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This paper studies a structured compound stochastic program (SP) involving multiple expectations coupled by nonconvex and nonsmooth functions. We present a successive convex programming-based sampling algorithm and establish its subsequential convergence. We describe stationary properties of the limit points for several classes of the compound SP. We further discuss probabilistic stopping rules based on the computable error bound for the algorithm. We present several risk measure minimization problems that can be formulated as such a compound stochastic program; these include generalized deviation optimization problems based on the optimized certainty equivalent and buffered probability of exceedance (bPOE), a distributionally robust bPOE optimization problem, and a multiclass classification problem employing the cost-sensitive error criteria with bPOE.

For the treatment of outliers, the paper “Risk-Based Robust Statistical Learning by Stochastic Difference-of-Convex Value-Function Optimization” by Junyi Liu and Jong-Shi Pang proposes a risk-based robust statistical learning model. Employing a variant of the conditional value-at-risk risk measure, called the interval conditional value-at-risk (In-CVaR), the model aims to exclude the risks associated with the left and right tails of the loss. The resulting nonsmooth and nonconvex model considers the population In-CVaR risk and distinguishes the upside and downside losses with asymmetric weights. For the solution of the model in both regression and classification, the authors show that the objective function is the difference of two convex functions each being the optimal objective value of a univariate convex stochastic program. A sampling and convex programming-based algorithm is developed with the appropriate control of incremental sample sizes, and its subsequential almost-sure convergence to a critical point is established. Numerical results illustrate the practical performance of the model and methodology.

Predictive analytics, empowered by machine learning, is usually followed by decision-making problems in prescriptive analytics. We extend the previous sequential prediction-optimization paradigm to a coupled scheme such that the prediction model can guide the decision problem to produce coordinated decisions yielding higher levels of performance. Specifically, for stochastic programming (SP) models with latently decision-dependent uncertainty, without any parametric assumption of the latent dependency, we develop a coupled learning enabled optimization (CLEO) algorithm in which the learning step of predicting the local dependency and the optimization step of computing a candidate decision are conducted interactively. The CLEO algorithm automatically balances the exploration and exploitation via the trust region method with active sampling. Under certain assumptions, we show that the sequence of solutions provided by CLEO converges to a directional stationary point of the original nonconvex and nonsmooth SP problem with probability 1. In addition, we present preliminary experimental results which demonstrate the computational potential of this data-driven approach.

Cybersecurity breaches are common anomalies for distributed cyber-physical systems (CPS). However, the cyber security breach classification is still a difficult problem, even using cutting-edge artificial intelligence (AI) approaches. In this paper, we study a multi-class classification problem in cyber security for attack detection. A challenging multi-node data-censoring case is considered. In such a case, data within each data center/node cannot be shared while the local data is incomplete. Particularly, local nodes contain only a part of the multiple classes. In order to train a global multi-class classifier without sharing the raw data across all nodes, we design a multi-node multi-class classification ensemble approach which is the main result of our study. By gathering the estimated parameters of the binary classifiers and data densities from each local node, the missing information for each local node is completed to build the global multi-class classifier. Numerical experiments are given to validate the effectiveness of the proposed approach under the multi-node data-censoring case. Under such a case, we even show the out-performance of the proposed approach over the full-data approach.