Maximum mean discrepancy (MMD) has been widely employed to measure the distance between probability distributions. In this paper, we propose using MMD to solve continuous multi-objective optimization problems (MOPs). For solving MOPs, a common approach is to minimize the distance (e.g., Hausdorff) between a finite approximate set of the Pareto front and a reference set. Viewing these two sets as empirical measures, we propose using MMD to measure the distance between them. To minimize the MMD value, we provide the analytical expression of its gradient and Hessian matrix w.r.t. the search variables, and use them to devise a novel set-oriented, MMD-based Newton (MMDN) method. Also, we analyze the theoretical properties of MMD's gradient and Hessian, including the first-order stationary condition and the eigenspectrum of the Hessian, which are important for verifying the correctness of MMDN. To solve complicated problems, we propose hybridizing MMDN with multiobjective evolutionary algorithms (MOEAs), where we first execute an EA for several iterations to get close to the global Pareto front and then warm-start MMDN with the result of the MOEA to efficiently refine the approximation. We empirically test the hybrid algorithm on 11 widely used benchmark problems, and the results show the hybrid (MMDN + MOEA) can achieve a much better optimization accuracy than EA alone with the same computation budget.

Sim-to-real discrepancies hinder learning-based policies from achieving high-precision tasks in the real world. While Domain Randomization (DR) is commonly used to bridge this gap, it often relies on heuristics and can lead to overly conservative policies with degrading performance when not properly tuned. System Identification (Sys-ID) offers a targeted approach, but standard techniques rely on differentiable dynamics and/or direct torque measurement, assumptions that rarely hold for contact-rich legged systems. To this end, we present SPI-Active (Sampling-based Parameter Identification with Active Exploration), a two-stage framework that estimates physical parameters of legged robots to minimize the sim-to-real gap. SPI-Active robustly identifies key physical parameters through massive parallel sampling, minimizing state prediction errors between simulated and real-world trajectories. To further improve the informativeness of collected data, we introduce an active exploration strategy that maximizes the Fisher Information of the collected real-world trajectories via optimizing the input commands of an exploration policy. This targeted exploration leads to accurate identification and better generalization across diverse tasks. Experiments demonstrate that SPI-Active enables precise sim-to-real transfer of learned policies to the real world, outperforming baselines by 42-63% in various locomotion tasks.

Adversarial Patrolling games form a subclass of Security games where a Defender moves between locations, guarding vulnerable targets. The main algorithmic problem is constructing a strategy for the Defender that minimizes the worst damage an Attacker can cause. We focus on the class of finite-memory (also known as regular) Defender's strategies that experimentally outperformed other competing classes. A finite-memory strategy can be seen as a positional strategy on a finite set of states. Each state consists of a pair of a location and a certain integer value--called memory. Existing algorithms improve the transitional probabilities between the states but require that the available memory size itself is assigned at each location manually. Choosing the right memory assignment is a well-known open and hard problem that hinders the usability of finite-memory strategies. We solve this issue by developing a general method that iteratively changes the memory assignment. Our algorithm can be used in connection with \emph{any} black-box strategy optimization tool. We evaluate our method on various experiments and show its robustness by solving instances of various patrolling models.

In this paper we propose for the first time the hyperparameter optimization (HPO) algorithm POCAII. POCAII differs from the Hyperband and Successive Halving literature by explicitly separating the search and evaluation phases and utilizing principled approaches to exploration and exploitation principles during both phases. Such distinction results in a highly flexible scheme for managing a hyperparameter optimization budget by focusing on search (i.e., generating competing configurations) towards the start of the HPO process while increasing the evaluation effort as the HPO comes to an end. POCAII was compared to state of the art approaches SMAC, BOHB and DEHB. Our algorithm shows superior performance in low-budget hyperparameter optimization regimes. Since many practitioners do not have exhaustive resources to assign to HPO, it has wide applications to real-world problems. Moreover, the empirical evidence showed how POCAII demonstrates higher robustness and lower variance in the results. This is again very important when considering realistic scenarios with extremely expensive models to train.

We introduce proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a principled foundation for optimal transport proximals and proximal optimization methods frequently used in generative modeling. We explore its mathematical properties, including smoothness, boundedness, and computational tractability, and establish connections to primal-dual formulation and adversarial learning. Building on the Benamou-Brenier dynamic formulation of optimal transport cost, we also establish a dynamic formulation for proximal OT divergences. The resulting dynamic formulation is a first order mean-field game whose optimality conditions are governed by a pair of nonlinear partial differential equations, a backward Hamilton-Jacobi and a forward continuity partial differential equations.

