The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it raises even more issues related to tractability and scalability. We study a combined Set Covering and Traveling Salesman problem and provide a mixed integer programming formulation to solve the problem. Motivated by applications where the optimal policy needs to be updated on a regular basis and repetitively solving this via MIP can be computationally expensive, we propose a machine learning approach to effectively deal with this problem by providing an opportunity to learn from historical optimal solutions that are derived from the MIP formulation. We also present a case study using the vaccine distribution chain of the World Health Organization, and provide numerical results with data derived from four countries in sub-Saharan Africa.

In this paper, we propose and study the cascade submodular maximization problem under the adaptive setting. The input of our problem is a set of items, each item is in a particular state (i.e., the marginal contribution of an item) which is drawn from a known probability distribution. However, we can not know its actual state before selecting it. As compared with existing studies on stochastic submodular maximization, one unique setting of our problem is that each item is associated with a continuation probability which represents the probability that one can continue to select the next item after selecting the current one. Intuitively, this term captures the externality of one item to all its subsequent items in terms of the opportunity of being selected. Therefore, the actual set of items that can be selected by a policy depends on the specific ordering it adopts to select items, this makes our problem fundamentally different from classical submodular set optimization problems. Our objective is to identify the best sequence of selecting items so as to maximize the expected utility of the selected items. We propose a class of stochastic utility functions, \emph{adaptive cascade submodular functions}, and show that the objective functions in many practical application domains satisfy adaptive cascade submodularity. Then we develop a $\frac{1-1/e}{8}$ approximation algorithm to the adaptive cascade submodular maximization problem.

Motivated by kidney exchange, we study a stochastic cycle and chain packing problem, where we aim to identify structures in a directed graph to maximize the expectation of matched edge weights. All edges are subject to failure, and the failures can have nonidentical probabilities. To the best of our knowledge, the state-of-the-art approaches are only tractable when failure probabilities are identical. We formulate a relevant non-convex optimization problem and propose a tractable mixed-integer linear programming reformulation to solve it. In addition, we propose a model that integrates both risks and the expected utilities of the matching by incorporating conditional value at risk (CVaR) into the objective function, providing a robust formulation for this problem. Subsequently, we propose a sample-average-approximation (SAA) based approach to solve this problem. We test our approaches on data from the United Network for Organ Sharing (UNOS) and compare against state-of-the-art approaches. Our model provides better performance with the same running time as a leading deterministic approach (PICEF). Our CVaR extensions with an SAA-based method improves the $\alpha \times 100\%$ ($0<\alpha\leqslant 1$) worst-case performance substantially compared to existing models.

Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including multi-objective, multi-fidelity, parallelization, latent-variable model, have been proposed to improve the limitation of the classical BO framework. In this work, we propose a novel multi-objective (MO) extension, called srMO-BO-3GP, to solve the MO optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each of the GP is assigned with a different task: the first GP is used to approximate the single-objective function, the second GP is used to learn the unknown constraints, and the third GP is used to learn the uncertain Pareto frontier. At each iteration, a MO augmented Tchebycheff function converting MO to single-objective is adopted and extended with a regularized ridge term, where the regularization is introduced to smoothen the single-objective function. Finally, we couple the third GP along with the classical BO framework to promote the richness and diversity of the Pareto frontier by the exploitation and exploration acquisition function. The proposed framework is demonstrated using several numerical benchmark functions, as well as a thermomechanical finite element model for flip-chip package design optimization.

For the challenging computational environment of IOT/edge computing, personalized federated learning allows every client to train a strong personalized cloud model by effectively collaborating with the other clients in a privacy-preserving manner. The performance of personalized federated learning is largely determined by the effectiveness of inter-client collaboration. However, when the data is non-IID across all clients, it is challenging to infer the collaboration relationships between clients without knowing their data distributions. In this paper, we propose to tackle this problem by a novel framework named federated attentive message passing (FedAMP) that allows each client to collaboratively train its own personalized cloud model without using a global model. FedAMP implements an attentive collaboration mechanism by iteratively encouraging clients with more similar model parameters to have stronger collaborations. This adaptively discovers the underlying collaboration relationships between clients, which significantly boosts effectiveness of collaboration and leads to the outstanding performance of FedAMP. We establish the convergence of FedAMP for both convex and non-convex models, and further propose a heuristic method that resembles the FedAMP framework to further improve its performance for federated learning with deep neural networks. Extensive experiments demonstrate the superior performance of our methods in handling non-IID data, dirty data and dropped clients.

