Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In this paper, we design and analyze stochastic inexact augmented Lagrangian methods (Stoc-iALM) to solve problems involving a nonconvex composite (i.e. smooth+nonsmooth) objective and nonconvex smooth functional constraints. We adopt the standard iALM framework and design a subroutine by using the momentum-based variance-reduced proximal stochastic gradient method (PStorm) and a postprocessing step. Under certain regularity conditions (assumed also in existing works), to reach an $\varepsilon$-KKT point in expectation, we establish an oracle complexity result of $O(\varepsilon^{-5})$, which is better than the best-known $O(\varepsilon^{-6})$ result. Numerical experiments on the fairness constrained problem and the Neyman-Pearson classification problem with real data demonstrate that our proposed method outperforms an existing method with the previously best-known complexity result.

In this review, we discuss approaches for learning causal structure from data, also called causal discovery. In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some variables to be unobserved in the available data. We devote special attention to two fundamental combinatorial aspects of causal structure learning. First, we discuss the structure of the search space over causal graphs. Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can be refined by adding interventional data.

Reinforcement learning-based (RL-based) energy management strategy (EMS) is considered a promising solution for the energy management of electric vehicles with multiple power sources. It has been shown to outperform conventional methods in energy management problems regarding energy-saving and real-time performance. However, previous studies have not systematically examined the essential elements of RL-based EMS. This paper presents an empirical analysis of RL-based EMS in a Plug-in Hybrid Electric Vehicle (PHEV) and Fuel Cell Electric Vehicle (FCEV). The empirical analysis is developed in four aspects: algorithm, perception and decision granularity, hyperparameters, and reward function. The results show that the Off-policy algorithm effectively develops a more fuel-efficient solution within the complete driving cycle compared with other algorithms. Improving the perception and decision granularity does not produce a more desirable energy-saving solution but better balances battery power and fuel consumption. The equivalent energy optimization objective based on the instantaneous state of charge (SOC) variation is parameter sensitive and can help RL-EMSs to achieve more efficient energy-cost strategies.

Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on parameter estimation in linear mixed models by exploiting the intrinsic geometry of the parameter space. We formulate the problem of residual maximum likelihood estimation as an optimization problem on a Riemannian manifold. Based on the introduced formulation, we give geometric higher-order information on the problem via the Riemannian gradient and the Riemannian Hessian. Based on that, we test our approach with Riemannian optimization algorithms numerically. Our approach yields a higher quality of the variance parameter estimates compared to existing approaches.

In this paper, the CONFIG algorithm, a simple and provably efficient constrained global optimization algorithm, is applied to optimize the closed-loop control performance of an unknown system with unmodeled constraints. Existing Gaussian process based closed-loop optimization methods, either can only guarantee local convergence (e.g., SafeOPT), or have no known optimality guarantee (e.g., constrained expected improvement) at all, whereas the recently introduced CONFIG algorithm has been proven to enjoy a theoretical global optimality guarantee. In this study, we demonstrate the effectiveness of CONFIG algorithm in the applications. The algorithm is first applied to an artificial numerical benchmark problem to corroborate its effectiveness. It is then applied to a classical constrained steady-state optimization problem of a continuous stirred-tank reactor. Simulation results show that our CONFIG algorithm can achieve performance competitive with the popular CEI (Constrained Expected Improvement) algorithm, which has no known optimality guarantee. As such, the CONFIG algorithm offers a new tool, with both a provable global optimality guarantee and competitive empirical performance, to optimize the closed-loop control performance for a system with soft unmodeled constraints. Last, but not least, the open-source code is available as a python package to facilitate future applications.

