Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly. We develop a nonconvex reformulation designed to exploit this staged structure. Our reformulation has only simple bound constraints, enabling solution via projected gradient methods and their accelerated variants. The method automatically generates a sequence of primal and dual feasible solutions to the original convex problem, making optimality certification easy.

Constrained stochastic nonlinear optimization problems have attracted significant attention for their ability to model complex real-world scenarios in physics, economics, and biology. As datasets continue to grow, online inference methods have become crucial for enabling real-time decision-making without the need to store historical data. In this work, we develop an online inference procedure for constrained stochastic optimization by leveraging a method called Sketched Stochastic Sequential Quadratic Programming (SSQP). As a direct generalization of sketched Newton methods, SSQP approximates the objective with a quadratic model and the constraints with a linear model at each step, then applies a sketching solver to inexactly solve the resulting subproblem. Building on this design, we propose a new online inference procedure called random scaling. In particular, we construct a test statistic based on SSQP iterates whose limiting distribution is free of any unknown parameters. Compared to existing online inference procedures, our approach offers two key advantages: (i) it enables the construction of asymptotically valid confidence intervals; and (ii) it is matrix-free, i.e. the computation involves only primal-dual SSQP iterates $(\boldsymbol{x}_t, \boldsymbolλ_t)$ without requiring any matrix inversions. We validate our theory through numerical experiments on nonlinearly constrained regression problems and demonstrate the superior performance of our random scaling method over existing inference procedures.

Guidance is a cornerstone of modern diffusion models, playing a pivotal role in conditional generation and enhancing the quality of unconditional samples. However, current approaches to guidance scheduling--determining the appropriate guidance weight--are largely heuristic and lack a solid theoretical foundation. This work addresses these limitations on two fronts. First, we provide a theoretical formalization that precisely characterizes the relationship between guidance strength and classifier confidence. Second, building on this insight, we introduce a stochastic optimal control framework that casts guidance scheduling as an adaptive optimization problem. In this formulation, guidance strength is not fixed but dynamically selected based on time, the current sample, and the conditioning class, either independently or in combination. By solving the resulting control problem, we establish a principled foundation for more effective guidance in diffusion models.

Traditional Reinforcement Learning from Human Feedback (RLHF) often relies on reward models, frequently assuming preference structures like the Bradley-Terry model, which may not accurately capture the complexities of real human preferences (e.g., intransitivity). Nash Learning from Human Feedback (NLHF) offers a more direct alternative by framing the problem as finding a Nash equilibrium of a game defined by these preferences. In this work, we introduce Nash Mirror Prox ($\mathtt{Nash-MP}$), an online NLHF algorithm that leverages the Mirror Prox optimization scheme to achieve fast and stable convergence to the Nash equilibrium. Our theoretical analysis establishes that Nash-MP exhibits last-iterate linear convergence towards the $β$-regularized Nash equilibrium. Specifically, we prove that the KL-divergence to the optimal policy decreases at a rate of order $(1+2β)^{-N/2}$, where $N$ is a number of preference queries. We further demonstrate last-iterate linear convergence for the exploitability gap and uniformly for the span semi-norm of log-probabilities, with all these rates being independent of the size of the action space. Furthermore, we propose and analyze an approximate version of Nash-MP where proximal steps are estimated using stochastic policy gradients, making the algorithm closer to applications. Finally, we detail a practical implementation strategy for fine-tuning large language models and present experiments that demonstrate its competitive performance and compatibility with existing methods.

We address the optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions. This type of Multi-Objective Distributional Optimization commonly arises in machine learning and statistics, with applications in areas such as multiple target sampling, multi-task learning, and multi-objective generative modeling. To solve this problem, we propose an iterative particle-based algorithm, which we call Muliple Wasserstein Gradient Descent (MWGraD), which constructs a flow of intermediate empirical distributions, each being represented by a set of particles, which gradually minimize the multiple objective functionals simultaneously. Specifically, MWGraD consists of two key steps at each iteration. First, it estimates the Wasserstein gradient for each objective functional based on the current particles. Then, it aggregates these gradients into a single Wasserstein gradient using dynamically adjusted weights and updates the particles accordingly. In addition, we provide theoretical analysis and present experimental results on both synthetic and real-world datasets, demonstrating the effectiveness of MWGraD.

Perovskite solar cells (PSCs) without a hole transport layer (HTL) offer a cost-effective and stable alternative to conventional architectures, utilizing only an absorber layer and an electron transport layer (ETL). This study presents a machine learning (ML)-driven framework to optimize the efficiency and stability of HTL-free PSCs by integrating experimental validation with numerical simulations. Excellent agreement is achieved between a fabricated device and its simulated counterpart at a molar fraction \( x = 68.7\% \) in \(\mathrm{MAPb}_{1-x}\mathrm{Sb}_{2x/3}\mathrm{I}_3\), where MA is methylammonium. A dataset of 1650 samples is generated by varying molar fraction, absorber defect density, thickness, and ETL doping, with corresponding efficiency and 50-hour degradation as targets. A fourth-degree polynomial regressor (PR-4) shows the best performance, achieving RMSEs of 0.0179 and 0.0117, and \( R^2 \) scores of 1 and 0.999 for efficiency and degradation, respectively. The derived model generalizes beyond the training range and is used in an L-BFGS-B optimization algorithm with a weighted objective function to maximize efficiency and minimize degradation. This improves device efficiency from 13.7\% to 16.84\% and reduces degradation from 6.61\% to 2.39\% over 1000 hours. Finally, the dataset is labeled into superior and inferior classes, and a multilayer perceptron (MLP) classifier achieves 100\% accuracy, successfully identifying optimal configurations.

