Risk assessment is the process where we identify hazards, analyze or evaluate the risk associated with that hazard, and determine appropriate ways to eliminate or control the hazard. Risk assessment techniques have been widely applied in many area including quantitative financial engineering (Krokhmal et al. 2002), health and environment study (Zhang and Wang 2012; Van Asselt et al. 2013), transportation science (Liu et al. 2017), etc. Paltrinieri et al. (2014) point out that traditional risk assessment methods are often limited by static, onetime processes performed during the design phase of industrial processes. As such they often use older data or generic data on potential hazards and failure rates of equipment and processes and cannot be easily updated in order to take into account new information, giving a more complete view of the related risks. This failure to account for new information can lead to unrecognized hazards, or misunderstandings about the real probability of their occurrence under current management and safety precautions. With the rapid development of computational intelligence and corresponding decision support system, as well as the launch of "Big data" era, nowadays, new risk assessment technique should allow decision maker to update the assessment results by observing new information or data and realize quick response to dynamic environment. In this paper, we develop a satisficing measure based model to assess, compare and ranking random outcomes, and propose both online and offline data-driven computational frameworks.

Metastasis is the migration of cancerous cells from a primary tumor to other anatomical sites. Although metastasis was long thought to result from monoclonal seeding, or single cellular migrations, recent phylogenetic analyses of metastatic cancers have reported complex patterns of cellular migrations between sites, including polyclonal migrations and reseeding. However, accurate determination of migration patterns from somatic mutation data is complicated by intratumor heterogeneity and discordance between clonal lineage and cellular migration. We introduce MACHINA, a multi-objective optimization algorithm that jointly infers clonal lineages and parsimonious migration histories of metastatic cancers from DNA sequencing data. MACHINA analysis of data from multiple cancers shows that migration patterns are often not uniquely determined from sequencing data alone and that complicated migration patterns among primary tumors and metastases may be less prevalent than previously reported.

Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient descent are easily scaled for very large problems but may involve fine-tuning many hyper-parameters. Quasi-Newton approaches based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) update typically do not require manually tuning hyper-parameters but suffer from approximating a potentially indefinite Hessian with a positive-definite matrix. Hessian-free methods leverage the ability to perform Hessian-vector multiplication without needing the entire Hessian matrix, but each iteration's complexity is significantly greater than quasi-Newton methods. In this paper we propose an alternative approach for solving ML problems based on a quasi-Newton trust-region framework for solving large-scale optimization problems that allow for indefinite Hessian approximations. Numerical experiments on a standard testing data set show that with a fixed computational time budget, the proposed methods achieve better results than the traditional limited-memory BFGS and the Hessian-free methods.

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the empirical risk is, however, highly nonlinear. This presents a challenge to application and development of appropriate optimization algorithms for solving the problem. In this paper, we summarize the primary challenges involved and present the case for a Newton-based method incorporating directions of negative curvature, including promising numerical results on data arising from security anomally deetection.

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the empirical risk is, however, highly nonconvex. This alone presents a challenge to application and development of appropriate optimization algorithms for solving the problem. However, in addition, there are a number of interesting problems for which the objective function is non- smooth and nonseparable. In this paper, we summarize the primary challenges involved, the state of the art, and present some numerical results on an interesting and representative class of problems.

We present a principled way of extending a classical AI planning formalism with systems of state constraints, which relate - sometimes determine - the values of variables in each state traversed by the plan. This extension occupies an attractive middle ground between expressivity and complexity. It enables modelling a new range of problems, as well as formulating more efficient models of classical planning problems. An example of the former is planning-based control of networked physical systems - power networks, for example - in which a local, discrete control action can have global effects on continuous quantities, such as altering flows across the entire network. At the same time, our extension remains decidable as long as the satisfiability of sets of state constraints is decidable, including in the presence of numeric state variables, and we demonstrate that effective techniques for cost-optimal planning known in the classical setting - in particular, relaxation-based admissible heuristics - can be adapted to the extended formalism. In this paper, we apply our approach to constraints in the form of linear or non-linear equations over numeric state variables, but the approach is independent of the type of state constraints, as long as there exists a procedure that decides their consistency. The planner and the constraint solver interact through a well-defined, narrow interface, in which the solver requires no specialisation to the planning context.

Classifiers can be trained with data-dependent constraints to satisfy fairness goals, reduce churn, achieve a targeted false positive rate, or other policy goals. We study the generalization performance for such constrained optimization problems, in terms of how well the constraints are satisfied at evaluation time, given that they are satisfied at training time. To improve generalization performance, we frame the problem as a two-player game where one player optimizes the model parameters on a training dataset, and the other player enforces the constraints on an independent validation dataset. We build on recent work in two-player constrained optimization to show that if one uses this two-dataset approach, then constraint generalization can be significantly improved. As we illustrate experimentally, this approach works not only in theory, but also in practice.

Given a classifier ensemble and a set of examples to be classified, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble are evaluated. This can reduce both mean latency and CPU while maintaining the high accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing a fixed evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution for certain cases. For those cases, this is also the best achievable polynomial time approximation bound unless $P = NP$. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed-up average evaluation time by $2$x--$4$x, and is around $1.5$x faster than prior work. QWYC's joint optimization of ordering and thresholds also performed better in experiments than various fixed orderings, including gradient boosted trees' ordering.

In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex functions. The proposed framework is based on a nontrivial combination of the majorization-minimization framework and the successive convex approximation framework proposed in literature for a convex regularization function. The proposed framework has several attractive features, namely, i) flexibility, as different choices of the approximate function lead to different type of algorithms; ii) fast convergence, as the problem structure can be better exploited by a proper choice of the approximate function and the stepsize is calculated by the line search; iii) low complexity, as the approximate function is convex and the line search scheme is carried out over a differentiable function; iv) guaranteed convergence to a stationary point. We demonstrate these features by two example applications in subspace learning, namely, the network anomaly detection problem and the sparse subspace clustering problem. Customizing the proposed framework by adopting the best-response type approximation, we obtain soft-thresholding with exact line search algorithms for which all elements of the unknown parameter are updated in parallel according to closed-form expressions. The attractive features of the proposed algorithms are illustrated numerically.

We study a stylized dynamic assortment planning problem during a selling season of finite length $T$, by considering a nested multinomial logit model with $M$ nests and $N$ items per nest. Our policy simultaneously learns customers' choice behavior and makes dynamic decisions on assortments based on the current knowledge. It achieves the regret at the order of $\tilde{O}(\sqrt{MNT}+MN^2)$, where $M$ is the number of nests and $N$ is the number of products in each nest. We further provide a lower bound result of $\Omega(\sqrt{MT})$, which shows the optimality of the upper bound when $T>M$ and $N$ is small. However, the $N^2$ term in the upper bound is not ideal for applications where $N$ is large as compared to $T$. To address this issue, we further generalize our first policy by introducing a discretization technique, which leads to a regret of $\tilde{O}(\sqrt{M}T^{2/3}+MNT^{1/3})$ with a specific choice of discretization granularity. It improves the previous regret bound whenever $N>T^{1/3}$. We provide numerical results to demonstrate the empirical performance of both proposed policies.