Integrated space-air-ground networks promise to offer a valuable solution space for empowering the sixth generation of communication networks (6G), particularly in the context of connecting the unconnected and ultraconnecting the connected. Such digital inclusion thrive makes resource management problems, especially those accounting for load-balancing considerations, of particular interest. The conventional model-based optimization methods, however, often fail to meet the real-time processing and quality-of-service needs, due to the high heterogeneity of the space-air-ground networks, and the typical complexity of the classical algorithms. Given the premises of artificial intelligence at automating wireless networks design and the large-scale heterogeneity of non-terrestrial networks, this paper focuses on showcasing the prospects of machine learning in the context of user scheduling in integrated space-air-ground communications. The paper first overviews the most relevant state-of-the art in the context of machine learning applications to the resource allocation problems, with a dedicated attention to space-air-ground networks. The paper then proposes, and shows the benefit of, one specific use case that uses ensembling deep neural networks for optimizing the user scheduling policies in integrated space-high altitude platform station (HAPS)-ground networks. Finally, the paper sheds light on the challenges and open issues that promise to spur the integration of machine learning in space-air-ground networks, namely, online HAPS power adaptation, learning-based channel sensing, data-driven multi-HAPSs resource management, and intelligent flying taxis-empowered systems.

The chimp optimization algorithm (ChOA) is a hunting-based model and can be utilized as a set of optimization rules to tackle optimization problems. Although ChOA has shown promising results on optimization functions, it suffers from a slow convergence rate and low exploration capability. Therefore, in this paper, a modified ChOA is proposed to improve the exploration and exploitation capabilities of the ChOA. This improvement is performed using greedy search and opposition-based learning (OBL), respectively. In order to investigate the efficiency of the OBLChOA, the OBLChOA's performance is evaluated by twenty-three standard benchmark functions, ten suit tests of IEEE CEC06-2019, randomly generated landscape, and twelve real-world Constrained Optimization Problems (IEEE COPs-2020) from a variety of engineering fields, including industrial chemical producer, power system, process design and synthesis, mechanical design, power-electronic, and livestock feed ration.

Machine learning methods have been used to accelerate the molecule optimization process. However, efficient search for optimized molecules satisfying several properties with scarce labeled data remains a challenge for machine learning molecule optimization. In this study, we propose MOMO, a multi-objective molecule optimization framework to address the challenge by combining learning of chemical knowledge with Pareto-based multi-objective evolutionary search. To learn chemistry, it employs a self-supervised codec to construct an implicit chemical space and acquire the continues representation of molecules. To explore the established chemical space, MOMO uses multi-objective evolution to comprehensively and efficiently search for similar molecules with multiple desirable properties. We demonstrate the high performance of MOMO on four multi-objective property and similarity optimization tasks, and illustrate the search capability of MOMO through case studies. Remarkably, our approach significantly outperforms previous approaches in optimizing three objectives simultaneously. The results show the optimization capability of MOMO, suggesting to improve the success rate of lead molecule optimization.

We extend best-subset selection to linear Multi-Task Learning (MTL), where a set of linear models are jointly trained on a collection of datasets (``tasks''). Allowing the regression coefficients of tasks to have different sparsity patterns (i.e., different supports), we propose a modeling framework for MTL that encourages models to share information across tasks, for a given covariate, through separately 1) shrinking the coefficient supports together, and/or 2) shrinking the coefficient values together. This allows models to borrow strength during variable selection even when the coefficient values differ markedly between tasks. We express our modeling framework as a Mixed-Integer Program, and propose efficient and scalable algorithms based on block coordinate descent and combinatorial local search. We show our estimator achieves statistically optimal prediction rates. Importantly, our theory characterizes how our estimator leverages the shared support information across tasks to achieve better variable selection performance. We evaluate the performance of our method in simulations and two biology applications. Our proposed approaches outperform other sparse MTL methods in variable selection and prediction accuracy. Interestingly, penalties that shrink the supports together often outperform penalties that shrink the coefficient values together. We will release an R package implementing our methods.

Knowledge Distillation (KD) is a commonly used technique for improving the generalization of compact Pre-trained Language Models (PLMs) on downstream tasks. However, such methods impose the additional burden of training a separate teacher model for every new dataset. Alternatively, one may directly work on the improvement of the optimization procedure of the compact model toward better generalization. Recent works observe that the flatness of the local minimum correlates well with better generalization. In this work, we adapt Stochastic Weight Averaging (SWA), a method encouraging convergence to a flatter minimum, to fine-tuning PLMs. We conduct extensive experiments on various NLP tasks (text classification, question answering, and generation) and different model architectures and demonstrate that our adaptation improves the generalization without extra computation cost. Moreover, we observe that this simple optimization technique is able to outperform the state-of-the-art KD methods for compact models.