Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

summary:In this paper, a novel consensus algorithm is presented to handle with the leader-following consensus problem for lower-triangular nonlinear MASs (multi-agent systems) with unknown controller and measurement sensitivities under a given undirected topology. As distinguished from the existing results, the proposed consensus algorithm can tolerate to a relative wide range of controller and measurement sensitivities. We present some important matrix inequalities, especially a class of matrix inequalities with multiplicative noises. Based on these results and a dual-domination gain method, the output consensus error with unknown measurement noises can be used to construct the compensator for each follower directly. Then, a new distributed output feedback control is designed to enable the MASs to reach consensus in the presence of large controller perturbations. In view of a Lyapunov function, sufficient conditions are presented to guarantee that the states of the leader and followers can achieve consensus asymptotically. In the end, the proposed consensus algorithm is tested and verified by an illustrative example

Automatic Answerability Evaluation for Question Generation

Conventional automatic evaluation metrics, such as BLEU and ROUGE, developed for natural language generation (NLG) tasks, are based on measuring the n-gram overlap between the generated and reference text. These simple metrics may be insufficient for more complex tasks, such as question generation (QG), which requires generating questions that are answerable by the reference answers. Developing a more sophisticated automatic evaluation metric, thus, remains as an urgent problem in QG research. This work proposes a Prompting-based Metric on ANswerability (PMAN), a novel automatic evaluation metric to assess whether the generated questions are answerable by the reference answers for the QG tasks. Extensive experiments demonstrate that its evaluation results are reliable and align with human evaluations. We further apply our metric to evaluate the performance of QG models, which shows our metric complements conventional metrics. Our implementation of a ChatGPT-based QG model achieves state-of-the-art (SOTA) performance in generating answerable questions

Scaling in Depth: Unlocking Robustness Certification on ImageNet

Despite the promise of Lipschitz-based methods for provably-robust deep learning with deterministic guarantees, current state-of-the-art results are limited to feed-forward Convolutional Networks (ConvNets) on low-dimensional data, such as CIFAR-10. This paper investigates strategies for expanding certifiably robust training to larger, deeper models. A key challenge in certifying deep networks is efficient calculation of the Lipschitz bound for residual blocks found in ResNet and ViT architectures. We show that fast ways of bounding the Lipschitz constant for conventional ResNets are loose, and show how to address this by designing a new residual block, leading to the \emph{Linear ResNet} (LiResNet) architecture. We then introduce \emph{Efficient Margin MAximization} (EMMA), a loss function that stabilizes robust training by simultaneously penalizing worst-case adversarial examples from \emph{all} classes. Together, these contributions yield new \emph{state-of-the-art} robust accuracy on CIFAR-10/100 and Tiny-ImageNet under $\ell_2$ perturbations. Moreover, for the first time, we are able to scale up fast deterministic robustness guarantees to ImageNet, demonstrating that this approach to robust learning can be applied to real-world applications. We release our code on Github: \url{https://github.com/klasleino/gloro}

Convergence Analysis of the Best Response Algorithm for Time-Varying Games

This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best respond to other agents' previous actions; we call this a best response scheme. We start by analyzing the convergence rate of this best response scheme for standard time-invariant games. Specifically, we provide a sufficient condition on the strong monotonicity parameter of the time-invariant games under which the proposed best response algorithm achieves exponential convergence to the static Nash equilibrium. We further illustrate that this best response algorithm may oscillate when the proposed sufficient condition fails to hold, which indicates that this condition is tight. Next, we analyze this best response algorithm for time-varying games where the cost functions of each agent change over time. Under similar conditions as for time-invariant games, we show that the proposed best response algorithm stays asymptotically close to the evolving equilibrium. We do so by analyzing both the equilibrium tracking error and the dynamic regret. Numerical experiments on economic market problems are presented to validate our analysis