The optimization of large-scale multibody systems is a numerically challenging task, in particular when considering multiple conflicting criteria at the same time. In this situation, we need to approximate the Pareto set of optimal compromises, which is significantly more expensive than finding a single optimum in single-objective optimization. To prevent large costs, the usage of surrogate models, constructed from a small but informative number of expensive model evaluations, is a very popular and widely studied approach. The central challenge then is to ensure a high quality (that is, near-optimality) of the solutions that were obtained using the surrogate model, which can be hard to guarantee with a single pre-computed surrogate. We present a back-and-forth approach between surrogate modeling and multi-objective optimization to improve the quality of the obtained solutions. Using the example of an expensive-to-evaluate multibody system, we compare different strategies regarding multi-objective optimization, sampling and also surrogate modeling, to identify the most promising approach in terms of computational efficiency and solution quality.

Vector-quantized networks (VQNs) have exhibited remarkable performance across various tasks, yet they are prone to training instability, which complicates the training process due to the necessity for techniques such as subtle initialization and model distillation. In this study, we identify the local minima issue as the primary cause of this instability. To address this, we integrate an optimal transport method in place of the nearest neighbor search to achieve a more globally informed assignment. We introduce OptVQ, a novel vector quantization method that employs the Sinkhorn algorithm to optimize the optimal transport problem, thereby enhancing the stability and efficiency of the training process. To mitigate the influence of diverse data distributions on the Sinkhorn algorithm, we implement a straightforward yet effective normalization strategy. Our comprehensive experiments on image reconstruction tasks demonstrate that OptVQ achieves 100% codebook utilization and surpasses current state-of-the-art VQNs in reconstruction quality.

Mixed Integer Linear Program (MILP) solvers are mostly built upon a Branch-and-Bound (B\&B) algorithm, where the efficiency of traditional solvers heavily depends on hand-crafted heuristics for branching. The past few years have witnessed the increasing popularity of data-driven approaches to automatically learn these heuristics. However, the success of these methods is highly dependent on the availability of high-quality demonstrations, which requires either the development of near-optimal heuristics or a time-consuming sampling process. This paper averts this challenge by proposing Suboptimal-Demonstration-Guided Reinforcement Learning (SORREL) for learning to branch. SORREL selectively learns from suboptimal demonstrations based on value estimation. It utilizes suboptimal demonstrations through both offline reinforcement learning on the demonstrations generated by suboptimal heuristics and self-imitation learning on past good experiences sampled by itself. Our experiments demonstrate its advanced performance in both branching quality and training efficiency over previous methods for various MILPs.

Inspection of infrastructure using static sensor nodes has become a well established approach in recent decades. In this work, we present an experimental setup to address a binary inspection task using mobile sensor nodes. The objective is to identify the predominant tile type in a 1mx1m tiled surface composed of vibrating and non-vibrating tiles. A swarm of miniaturized robots, equipped with onboard IMUs for sensing and IR sensors for collision avoidance, performs the inspection. The decision-making approach leverages a Bayesian algorithm, updating robots' belief using inference. The original algorithm uses one of two information sharing strategies. We introduce a novel information sharing strategy, aiming to accelerate the decision-making. To optimize the algorithm parameters, we develop a simulation framework calibrated to our real-world setup in the high-fidelity Webots robotic simulator. We evaluate the three information sharing strategies through simulations and real-world experiments. Moreover, we test the effectiveness of our optimization by placing swarms with optimized and non-optimized parameters in increasingly complex environments with varied spatial correlation and fill ratios. Results show that our proposed information sharing strategy consistently outperforms previously established information-sharing strategies in decision time. Additionally, optimized parameters yield robust performance across different environments. Conversely, non-optimized parameters perform well in simpler scenarios but show reduced accuracy in complex settings.

This thesis aims to provide a complete structural analysis and efficient algorithmic solutions to tabletop object rearrangement with overhand grasps (TORO). This problem captures a common task that we solve on a daily basis and is essential in enabling truly intelligent robotic manipulation. When rearranging many objects in a confined workspace, on the one hand, action sequencing with the least pick-n-places in TORO is NP-hard[han2018complexity]; on the other hand, temporarily relocating objects to some free space ("buffer poses") may be necessary but highly challenging in a cluttered environment. Focusing on these two challenges, the thesis covers TORO in four different setups, including varied workspace assumptions (with/without external buffers) and manipulator settings (single/dual-arms or a mobile manipulator). The thesis first explores TORO with external buffers (TORE), addressing the size of needed space for temporary object relocation ("running buffers"). This study shows that finding the maximum running buffers (MRB) is NP-hard and that MRB can grow unbounded with an increasing number of objects, even with uniform shapes. Exact algorithms developed for both labeled and unlabeled settings can scale to over 100 objects. The thesis further extends the TORE algorithms to tabletop rearrangement with internal buffers (TORI), where all temporary object placements need to be inside the workspace.

