Generalizing out-of-distribution (OoD) is critical but challenging in real applications such as unmanned aerial vehicle (UAV) flight control. Previous machine learning-based control has shown promise in dealing with complex real-world environments but suffers huge performance degradation facing OoD scenarios, posing risks to the stability and safety of UAVs. In this paper, we found that the introduced random noises during training surprisingly yield theoretically guaranteed performances via a proposed functional optimization framework. More encouragingly, this framework does not involve common Lyapunov assumptions used in this field, making it more widely applicable. With this framework, the upperbound for control error is induced. We also proved that the induced random noises can lead to lower OoD control errors. Based on our theoretical analysis, we further propose OoD-Control to generalize control in unseen environments. Numerical experiments demonstrate the superiority of the proposed algorithm, surpassing previous state-of-the-art by 65% under challenging unseen environments. We further extend to outdoor real-world experiments and found that the control error is reduced by 50% approximately.

Machine learning methods suffer from test-time performance degeneration when faced with out-of-distribution (OoD) data whose distribution is not necessarily the same as training data distribution. Although a plethora of algorithms have been proposed to mitigate this issue, it has been demonstrated that achieving better performance than ERM simultaneously on different types of distributional shift datasets is challenging for existing approaches. Besides, it is unknown how and to what extent these methods work on any OoD datum without theoretical guarantees. In this paper, we propose a certifiable out-of-distribution generalization method that provides provable OoD generalization performance guarantees via a functional optimization framework leveraging random distributions and max-margin learning for each input datum. With this approach, the proposed algorithmic scheme can provide certified accuracy for each input datum's prediction on the semantic space and achieves better performance simultaneously on OoD datasets dominated by correlation shifts or diversity shifts. Our code is available at https://github.com/ZlatanWilliams/StochasticDisturbanceLearning.