Covariance analysis as a measure of policy robustness

In this paper we propose covariance analysis as a metric for reinforcement learning to improve the robustness of a learned policy. The local optima found during the exploration are analyzed in terms of the total cumulative reward and the local behavior of the system in the neighborhood of the optima. The analysis is performed in the solution space to select a policy that exhibits robustness in uncertain and noisy environments. We demonstrate the utility of the method using our previously developed system where an autonomous underwater vehicle (AUV) has to recover from a thruster failure [1]. When a failure is detected the recovery system is invoked, which uses simulations to learn a new controller that utilizes the remaining functioning thrusters to achieve the goal of the AUV, that is, to reach a target position. In this paper, we use covariance analysis to examine the performance of the top, n, policies output by the previous algorithm. We propose a scoring metric that uses the output of the covariance analysis, the time it takes the AUV to reach the target position and the distance between the target position and the AUV's final position. The top polices are simulated in a noisy environment and evaluated using the proposed scoring metric to analyze the effect of noise on their performance. The policy that exhibits more tolerance to noise is selected. We show experimental results where covariance analysis successfully selects a more robust policy that was ranked lower by the original algorithm.