In cloud services, virtual machine (VM) scheduling is a typical Online Dynamic Multidimensional Bin Packing (ODMBP) problem, characterized by large-scale complexity and fluctuating demands. Traditional optimization methods struggle to adapt to real-time changes, domain-expert-designed heuristic approaches suffer from rigid strategies, and existing learning-based methods often lack generalizability and interpretability. To address these limitations, this paper proposes a hierarchical language agent framework named MiCo, which provides a large language model (LLM)-driven heuristic design paradigm for solving ODMBP. Specifically, ODMBP is formulated as a Semi-Markov Decision Process with Options (SMDP-Option), enabling dynamic scheduling through a two-stage architecture, i.e., Option Miner and Option Composer. Option Miner utilizes LLMs to discover diverse and useful non-context-aware strategies by interacting with constructed environments. Option Composer employs LLMs to discover a composing strategy that integrates the non-context-aware strategies with the contextual ones. Extensive experiments on real-world enterprise datasets demonstrate that MiCo achieves a 96.9\% competitive ratio in large-scale scenarios involving more than 10,000 virtual machines. It maintains high performance even under nonstationary request flows and diverse configurations, thus validating its effectiveness in complex and large-scale cloud environments.

As modern software systems expand in scale and complexity, the challenges associated with their modeling and formulation grow increasingly intricate. Traditional approaches often fall short in effectively addressing these complexities, particularly in tasks such as design pattern detection for maintenance and assessment, as well as code refactoring for optimization and long-term sustainability. This growing inadequacy underscores the need for a paradigm shift in how such challenges are approached and resolved. This paper presents Analytical Software Engineering (ASE), a novel design paradigm aimed at balancing abstraction, tool accessibility, compatibility, and scalability. ASE enables effective modeling and resolution of complex software engineering problems. The paradigm is evaluated through two frameworks Behavioral-Structural Sequences (BSS) and Optimized Design Refactoring (ODR), both developed in accordance with ASE principles. BSS offers a compact, language-agnostic representation of codebases to facilitate precise design pattern detection. ODR unifies artifact and solution representations to optimize code refactoring via heuristic algorithms while eliminating iterative computational overhead. By providing a structured approach to software design challenges, ASE lays the groundwork for future research in encoding and analyzing complex software metrics.

In embedded systems, robots must perceive and interpret their environment efficiently to operate reliably in real-world conditions. Visual Semantic SLAM (Simultaneous Localization and Mapping) enhances standard SLAM by incorporating semantic information into the map, enabling more informed decision-making. However, implementing such systems on resource-limited hardware involves trade-offs between accuracy, computing efficiency, and power usage. This paper provides a comparative review of recent Semantic Visual SLAM methods with a focus on their applicability to embedded platforms. We analyze three main types of architectures - Geometric SLAM, Neural Radiance Fields (NeRF), and 3D Gaussian Splatting - and evaluate their performance on constrained hardware, specifically the NVIDIA Jetson AGX Orin. We compare their accuracy, segmentation quality, memory usage, and energy consumption. Our results show that methods based on NeRF and Gaussian Splatting achieve high semantic detail but demand substantial computing resources, limiting their use on embedded devices. In contrast, Semantic Geometric SLAM offers a more practical balance between computational cost and accuracy. The review highlights a need for SLAM algorithms that are better adapted to embedded environments, and it discusses key directions for improving their efficiency through algorithm-hardware co-design.

Parameter-efficient fine-tuning (PEFT) is a highly effective approach for adapting large pre-trained models to downstream tasks with minimal computational overhead. At the core, PEFT methods freeze most parameters and only trains a small subset (say $<0.1\%$ of total parameters). Notably, different PEFT methods select different subsets, resulting in varying levels of performance. This variation prompts a key question: how to effectively select the most influential subset to train? We formulate the subset selection as a multi-task problem: maximizing the performance and minimizing the number of trainable parameters. We leverage a series of transformations -- including $ε$-constraint method and second-order Taylor approximation -- to arrive at the classical 0-1 knapsack problem, which we solve through the lens of Pareto optimality. Consequently, we propose AdaPEFT, a Hessian-informed PEFT that adapts to various tasks and models, in which the selected subset empirically transfers across training horizons and model sizes.

Physics-informed machine learning (PIML) is crucial in modern traffic flow modeling because it combines the benefits of both physics-based and data-driven approaches. In conventional PIML, physical information is typically incorporated by constructing a hybrid loss function that combines data-driven loss and physics loss through linear scalarization. The goal is to find a trade-off between these two objectives to improve the accuracy of model predictions. However, from a mathematical perspective, linear scalarization is limited to identifying only the convex region of the Pareto front, as it treats data-driven and physics losses as separate objectives. Given that most PIML loss functions are non-convex, linear scalarization restricts the achievable trade-off solutions. Moreover, tuning the weighting coefficients for the two loss components can be both time-consuming and computationally challenging. To address these limitations, this paper introduces a paradigm shift in PIML by reformulating the training process as a multi-objective optimization problem, treating data-driven loss and physics loss independently. We apply several multi-gradient descent algorithms (MGDAs), including traditional multi-gradient descent (TMGD) and dual cone gradient descent (DCGD), to explore the Pareto front in this multi-objective setting. These methods are evaluated on both macroscopic and microscopic traffic flow models. In the macroscopic case, MGDAs achieved comparable performance to traditional linear scalarization methods. Notably, in the microscopic case, MGDAs significantly outperformed their scalarization-based counterparts, demonstrating the advantages of a multi-objective optimization approach in complex PIML scenarios.