Federated Adversarial Learning (FAL) is a robust framework for resisting adversarial attacks on federated learning. Although some FAL studies have developed efficient algorithms, they primarily focus on convergence performance and overlook generalization. Generalization is crucial for evaluating algorithm performance on unseen data. However, generalization analysis is more challenging due to non-smooth adversarial loss functions. A common approach to addressing this issue is to leverage smoothness approximation. In this paper, we develop algorithm stability measures to evaluate the generalization performance of two popular FAL algorithms: \textit{Vanilla FAL (VFAL)} and {\it Slack FAL (SFAL)}, using three different smooth approximation methods: 1) \textit{Surrogate Smoothness Approximation (SSA)}, (2) \textit{Randomized Smoothness Approximation (RSA)}, and (3) \textit{Over-Parameterized Smoothness Approximation (OPSA)}. Based on our in-depth analysis, we answer the question of how to properly set the smoothness approximation method to mitigate generalization error in FAL. Moreover, we identify RSA as the most effective method for reducing generalization error. In highly data-heterogeneous scenarios, we also recommend employing SFAL to mitigate the deterioration of generalization performance caused by heterogeneity. Based on our theoretical results, we provide insights to help develop more efficient FAL algorithms, such as designing new metrics and dynamic aggregation rules to mitigate heterogeneity.

Numerous remarkable advancements have been made in accuracy, speed, and parallelism for solving the Unmanned Aerial Vehicle Route Planing (UAVRP). However, existing UAVRP solvers face challenges when attempting to scale effectively and efficiently for larger instances. In this paper, we present a generalization framework that enables current UAVRP solvers to robustly extend their capabilities to larger instances, accommodating up to 10,000 points, using widely recognized test sets. The UAVRP under a large number of patrol points is a typical large-scale TSP problem.Our proposed framework comprises three distinct steps. Firstly, we employ Delaunay triangulation to extract subgraphs from large instances while preserving global features. Secondly, we utilize an embedded TSP solver to obtain sub-results, followed by graph fusion. Finally, we implement a decoding strategy customizable to the user's requirements, resulting in high-quality solutions, complemented by a warming-up process for the heatmap. To demonstrate the flexibility of our approach, we integrate two representative TSP solvers into our framework and conduct a comprehensive comparative analysis against existing algorithms using large TSP benchmark datasets. The results unequivocally demonstrate that our framework efficiently scales existing TSP solvers to handle large instances and consistently outperforms state-of-the-art (SOTA) methods. Furthermore, since our proposed framework does not necessitate additional training or fine-tuning, we believe that its generality can significantly advance research on end-to-end UAVRP solvers, enabling the application of a broader range of methods to real-world scenarios.

Group distributionally robust optimization, which aims to improve robust accuracies -- worst-group and unbiased accuracies -- is a prominent algorithm used to mitigate spurious correlations and address dataset bias. Although existing approaches have reported improvements in robust accuracies, these gains often come at the cost of average accuracy due to inherent trade-offs. To control this trade-off flexibly and efficiently, we propose a simple class-specific scaling strategy, directly applicable to existing debiasing algorithms with no additional training. We further develop an instance-wise adaptive scaling technique to alleviate this trade-off, even leading to improvements in both robust and average accuracies. Our approach reveals that a na\"ive ERM baseline matches or even outperforms the recent debiasing methods by simply adopting the class-specific scaling technique. Additionally, we introduce a novel unified metric that quantifies the trade-off between the two accuracies as a scalar value, allowing for a comprehensive evaluation of existing algorithms. By tackling the inherent trade-off and offering a performance landscape, our approach provides valuable insights into robust techniques beyond just robust accuracy. We validate the effectiveness of our framework through experiments across datasets in computer vision and natural language processing domains.

The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions on the evolution of dy-namical systems, the underlying differential equations have to fulfill specific constraints in time and space. This class of problems is known as boundary value problems. This thesis presents novel approaches to learn time-reversible deterministic and stochastic dynamics constrained by initial and final conditions. The dynamics are inferred by machine learning algorithms from observed data, which is in contrast to the traditional approach of solving differential equations by numerical integration. The work in this thesis examines a set of problems of increasing difficulty each of which is concerned with learning a different aspect of the dynamics. Initially, we consider learning deterministic dynamics from ground truth solutions which are constrained by deterministic boundary conditions. Secondly, we study a boundary value problem in discrete state spaces, where the forward dynamics follow a stochastic jump process and the boundary conditions are discrete probability distributions. In particular, the stochastic dynamics of a specific jump process, the Ehrenfest process, is considered and the reverse time dynamics are inferred with machine learning. Finally, we investigate the problem of inferring the dynamics of a continuous-time stochastic process between two probability distributions without any reference information. Here, we propose a novel criterion to learn time-reversible dynamics of two stochastic processes to solve the Schr\"odinger Bridge Problem.

The biophysical interactions between the T cell receptor (TCR) and its ligands determine the specificity of the cellular immune response. However, the immense diversity of receptors and ligands has made it challenging to discover generalizable rules across the distinct binding affinity landscapes created by different ligands. Here, we present an optimization framework for discovering biophysical rules that predict whether TCRs share specificity to a ligand. Applying this framework to TCRs associated with a collection of SARS-CoV-2 peptides we establish how co-specificity depends on the type and position of amino-acid differences between receptors. We also demonstrate that the inferred rules generalize to ligands not seen during training. Our analysis reveals that matching of steric properties between substituted amino acids is important for receptor co-specificity, in contrast with the hydrophobic properties that more prominently determine evolutionary substitutability. We furthermore find that positions not in direct contact with the peptide still significantly impact specificity. These findings highlight the potential for data-driven approaches to uncover the molecular mechanisms underpinning the specificity of adaptive immune responses.