In this paper, we propose a novel primal-dual proximal splitting algorithm (PD-PSA), named BALPA, for the composite optimization problem with equality constraints, where the loss function consists of a smooth term and a nonsmooth term composed with a linear mapping. In BALPA, the dual update is designed as a proximal point for a time-varying quadratic function, which balances the implementation of primal and dual update and retains the proximity-induced feature of classic PD-PSAs. In addition, by this balance, BALPA eliminates the inefficiency of classic PD-PSAs for composite optimization problems in which the Euclidean norm of the linear mapping or the equality constraint mapping is large. Therefore, BALPA not only inherits the advantages of simple structure and easy implementation of classic PD-PSAs but also ensures a fast convergence when these norms are large. Moreover, we propose a stochastic version of BALPA (S-BALPA) and apply the developed BALPA to distributed optimization to devise a new distributed optimization algorithm. Furthermore, a comprehensive convergence analysis for BALPA and S-BALPA is conducted, respectively. Finally, numerical experiments demonstrate the efficiency of the proposed algorithms.

Valuing mineral assets is a challenging task that is highly dependent on the supply (geological) uncertainty surrounding resources and reserves, and the uncertainty of demand (commodity prices). In this work, a graph-based reasoning, modeling and solution approach is proposed to jointly address mineral asset valuation and mine plan scheduling and optimization under supply and demand uncertainty in the "mining complex" framework. Three graph-based solutions are proposed: (i) a neural branching policy that learns a block-sampling ore body representation, (ii) a guiding policy that learns to explore a heuristic selection tree, (iii) a hyper-heuristic that manages the value/supply chain optimization and dynamics modeled as a graph structure. Results on two large-scale industrial mining complexes show a reduction of up to three orders of magnitude in primal suboptimality, execution time, and number of iterations, and an increase of up to 40% in the mineral asset value.

In this paper, we design a resource management scheme to support stateful applications, which will be prevalent in 6G networks. Different from stateless applications, stateful applications require context data while executing computing tasks from user terminals (UTs). Using a multi-tier computing paradigm with servers deployed at the core network, gateways, and base stations to support stateful applications, we aim to optimize long-term resource reservation by jointly minimizing the usage of computing, storage, and communication resources and the cost from reconfiguring resource reservation. The coupling among different resources and the impact of UT mobility create challenges in resource management. To address the challenges, we develop digital twin (DT) empowered network planning with two elements, i.e., multiresource reservation and resource reservation reconfiguration. First, DTs are designed for collecting UT status data, based on which UTs are grouped according to their mobility patterns. Second, an algorithm is proposed to customize resource reservation for different groups to satisfy their different resource demands. Last, a Meta-learning-based approach is developed to reconfigure resource reservation for balancing the network resource usage and the reconfiguration cost. Simulation results demonstrate that the proposed DT-empowered network planning outperforms benchmark frameworks by using less resources and incurring lower reconfiguration costs. C. Zhou, X. Shen, and W. Zhuang are with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada (e-mail: c89zhou@uwaterloo.ca; J. Gao is with the School of Information Technology, Carleton University, Ottawa, ON, K1S 5B6, Canada (email: jie.gao6@carleton.ca).

This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian inference applications, a multielement Polynomial Chaos Expansion based Kriging metamodel is proposed. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping subdomains of the stochastic input space. Therewith, the presence of non-smoothness in the response of the forward model (e.g.~ nonlinearities and sparseness) can be reproduced by the proposed metamodel with minimum computational costs owing to its local adaptation capabilities. The model parameter inference is conducted through a Markov chain Monte Carlo approach comprising adaptive exploration and delayed rejection. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study. The latter relates the partial differential equation governing the hydrogen diffusion phenomenon of metallic materials in Thermal Desorption Spectroscopy tests.

Minimax optimization problems have attracted significant attention in recent years due to their widespread application in numerous machine learning models. To solve the minimax optimization problem, a wide variety of stochastic optimization methods have been proposed. However, most of them ignore the distributed setting where the training data is distributed on multiple workers. In this paper, we developed a novel decentralized stochastic gradient descent ascent method for the finite-sum minimax optimization problem. In particular, by employing the variance-reduced gradient, our method can achieve $O(\frac{\sqrt{n}\kappa^3}{(1-\lambda)^2\epsilon^2})$ sample complexity and $O(\frac{\kappa^3}{(1-\lambda)^2\epsilon^2})$ communication complexity for the nonconvex-strongly-concave minimax optimization problem. As far as we know, our work is the first one to achieve such theoretical complexities for this kind of problem. At last, we apply our method to optimize the AUC maximization problem and the experimental results confirm the effectiveness of our method.

