We propose a novel approach for performing dynamical system identification, based upon the comparison of simulated and observed physical invariant measures. While standard methods adopt a Lagrangian perspective by directly treating time-trajectories as inference data, we take on an Eulerian perspective and instead seek models fitting the observed global time-invariant statistics. With this change in perspective, we gain robustness against pervasive challenges in system identification including noise, chaos, and slow sampling. In the first half of this paper, we pose the system identification task as a partial differential equation (PDE) constrained optimization problem, in which synthetic stationary solutions of the Fokker-Planck equation, obtained as fixed points of a finite-volume discretization, are compared to physical invariant measures extracted from observed trajectory data. In the latter half of the paper, we improve upon this approach in two crucial directions. First, we develop a Galerkin-inspired modification to the finite-volume surrogate model, based on data-adaptive unstructured meshes and Monte-Carlo integration, enabling the approach to efficiently scale to high-dimensional problems. Second, we leverage Takens' seminal time-delay embedding theory to introduce a critical data-dependent coordinate transformation which can guarantee unique system identifiability from the invariant measure alone. This contribution resolves a major challenge of system identification through invariant measures, as systems exhibiting distinct transient behaviors may still share the same time-invariant statistics in their state-coordinates. Throughout, we present comprehensive numerical tests which highlight the effectiveness of our approach on a variety of challenging system identification tasks.

We provide a new online learning algorithm for tackling the Multinomial Logit Bandit (MNL-Bandit) problem. Despite the challenges posed by the combinatorial nature of the MNL model, we develop a novel Upper Confidence Bound (UCB)-based method that achieves Pareto optimality by balancing regret minimization and estimation error of the assortment revenues and the MNL parameters. We develop theoretical guarantees characterizing the tradeoff between regret and estimation error for the MNL-Bandit problem through information-theoretic bounds, and propose a modified UCB algorithm that incorporates forced exploration to improve parameter estimation accuracy while maintaining low regret. Our analysis sheds critical insights into how to optimally balance the collected revenues and the treatment estimation in dynamic assortment optimization.

This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative algorithm. However, we observed that directly applying LD often leads to limited exploration. To overcome this limitation, we propose the Regularized Langevin Dynamics (RLD), which enforces an expected distance between the sampled and current solutions, effectively avoiding local minima. We develop two CO solvers on top of RLD, one based on simulated annealing (SA) and the other one based on neural network (NN). Empirical results on three classical CO problems demonstrate that both of our methods can achieve comparable or better performance against the previous state-of-the-art (SOTA) SA and NN-based solvers. In particular, our SA algorithm reduces the running time of the previous SOTA SA method by up to 80\%, while achieving equal or superior performance. In summary, RLD offers a promising framework for enhancing both traditional heuristics and NN models to solve CO problems.

Intelligent transportation systems have recently emerged to address the growing interest for safer, more efficient, and sustainable transportation solutions. In this direction, this paper presents distributed algorithms for control and optimization over vehicular networks. First, we formulate the autonomous vehicle platooning framework based on model-predictive-control (MPC) strategies and present its objective optimization as a cooperative quadratic cost function. Then, we propose a distributed algorithm to locally optimize this objective at every vehicle subject to data quantization over the communication network of vehicles. In contrast to most existing literature that assumes ideal communication channels, log-scale data quantization over the network is addressed in this work, which is more realistic and practical. In particular, we show by simulation that the proposed log-quantized algorithm reaches optimal convergence with less residual and optimality gap. This outperforms the existing literature considering uniform quantization which leads to a large optimality gap and residual.

Ensemble technique and under-sampling technique are both effective tools used for imbalanced dataset classification problems. In this paper, a novel ensemble method combining the advantages of both ensemble learning for biasing classifiers and a new under-sampling method is proposed. The under-sampling method is named Binary PSO instance selection; it gathers with ensemble classifiers to find the most suitable length and combination of the majority class samples to build a new dataset with minority class samples. The proposed method adopts multi-objective strategy, and contribution of this method is a notable improvement of the performances of imbalanced classification, and in the meantime guaranteeing a best integrity possible for the original dataset. We experimented the proposed method and compared its performance of processing imbalanced datasets with several other conventional basic ensemble methods. Experiment is also conducted on these imbalanced datasets using an improved version where ensemble classifiers are wrapped in the Binary PSO instance selection. According to experimental results, our proposed methods outperform single ensemble methods, state-of-the-art under-sampling methods, and also combinations of these methods with the traditional PSO instance selection algorithm.

