Related papers: Extending robustness & randomization from Consensu…

This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties,…

Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…

The question why deep learning algorithms generalize so well has attracted increasing research interest. However, most of the well-established approaches, such as hypothesis capacity, stability or sparseness, have not provided complete…

We demonstrate the advantages of randomization in coherent quantum dynamical control. For systems which are either time-varying or require decoupling cycles involving a large number of operations, we find that simple randomized protocols…

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…

We consider regularized support vector machines (SVMs) and show that they are precisely equivalent to a new robust optimization formulation. We show that this equivalence of robust optimization and regularization has implications for both…

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel…

This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…

This paper proposes the matrix-weighted consensus algorithm, which is a generalization of the consensus algorithm in the literature. Given a networked dynamical system where the interconnections between agents are weighted by nonnegative…

We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that…

Distributed control increases system scalability, flexibility, and redundancy. Foundational to such decentralisation is consensus formation, by which decision-making and coordination are achieved. However, decentralised multi-agent systems…

Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…

This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These…

We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…

There has been substantial work studying consensus problems for which there is a single common final state, although there are many real-world complex networks for which the complete consensus may be undesirable. More recently, the concept…

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest…

We consider the problem of robustness in large consensus networks that occur in many areas such as distributed optimization. Robustness, in this context, is the scaling of performance measures, e.g. H2-norm, as a function of network…