A novel simulator called VMAgent is introduced to help RL researchers better explore new methods, especially for virtual machine scheduling. VMAgent is inspired by practical virtual machine (VM) scheduling tasks and provides an efficient simulation platform that can reflect the real situations of cloud computing. Three scenarios (fading, recovering, and expansion) are concluded from practical cloud computing and corresponds to many reinforcement learning challenges (high dimensional state and action spaces, high non-stationarity, and life-long demand). VMAgent provides flexible configurations for RL researchers to design their customized scheduling environments considering different problem features. From the VM scheduling perspective, VMAgent also helps to explore better learning-based scheduling solutions.

The modeling and control of complex physical systems are essential in real-world problems. We propose a novel framework that is generally applicable to solving PDE-constrained optimal control problems by introducing surrogate models for PDE solution operators with special regularizers. The procedure of the proposed framework is divided into two phases: solution operator learning for PDE constraints (Phase 1) and searching for optimal control (Phase 2). Once the surrogate model is trained in Phase 1, the optimal control can be inferred in Phase 2 without intensive computations. Our framework can be applied to both data-driven and data-free cases. We demonstrate the successful application of our method to various optimal control problems for different control variables with diverse PDE constraints from the Poisson equation to Burgers' equation.

Hyperparameter optimization (HPO) is a necessary step to ensure the best possible performance of Machine Learning (ML) algorithms. Several methods have been developed to perform HPO; most of these are focused on optimizing one performance measure (usually an error-based measure), and the literature on such single-objective HPO problems is vast. Recently, though, algorithms have appeared which focus on optimizing multiple conflicting objectives simultaneously. This article presents a systematic survey of the literature published between 2014 and 2020 on multi-objective HPO algorithms, distinguishing between metaheuristic-based algorithms, metamodel-based algorithms, and approaches using a mixture of both. We also discuss the quality metrics used to compare multi-objective HPO procedures and present future research directions.

Bayesian optimization is a procedure that allows obtaining the global optimum of black-box functions and that is useful in applications such as hyper-parameter optimization. Uncertainty estimates over the shape of the objective function are instrumental in guiding the optimization process. However, these estimates can be inaccurate if the objective function violates assumptions made within the underlying model (e.g., Gaussianity). We propose a simple algorithm to calibrate the uncertainty of posterior distributions over the objective function as part of the Bayesian optimization process. We show that by improving the uncertainty estimates of the posterior distribution with calibration, Bayesian optimization makes better decisions and arrives at the global optimum in fewer steps. We show that this technique improves the performance of Bayesian optimization on standard benchmark functions and hyperparameter optimization tasks.

Causal discovery aims to learn a causal graph from observational data. To date, most causal discovery methods require data to be stored in a central server. However, data owners gradually refuse to share their personalized data to avoid privacy leakage, making this task more troublesome by cutting off the first step. A puzzle arises: $\textit{how do we infer causal relations from decentralized data?}$ In this paper, with the additive noise model assumption of data, we take the first step in developing a gradient-based learning framework named DAG-Shared Federated Causal Discovery (DS-FCD), which can learn the causal graph without directly touching local data and naturally handle the data heterogeneity. DS-FCD benefits from a two-level structure of each local model. The first level learns the causal graph and communicates with the server to get model information from other clients, while the second level approximates causal mechanisms and personally updates from its own data to accommodate the data heterogeneity. Moreover, DS-FCD formulates the overall learning task as a continuous optimization problem by taking advantage of an equality acyclicity constraint, which can be naturally solved by gradient descent methods. Extensive experiments on both synthetic and real-world datasets verify the efficacy of the proposed method.

Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a sub-problem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of the current subproblem. The new columns are generated as needed by repeatedly solving a pricing problem, which is often NP-hard and is a bottleneck of the CG approach. To tackle this, we propose a Machine-Learning-based Pricing Heuristic (MLPH)that can generate many high-quality columns efficiently. In each iteration of CG, our MLPH leverages an ML model to predict the optimal solution of the pricing problem, which is then used to guide a sampling method to efficiently generate multiple high-quality columns. Using the graph coloring problem, we empirically show that MLPH significantly enhancesCG as compared to six state-of-the-art methods, and the improvement in CG can lead to substantially better performance of the branch-and-price exact method.