Retrieval-Augmented Generation (RAG) pipelines are central to applying large language models (LLMs) to proprietary or dynamic data. However, building effective RAG flows is complex, requiring careful selection among vector databases, embedding models, text splitters, retrievers, and synthesizing LLMs. The challenge deepens with the rise of agentic paradigms. Modules like verifiers, rewriters, and rerankers-each with intricate hyperparameter dependencies have to be carefully tuned. Balancing tradeoffs between latency, accuracy, and cost becomes increasingly difficult in performance-sensitive applications. We introduce syftr, a framework that performs efficient multi-objective search over a broad space of agentic and non-agentic RAG configurations. Using Bayesian Optimization, syftr discovers Pareto-optimal flows that jointly optimize task accuracy and cost. A novel early-stopping mechanism further improves efficiency by pruning clearly suboptimal candidates. Across multiple RAG benchmarks, syftr finds flows which are on average approximately 9 times cheaper while preserving most of the accuracy of the most accurate flows on the Pareto-frontier. Furthermore, syftr's ability to design and optimize allows integrating new modules, making it even easier and faster to realize high-performing generative AI pipelines.

In cluttered spaces, such as forests, drone picking up a payload via an abseil claw is an open challenge, as the cable is likely tangled and blocked by the branches and obstacles. To address such a challenge, in this work, a cooperative aerial system is proposed, which consists of a payload drone and a dexterous rappelling end droid. The two ends are linked via a Kevlar tether cable. The end droid is actuated by four propellers, which enable mid-air dexterous adjustment of clawing angle and guidance of cable movement. To avoid tanglement and rappelling obstacles, a trajectory optimization method that integrates cable length constraints and dynamic feasibility is developed, which guarantees safe pickup. A tether cable dynamic model is established to evaluate real-time cable status, considering both taut and sagging conditions. Simulation and real-world experiments are conducted to demonstrate that the proposed system is capable of picking up payload in cluttered spaces. As a result, the end droid can reach the target point successfully under cable constraints and achieve passive retrieval during the lifting phase without propulsion, which enables effective and efficient aerial manipulation.

The growing adoption of Graph Neural Networks (GNNs) in high-stakes domains like healthcare and finance demands reliable explanations of their decision-making processes. While inherently interpretable GNN architectures like Graph Multi-linear Networks (GMT) have emerged, they remain vulnerable to generating explanations based on spurious correlations, potentially undermining trust in critical applications. We present MetaGMT, a meta-learning framework that enhances explanation fidelity through a novel bi-level optimization approach. We demonstrate that MetaGMT significantly improves both explanation quality (AUC-ROC, Precision@K) and robustness to spurious patterns, across BA-2Motifs, MUTAG, and SP-Motif benchmarks. Our approach maintains competitive classification accuracy while producing more faithful explanations (with an increase up to 8% of Explanation ROC on SP-Motif 0.5) compared to baseline methods. These advancements in interpretability could enable safer deployment of GNNs in sensitive domains by (1) facilitating model debugging through more reliable explanations, (2) supporting targeted retraining when biases are identified, and (3) enabling meaningful human oversight. By addressing the critical challenge of explanation reliability, our work contributes to building more trustworthy and actionable GNN systems for real-world applications.

--Data centers are the backbone of computing capacity. Operating data centers in the tropical regions faces unique challenges due to consistently high ambient temperature and elevated relative humidity throughout the year . These conditions result in increased cooling costs to maintain the reliability of the computing systems. While existing machine learning-based approaches have demonstrated potential to elevate operations to a more proactive and intelligent level, their deployment remains dubious due to concerns about model extrapolation capabilities and associated system safety issues. T o address these concerns, this article proposes incorporating the physical characteristics of data centers into traditional data-driven machine learning solutions. We begin by introducing the data center system, including the relevant multiphysics processes and the data-physics availability. Next, we outline the associated modeling and optimization problems and propose an integrated, physics-informed machine learning system to address them. Using the proposed system, we present relevant applications across varying levels of operational intelligence. A case study on an industry-grade tropical data center is provided to demonstrate the effectiveness of our approach. Finally, we discuss key challenges and highlight potential future directions. He data center (DC) industry is experiencing rapid growth driven by the increasing demand for cloud computing, data storage, and artificial intelligence (AI) services. This expansion is also occurring in tropical regions, where digital infrastructure is being scaled up to meet regional computing needs [1]. As DCs grow in size and complexity, their power consumption increases accordingly, particularly in tropical climates where high ambient temperature and humidity place additional strain on the cooling systems. According to the International Energy Agency (IEA), global DC energy consumption could rise to 1050 TWh by 2026, up from 460 TWh in 2022 [2].