Variational quantum algorithms, such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale Quantum devices to address challenging combinatorial optimization tasks like the maximum cut problem. In this study, we utilize an evolutionary algorithm equipped with a unique fitness function. This approach targets hard maximum cut instances within the latent space of a Graph Autoencoder, identifying those that pose significant challenges or are particularly tractable for RQAOA, in contrast to the classic Goemans and Williamson algorithm. Our findings not only delineate the distinct capabilities and limitations of each algorithm but also expand our understanding of RQAOA's operational limits. Furthermore, the diverse set of graphs we have generated serves as a crucial benchmarking asset, emphasizing the need for more advanced algorithms to tackle combinatorial optimization challenges. Additionally, our results pave the way for new avenues in graph generation research, offering exciting opportunities for future explorations.

The goal of offline model-based optimization (MBO) is to propose new designs that maximize a reward function given only an offline dataset. However, an important desiderata is to also propose a diverse set of final candidates that capture many optimal and near-optimal design configurations. We propose Diversity in Adversarial Model-based Optimization (DynAMO) as a novel method to introduce design diversity as an explicit objective into any MBO problem. Our key insight is to formulate diversity as a distribution matching problem where the distribution of generated designs captures the inherent diversity contained within the offline dataset. Extensive experiments spanning multiple scientific domains show that DynAMO can be used with common optimization methods to significantly improve the diversity of proposed designs while still discovering high-quality candidates.

Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to reduce uncertainty about the function's optimum and are often considered fundamentally distinct from EI. In this work, we challenge this prevailing perspective by introducing a unified theoretical framework, Variational Entropy Search, which reveals that EI and information-theoretic acquisition functions are more closely related than previously recognized. We demonstrate that EI can be interpreted as a variational inference approximation of the popular information-theoretic acquisition function, named Max-value Entropy Search. Building on this insight, we propose VES-Gamma, a novel acquisition function that balances the strengths of EI and MES. Extensive empirical evaluations across both low- and high-dimensional synthetic and real-world benchmarks demonstrate that VES-Gamma is competitive with state-of-the-art acquisition functions and in many cases outperforms EI and MES.

Min cut is an important graph partitioning method. However, current solutions to the min cut problem suffer from slow speeds, difficulty in solving, and often converge to simple solutions. To address these issues, we relax the min cut problem into a dual-bounded constraint and, for the first time, treat the min cut problem as a dual-bounded nonlinear optimal transport problem. Additionally, we develop a method for solving dual-bounded nonlinear optimal transport based on the Frank-Wolfe method (abbreviated as DNF). Notably, DNF not only solves the size constrained min cut problem but is also applicable to all dual-bounded nonlinear optimal transport problems. We prove that for convex problems satisfying Lipschitz smoothness, the DNF method can achieve a convergence rate of \(\mathcal{O}(\frac{1}{t})\). We apply the DNF method to the min cut problem and find that it achieves state-of-the-art performance in terms of both the loss function and clustering accuracy at the fastest speed, with a convergence rate of \(\mathcal{O}(\frac{1}{\sqrt{t}})\). Moreover, the DNF method for the size constrained min cut problem requires no parameters and exhibits better stability.

Multi-access edge computing (MEC) technology is a promising solution to assist power-constrained IoT devices by providing additional computing resources for time-sensitive tasks. In this paper, we consider the problem of optimal task offloading in MEC systems with due consideration of the timeliness and scalability issues under two scenarios of equitable and priority access to the edge server (ES). In the first scenario, we consider a MEC system consisting of $N$ devices assisted by one ES, where the devices can split task execution between a local processor and the ES, with equitable access to the ES. In the second scenario, we consider a MEC system consisting of one primary user, $N$ secondary users and one ES. The primary user has priority access to the ES while the secondary users have equitable access to the ES amongst themselves. In both scenarios, due to the power consumption associated with utilizing the local resource and task offloading, the devices must optimize their actions. Additionally, since the ES is a shared resource, other users' offloading activity serves to increase latency incurred by each user. We thus model both scenarios using a non-cooperative game framework. However, the presence of a large number of users makes it nearly impossible to compute the equilibrium offloading policies for each user, which would require a significant information exchange overhead between users. Thus, to alleviate such scalability issues, we invoke the paradigm of mean-field games to compute approximate Nash equilibrium policies for each user using their local information, and further study the trade-offs between increasing information freshness and reducing power consumption for each user. Using numerical evaluations, we show that our approach can recover the offloading trends displayed under centralized solutions, and provide additional insights into the results obtained.