The multi-task learning (MTL) paradigm can be traced back to an early paper of Caruana (1997) in which it was argued that data from multiple tasks can be used with the aim to obtain a better performance over learning each task independently. A solution of MTL with conflicting objectives requires modelling the trade-off among them which is generally beyond what a straight linear combination can achieve. A theoretically principled and computationally effective strategy is finding solutions which are not dominated by others as it is addressed in the Pareto analysis. Multi-objective optimization problems arising in the multi-task learning context have specific features and require adhoc methods. The analysis of these features and the proposal of a new computational approach represent the focus of this work. Multi-objective evolutionary algorithms (MOEAs) can easily include the concept of dominance and therefore the Pareto analysis. The major drawback of MOEAs is a low sample efficiency with respect to function evaluations. The key reason for this drawback is that most of the evolutionary approaches do not use models for approximating the objective function. Bayesian Optimization takes a radically different approach based on a surrogate model, such as a Gaussian Process. In this thesis the solutions in the Input Space are represented as probability distributions encapsulating the knowledge contained in the function evaluations. In this space of probability distributions, endowed with the metric given by the Wasserstein distance, a new algorithm MOEA/WST can be designed in which the model is not directly on the objective function but in an intermediate Information Space where the objects from the input space are mapped into histograms. Computational results show that the sample efficiency and the quality of the Pareto set provided by MOEA/WST are significantly better than in the standard MOEA.

We consider distributed online min-max resource allocation with a set of parallel agents and a parameter server. Our goal is to minimize the pointwise maximum over a set of time-varying convex and decreasing cost functions, without a priori information about these functions. We propose a novel online algorithm, termed Distributed Online resource Re-Allocation (DORA), where non-stragglers learn to relinquish resource and share resource with stragglers. A notable feature of DORA is that it does not require gradient calculation or projection operation, unlike most existing online optimization strategies. This allows it to substantially reduce the computation overhead in large-scale and distributed networks. We show that the dynamic regret of the proposed algorithm is upper bounded by $O\left(T^{\frac{3}{4}}(1+P_T)^{\frac{1}{4}}\right)$, where $T$ is the total number of rounds and $P_T$ is the path-length of the instantaneous minimizers. We further consider an application to the bandwidth allocation problem in distributed online machine learning. Our numerical study demonstrates the efficacy of the proposed solution and its performance advantage over gradient- and/or projection-based resource allocation algorithms in reducing wall-clock time.

Multipartite entity resolution aims at integrating records from multiple datasets into one entity. We derive a mathematical formulation for a general class of record linkage problems in multipartite entity resolution across many datasets as a combinatorial optimization problem known as the multidimensional assignment problem. As a motivation for our approach, we illustrate the advantage of multipartite entity resolution over sequential bipartite matching. Because the optimization problem is NP-hard, we apply two heuristic procedures, a Greedy algorithm and very large scale neighborhood search, to solve the assignment problem and find the most likely matching of records from multiple datasets into a single entity. We evaluate and compare the performance of these algorithms and their modifications on synthetically generated data. We perform computational experiments to compare performance of recent heuristic, the very large-scale neighborhood search, with a Greedy algorithm, another heuristic for the MAP, as well as with two versions of genetic algorithm, a general metaheuristic. Importantly, we perform experiments to compare two alternative methods of re-starting the search for the former heuristic, specifically a random-sampling multi-start and a deterministic design-based multi-start. We find evidence that design-based multi-start can be more efficient as the size of databases grow large. In addition, we show that very large scale search, especially its multi-start version, outperforms simple Greedy heuristic. Hybridization of Greedy search with very large scale neighborhood search improves the performance. Using multi-start with as few as three additional runs of very large scale search offers some improvement in the performance of the very large scale search procedure. Last, we propose an approach to evaluating complexity of the very large-scale neighborhood search.

Many learning tasks require observing a sequence of images and making a decision. In a transportation problem of designing and planning for shipping boxes between nodes, we show how to treat the network of nodes and the flows between them as images. These images have useful structural information that can be statistically summarized. Using image compression techniques, we reduce an image down to a set of numbers that contain interpretable geographic information that we call geographic signatures. Using geographic signatures, we learn network structure that can be utilized to recommend future network connectivity. We develop a Bayesian reinforcement algorithm that takes advantage of statistically summarized network information as priors and user-decisions to reinforce an agent's probabilistic decision.