interconnected with a fixed RL policy
The present analysis aims at offering stability certificates when applying RL to dynamical systems, which is orthogonal to the line of research that aims at improving the performance of the existing RL algorithms
Summary
R EINFORCEMENT learning (RL) aims at guiding an agent to perform a task as efficiently and skillfully as possible through interactions with the environment. The main challenge of these methods is that the robustness guarantee can be conservative due to coarse constraints on nonlinearity such as those based on Lipschitz constants [16], [17], leading to a limited search space for safe policies To mitigate this issue, the integral quadratic constraint (IQC) framework proposed in [18] can be employed, which has been widely used to analyze the stability of large-scale complex systems, such as aircraft control [19]. Existing techniques can be computational intensive for deep neural networks, and establishing necessary conditions for robustness has been limited to only a few cases (e.g., block-diagonal structured uncertainty operators with bounded singular values [20]) To address this issue, we introduce a more informative quadratic constraint and analyze the necessity of the certificate criterion as an extension of the preliminary conference.
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