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This work studies the learning ability of consensus and diffusion distributed learners from continuous streams of data arising from different but related statistical distributions. Four distinctive features for diffusion learners are…
We examine the evolutionary basis for risk aversion with respect to aggregate risk. We study populations in which agents face choices between alternatives with different levels of aggregate risk. We show that the choices that maximize the…
Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statistical methods for such data, we introduce the concept of…
Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In Part II of this paper, we introduce a new and unified Extended Convex Lifting (ECL) framework to reveal hidden convexity…
This paper studies indefinite stochastic linear-quadratic (LQ) optimal control for jump-diffusion systems with random coefficients. We construct an algebraic inverse flow from the zero-control base system, extract the semimartingale kernel…
Extreme Value Theory (EVT) is exploited to determine the global stability threshold $R_g$ of plane Couette flow --the flow of a viscous fluid in the space between two parallel plates-- whose laminar or turbulent behavior depends on the…
Empirical risk minimization (ERM) can be computationally expensive, with standard solvers scaling poorly even in the convex setting. We propose a novel lossless compression framework for convex ERM based on color refinement, extending prior…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
Expected Shortfall (ES, also known as CVaR) is the most important coherent risk measure in finance, insurance, risk management, and engineering. Recently, Wang and Zitikis (2021) put forward four economic axioms for portfolio risk…
In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
Consider the problem of learning a large number of response functions simultaneously based on the same input variables. The training data consist of a single independent random sample of the input variables drawn from a common distribution…
This paper addresses risk averse constrained optimization problems where the objective and constraint functions can only be computed by a blackbox subject to unknown uncertainties. To handle mixed aleatory/epistemic uncertainties, the…
We study the closure properties of the class of Bivariate Regular Variation, symbolically BRV , in standard and nonstandard cases, with respect to the randomly weighted sums. However, we take into consideration a weak dependence structure…
Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…
We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic…
We analyze the expressivity of a universal deep neural network that can be organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads. While the maximal expressive power increases with the depth of the…
Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…
Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable…
We propose a framework which generalizes "decision making with structured observations" by allowing robust (i.e. multivalued) models. In this framework, each model associates each decision with a convex set of probability distributions over…