We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of combinatorial problems, which involve a number of constraints that is polynomial in the problem dimension. The most important feature of our framework is that only a subset of the constraints is processed at each iteration, thus gaining a computational advantage over prior works that require full passes. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees. Preliminary numerical experiments are provided for illustrating the practical performance of the methods.

We propose a distributed, cubic-regularized Newton method for large-scale convex optimization over networks. The proposed method requires only local computations and communications and is suitable for federated learning applications over arbitrary network topologies. We show a $O(k^{{-}3})$ convergence rate when the cost function is convex with Lipschitz gradient and Hessian, with $k$ being the number of iterations. We further provide network-dependent bounds for the communication required in each step of the algorithm. We provide numerical experiments that validate our theoretical results.

Network embedding, aiming to project a network into a low-dimensional space, is increasingly becoming a focus of network research. Semi-supervised network embedding takes advantage of labeled data, and has shown promising performance. However, existing semi-supervised methods would get unappealing results in the completely-imbalanced label setting where some classes have no labeled nodes at all. To alleviate this, we propose two novel semi-supervised network embedding methods. The first one is a shallow method named RSDNE. Specifically, to benefit from the completely-imbalanced labels, RSDNE guarantees both intra-class similarity and inter-class dissimilarity in an approximate way. The other method is RECT which is a new class of graph neural networks. Different from RSDNE, to benefit from the completely-imbalanced labels, RECT explores the class-semantic knowledge. This enables RECT to handle networks with node features and multi-label setting. Experimental results on several real-world datasets demonstrate the superiority of the proposed methods.

The great amount of datasets generated by various data sources have posed the challenge to machine learning algorithm selection and hyperparameter configuration. For a specific machine learning task, it usually takes domain experts plenty of time to select an appropriate algorithm and configure its hyperparameters. If the problem of algorithm selection and hyperparameter optimization can be solved automatically, the task will be executed more efficiently with performance guarantee. Such problem is also known as the CASH problem. Early work either requires a large amount of human labor, or suffers from high time or space complexity. In our work, we present Auto-CASH, a pre-trained model based on meta-learning, to solve the CASH problem more efficiently. Auto-CASH is the first approach that utilizes Deep Q-Network to automatically select the meta-features for each dataset, thus reducing the time cost tremendously without introducing too much human labor. To demonstrate the effectiveness of our model, we conduct extensive experiments on 120 real-world classification datasets. Compared with classical and the state-of-art CASH approaches, experimental results show that Auto-CASH achieves better performance within shorter time.

Actual causality is increasingly well understood. Recent formal approaches, proposed by Halpern and Pearl, have made this concept mature enough to be amenable to automated reasoning. Actual causality is especially vital for building accountable, explainable systems. Among other reasons, causality reasoning is computationally hard due to the requirements of counterfactuality and the minimality of causes. Previous approaches presented either inefficient or restricted, and domain-specific, solutions to the problem of automating causality reasoning. In this paper, we present a novel approach to formulate different notions of causal reasoning, over binary acyclic models, as optimization problems, based on quantifiable notions within counterfactual computations. We contribute and compare two compact, non-trivial, and sound integer linear programming (ILP) and Maximum Satisfiability (MaxSAT) encodings to check causality. Given a candidate cause, both approaches identify what a minimal cause is. Also, we present an ILP encoding to infer causality without requiring a candidate cause. We show that both notions are efficiently automated. Using models with more than $8000$ variables, checking is computed in a matter of seconds, with MaxSAT outperforming ILP in many cases. In contrast, inference is computed in a matter of minutes.