Enhancing resilience in distributed networks in the face of malicious agents is an important problem for which many key theoretical results and applications require further development and characterization. This work focuses on the problem of distributed optimization in multi-agent cyberphysical systems, where a legitimate agent's dynamic is influenced both by the values it receives from potentially malicious neighboring agents, and by its own self-serving target function. We develop a new algorithmic and analytical framework to achieve resilience for the class of problems where stochastic values of trust between agents exist and can be exploited. In this case we show that convergence to the true global optimal point can be recovered, both in mean and almost surely, even in the presence of malicious agents. Furthermore, we provide expected convergence rate guarantees in the form of upper bounds on the expected squared distance to the optimal value. Finally, we present numerical results that validate the analytical convergence guarantees we present in this paper even when the malicious agents compose the majority of agents in the network.

We explore how observational and interventional causal discovery methods can be combined. A state-of-the-art observational causal discovery algorithm for time series capable of handling latent confounders and contemporaneous effects, called LPCMCI, is extended to profit from casual constraints found through randomized control trials. Numerical results show that, given perfect interventional constraints, the reconstructed structural causal models (SCMs) of the extended LPCMCI allow 84.6% of the time for the optimal prediction of the target variable. The implementation of interventional and observational causal discovery is modular, allowing causal constraints from other sources. The second part of this thesis investigates the question of regret minimizing control by simultaneously learning a causal model and planning actions through the causal model. The idea is that an agent to optimize a measured variable first learns the system's mechanics through observational causal discovery. The agent then intervenes on the most promising variable with randomized values allowing for the exploitation and generation of new interventional data. The agent then uses the interventional data to enhance the causal model further, allowing improved actions the next time. The extended LPCMCI can be favorable compared to the original LPCMCI algorithm. The numerical results show that detecting and using interventional constraints leads to reconstructed SCMs that allow 60.9% of the time for the optimal prediction of the target variable in contrast to the baseline of 53.6% when using the original LPCMCI algorithm. Furthermore, the induced average regret decreases from 1.2 when using the original LPCMCI algorithm to 1.0 when using the extended LPCMCI algorithm with interventional discovery.

The demand for resilient logistics networks has increased because of recent disasters. When we consider optimization problems, entropy regularization is a powerful tool for the diversification of a solution. In this study, we proposed a method for designing a resilient logistics network based on entropy regularization. Moreover, we proposed a method for analytical resilience criteria to reduce the ambiguity of resilience. First, we modeled the logistics network, including factories, distribution bases, and sales outlets in an efficient framework using entropy regularization. Next, we formulated a resilience criterion based on probabilistic cost and Kullback--Leibler divergence. Finally, our method was performed using a simple logistics network, and the resilience of the three logistics plans designed by entropy regularization was demonstrated.

Ego-pose estimation and dynamic object tracking are two critical problems for autonomous driving systems. The solutions to these problems are generally based on their respective assumptions, \ie{the static world assumption for simultaneous localization and mapping (SLAM) and the accurate ego-pose assumption for object tracking}. However, these assumptions are challenging to hold in dynamic road scenarios, where SLAM and object tracking become closely correlated. Therefore, we propose DL-SLOT, a dynamic LiDAR SLAM and object tracking method, to simultaneously address these two coupled problems. This method integrates the state estimations of both the autonomous vehicle and the stationary and dynamic objects in the environment into a unified optimization framework. First, we used object detection to identify all points belonging to potentially dynamic objects. Subsequently, a LiDAR odometry was conducted using the filtered point cloud. Simultaneously, we proposed a sliding window-based object association method that accurately associates objects according to the historical trajectories of tracked objects. The ego-states and those of the stationary and dynamic objects are integrated into the sliding window-based collaborative graph optimization. The stationary objects are subsequently restored from the potentially dynamic object set. Finally, a global pose-graph is implemented to eliminate the accumulated error. Experiments on KITTI datasets demonstrate that our method achieves better accuracy than SLAM and object tracking baseline methods. This confirms that solving SLAM and object tracking simultaneously is mutually advantageous, dramatically improving the robustness and accuracy of SLAM and object tracking in dynamic road scenarios.

In natural language processing (NLP), the problem of aligning monolingual embedding spaces to induce a shared cross-lingual vector space has been shown not only to be useful in a variety of tasks such as bilingual lexicon induction (BLI) (Mikolov et al., 2013; Barone, 2016; Artetxe et al., 2017; Aboagye et al., 2022), machine translation (Artetxe et al., 2018b), cross-lingual information retrieval (Vulić & Moens, 2015), but it plays a crucial role in facilitating the cross-lingual transfer of language technologies from high resource languages to low resource languages. Cross-lingual word embeddings (CLWEs) represent words from two or more languages in a shared cross-lingual vector space in which words with similar meanings obtain similar vectors regardless of their language. There has been a flurry of work dominated by the so-called projection-based CLWE models (Mikolov et al., 2013; Artetxe et al., 2016, 2017, 2018a; Smith et al., 2017; Ruder et al., 2019), which aim to improve CLWE model performance significantly. Projection-based CLWE models learn a transfer function or mapper between two independently trained monolingual word vector spaces with limited or no cross-lingual supervision. Famous among projection-based CLWE models are the unsupervised projection-based CLWE models (Artetxe et al., 2017; Lample et al., 2018; Alvarez-Melis & Jaakkola, 2018;