Gaussian Process differential equations (GPODE) have recently gained momentum due to their ability to capture dynamics behavior of systems and also represent uncertainty in predictions. Prior work has described the process of training the hyperparameters and, thereby, calibrating GPODE to data. How to design efficient algorithms to collect data for training GPODE models is still an open field of research. Nevertheless high-quality training data is key for model performance. Furthermore, data collection leads to time-cost and financial-cost and might in some areas even be safety critical to the system under test. Therefore, algorithms for safe and efficient data collection are central for building high quality GPODE models. Our novel Safe Active Learning (SAL) for GPODE algorithm addresses this challenge by suggesting a mechanism to propose efficient and non-safety-critical data to collect. SAL GPODE does so by sequentially suggesting new data, measuring it and updating the GPODE model with the new data. In this way, subsequent data points are iteratively suggested. The core of our SAL GPODE algorithm is a constrained optimization problem maximizing information of new data for GPODE model training constrained by the safety of the underlying system. We demonstrate our novel SAL GPODE's superiority compared to a standard, non-active way of measuring new data on two relevant examples.

In the real world, a learning-enabled system usually undergoes multiple cycles of model development to enhance the system's ability to handle difficult or emerging tasks. This continual model development process raises a significant issue that the model development for acquiring new or improving existing capabilities may inadvertently lose capabilities of the old model, also known as catastrophic forgetting. Existing continual learning studies focus on mitigating catastrophic forgetting by trading off performance on previous tasks and new tasks to ensure good average performance. However, they are inadequate for many applications especially in safety-critical domains, as failure to strictly preserve the good performance of the old model not only introduces safety risks and uncertainties but also imposes substantial expenses in the re-improving and re-validation of existing properties. To address this issue, we introduce model developmental safety as a guarantee of a learning system such that in the model development process the new model should strictly preserve the existing protected capabilities of the old model while improving its performance on target tasks. To ensure the model developmental safety, we present a retention-centric framework by formulating the model developmental safety as data-dependent constraints. Under this framework, we study how to develop a pretrained vision-language model, specifically the CLIP model, for acquiring new capabilities or improving existing capabilities of image classification. We propose an efficient constrained optimization algorithm with theoretical guarantee and use its insights to finetune a CLIP model with task-dependent heads for promoting the model developmental safety. Our experiments on improving vision perception capabilities on autonomous driving and scene recognition datasets demonstrate the efficacy of the proposed approach.

Grasping is essential in robotic manipulation, yet challenging due to object and gripper diversity and real-world complexities. Traditional analytic approaches often have long optimization times, while data-driven methods struggle with unseen objects. This paper formulates the problem as a rigid shape matching between gripper and object, which optimizes with Annealed Stein Iterative Closest Point (AS-ICP) and leverages GPU-based parallelization. By incorporating the gripper's tool center point and the object's center of mass into the cost function and using a signed distance field of the gripper for collision checking, our method achieves robust grasps with low computational time. Experiments with the Kinova KG3 gripper show an 87.3% success rate and 0.926 s computation time across various objects and settings, highlighting its potential for real-world applications.

Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue to grow, the development of efficient and reliable QP algorithms is becoming increasingly vital. In this context, this paper introduces a novel deep learning-aided distributed optimization architecture designed for tackling large-scale QP problems. First, we combine the state-of-the-art Operator Splitting QP (OSQP) method with a consensus approach to derive DistributedQP, a new method tailored for network-structured problems, with convergence guarantees to optimality. Subsequently, we unfold this optimizer into a deep learning framework, leading to DeepDistributedQP, which leverages learned policies to accelerate reaching to desired accuracy within a restricted amount of iterations. Our approach is also theoretically grounded through Probably Approximately Correct (PAC)-Bayes theory, providing generalization bounds on the expected optimality gap for unseen problems. The proposed framework, as well as its centralized version DeepQP, significantly outperform their standard optimization counterparts on a variety of tasks such as randomly generated problems, optimal control, linear regression, transportation networks and others. Notably, DeepDistributedQP demonstrates strong generalization by training on small problems and scaling to solve much larger ones (up to 50K variables and 150K constraints) using the same policy. Moreover, it achieves orders-of-magnitude improvements in wall-clock time compared to OSQP. The certifiable performance guarantees of our approach are also demonstrated, ensuring higher-quality solutions over traditional optimizers.

Multi-objective learning endeavors to concurrently optimize multiple objectives using a single model, aiming to achieve high and balanced performance across these diverse objectives. However, it often involves a more complex optimization problem, particularly when navigating potential conflicts between objectives, leading to solutions with higher memory requirements and computational complexity. This paper introduces a Multi-Objective Goal-Conditioned Supervised Learning (MOGCSL) framework for automatically learning to achieve multiple objectives from offline sequential data. MOGCSL extends the conventional Goal-Conditioned Supervised Learning (GCSL) method to multi-objective scenarios by redefining goals from one-dimensional scalars to multi-dimensional vectors. The need for complex architectures and optimization constraints can be naturally eliminated. MOGCSL benefits from filtering out uninformative or noisy instances that do not achieve desirable long-term rewards. It also incorporates a novel goal-choosing algorithm to model and select "high" achievable goals for inference. While MOGCSL is quite general, we focus on its application to the next action prediction problem in commercial-grade recommender systems. In this context, any viable solution needs to be reasonably scalable and also be robust to large amounts of noisy data that is characteristic of this application space. We show that MOGCSL performs admirably on both counts. Specifically, extensive experiments conducted on real-world recommendation datasets validate its efficacy and efficiency. Also, analysis and experiments are included to explain its strength in discounting the noisier portions of training data in recommender systems.

Recent advancements in large audio-language models (LALMs) have enabled speech-based user interactions, significantly enhancing user experience and accelerating the deployment of LALMs in real-world applications. However, ensuring the safety of LALMs is crucial to prevent risky outputs that may raise societal concerns or violate AI regulations. Despite the importance of this issue, research on jailbreaking LALMs remains limited due to their recent emergence and the additional technical challenges they present compared to attacks on DNNbased audio models. Specifically, the audio encoders in LALMs, which involve discretization operations, often lead to gradient shattering, hindering the effectiveness of attacks relying on gradient-based optimizations. The behavioral variability of LALMs further complicates the identification of effective (adversarial) optimization targets. Moreover, enforcing stealthiness constraints on adversarial audio waveforms introduces a reduced, non-convex feasible solution space, further intensifying the challenges of the optimization process. To overcome these challenges, we develop AdvWave, the first jailbreak framework against LALMs. We propose a dual-phase optimization method that addresses gradient shattering, enabling effective end-to-end gradient-based optimization. Additionally, we develop an adaptive adversarial target search algorithm that dynamically adjusts the adversarial optimization target based on the response patterns of LALMs for specific queries. To ensure that adversarial audio remains perceptually natural to human listeners, we design a classifier-guided optimization approach that generates adversarial noise resembling common urban sounds. Furthermore, we employ an iterative adversarial audio refinement technique to achieve near-perfect jailbreak success rates on black-box LALMs, requiring fewer than 30 queries per instance.

Model merging has shown great promise at combining expert models, but the benefit of merging is unclear when merging ``generalist'' models trained on many tasks. We explore merging in the context of large (~100B) models, by recycling checkpoints that exhibit tradeoffs among different tasks. Such checkpoints are often created in the process of developing a frontier model, and many suboptimal ones are usually discarded. Given a pool of model checkpoints obtained from different training runs (e.g., different stages, objectives, hyperparameters, and data mixtures), which naturally show tradeoffs across different language capabilities (e.g., instruction following vs. code generation), we investigate whether merging can recycle such suboptimal models into a Pareto-optimal one. Our optimization algorithm tunes the weight of each checkpoint in a linear combination, resulting in a Pareto-optimal models that outperforms both individual models and merge-based baselines. Further analysis shows that good merges tend to include almost all checkpoints with non-zero weights, indicating that even seemingly bad initial checkpoints can contribute to good final merges.

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.

This paper proposes a novel loss function, called 'Tube Loss', for simultaneous estimation of bounds of a Prediction Interval (PI) in the regression setup, and also for generating probabilistic forecasts from time series data solving a single optimization problem. The PIs obtained by minimizing the empirical risk based on the Tube Loss are shown to be of better quality than the PIs obtained by the existing methods in the following sense. First, it yields intervals that attain the prespecified confidence level $t \in(0,1)$ asymptotically. A theoretical proof of this fact is given. Secondly, the user is allowed to move the interval up or down by controlling the value of a parameter. This helps the user to choose a PI capturing denser regions of the probability distribution of the response variable inside the interval, and thus, sharpening its width. This is shown to be especially useful when the conditional distribution of the response variable is skewed. Further, the Tube Loss based PI estimation method can trade-off between the coverage and the average width by solving a single optimization problem. It enables further reduction of the average width of PI through re-calibration. Also, unlike a few existing PI estimation methods the gradient descent (GD) method can be used for minimization of empirical risk. Finally, through extensive experimentation, we have shown the efficacy of the Tube Loss based PI estimation in kernel machines, neural networks and deep networks and also for probabilistic forecasting tasks. The codes of the experiments are available at https://github.com/ltpritamanand/Tube_loss

Districting is a complex combinatorial problem that consists in partitioning a geographical area into small districts. In logistics, it is a major strategic decision determining operating costs for several years. Solving districting problems using traditional methods is intractable even for small geographical areas and existing heuristics often provide sub-optimal results. We present a structured learning approach to find high-quality solutions to real-world districting problems in a few minutes. It is based on integrating a combinatorial optimization layer, the capacitated minimum spanning tree problem, into a graph neural network architecture. To train this pipeline in a decision-aware fashion, we show how to construct target solutions embedded in a suitable space and learn from target solutions. Experiments show that our approach outperforms existing methods as it can significantly reduce costs on real-world cities.