Model training algorithms which observe a small portion of the training set in each computational step are ubiquitous in practical machine learning, and include both stochastic and online optimization methods. In the vast majority of cases, such algorithms typically observe the training samples via the gradients of the cost functions the samples incur. Thus, these methods exploit are the slope of the cost functions via their first-order approximations. To address limitations of gradient-based methods, such as sensitivity to step-size choice in the stochastic setting, or inability to use small function variability in the online setting, several streams of research attempt to exploit more information about the cost functions than just their gradients via the well-known proximal operators. However, implementing such methods in practice poses a challenge, since each iteration step boils down to computing the proximal operator, which may not be easy. In this work we devise a novel algorithmic framework, which exploits convex duality theory to achieve both algorithmic efficiency and software modularity of proximal operator implementations, in order to make experimentation with incremental proximal optimization algorithms accessible to a larger audience of researchers and practitioners, by reducing the gap between their theoretical description in research papers and their use in practice. We provide a reference Python implementation for the framework developed in this paper as an open source library at on https://github.com/alexshtf/inc_prox_pt/releases/tag/prox_pt_paper, along with examples which demonstrate our implementation on a variety of problems, and reproduce the numerical experiments in this paper. The pure Python reference implementation is not necessarily the most efficient, but is a basis for creating efficient implementations by combining Python with a native backend.

Optimization problems are ubiquitous in various fields, ranging from computer science and engineering to finance and healthcare. Whether the focus is on minimizing costs or improving efficiency, these challenges frequently involve finding the best outcome from a large pool of feasible solutions within defined constraints. Thanks to its ability to efficiently navigate this search space, Bayesian Optimization (BO) has emerged as a go-to solution to tackle these problems [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], especially in cases where running the objective function is expensive or time-consuming. In the typical BO setup [11], a surrogate model - often a Gaussian Process (GP) regression - is leveraged to estimate the target response function from given input data. An acquisition function is then used to suggest strategic new test points based on the uncertainty level of this model. If selected carefully, this sampling strategy allows BO to explore the parameter space to uncover promising regions with high uncertainty or exploit known favorable regions to refine the search toward the global optimum.

Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area which uses randomness to develop improved algorithms for ubiquitous matrix problems. The area has reached a certain level of maturity; but recent hardware trends, efforts to incorporate RandNLA algorithms into core numerical libraries, and advances in machine learning, statistics, and random matrix theory, have lead to new theoretical and practical challenges. This article provides a self-contained overview of RandNLA, in light of these developments.

Existing operations research (OR) models and tools play indispensable roles in smart-city operations, yet their practical implementation is limited by the complexity of modeling and deficiencies in optimization proficiency. To generate more relevant and accurate solutions to users' requirements, we propose a large language model (LLM)-based agent ("City-LEO") that enhances the efficiency and transparency of city management through conversational interactions. Specifically, to accommodate diverse users' requirements and enhance computational tractability, City-LEO leverages LLM's logical reasoning capabilities on prior knowledge to scope down large-scale optimization problems efficiently. In the human-like decision process, City-LEO also incorporates End-to-end (E2E) model to synergize the prediction and optimization. The E2E framework be conducive to coping with environmental uncertainties and involving more query-relevant features, and then facilitates transparent and interpretable decision-making process. In case study, we employ City-LEO in the operations management of e-bike sharing (EBS) system. The numerical results demonstrate that City-LEO has superior performance when benchmarks against the full-scale optimization problem. With less computational time, City-LEO generates more satisfactory and relevant solutions to the users' requirements, and achieves lower global suboptimality without significantly compromising accuracy. In a broader sense, our proposed agent offers promise to develop LLM-embedded OR tools for smart-city operations management.

The existing fine-tuning paradigm for language models is brittle in knowledge editing scenarios, where the model must incorporate new information without extensive retraining. This brittleness often results in overfitting, reduced performance, and unnatural language generation. To address this, we propose Consistent In-Context Editing (ICE), a novel approach that leverages the model's in-context learning capability to tune toward a contextual distribution rather than a one-hot target. ICE introduces a straightforward optimization framework that includes both a target and a procedure, enhancing the robustness and effectiveness of gradient-based tuning methods. We provide analytical insights into ICE across four critical aspects of knowledge editing: accuracy, locality, generalization, and linguistic quality, showing its advantages. Experimental results across four datasets confirm the effectiveness of ICE and demonstrate its potential for continual editing, ensuring that updated information is incorporated while preserving the integrity of the model.

Neural models produce promising results when solving Vehicle Routing Problems (VRPs), but often fall short in generalization. Recent attempts to enhance model generalization often incur unnecessarily large training cost or cannot be directly applied to other models solving different VRP variants. To address these issues, we take a novel perspective on model architecture in this study. Specifically, we propose a plug-and-play Entropy-based Scaling Factor (ESF) and a Distribution-Specific (DS) decoder to enhance the size and distribution generalization, respectively. ESF adjusts the attention weight pattern of the model towards familiar ones discovered during training when solving VRPs of varying sizes. The DS decoder explicitly models VRPs of multiple training distribution patterns through multiple auxiliary light decoders, expanding the model representation space to encompass a broader range of distributional scenarios. We conduct extensive experiments on both synthetic and widely recognized real-world benchmarking datasets and compare the performance with seven baseline models. The results demonstrate the effectiveness of using ESF and DS decoder to obtain a more generalizable model and showcase their applicability to solve different VRP variants, i.e., travelling salesman problem and capacitated VRP. Notably, our proposed generic components require minimal computational resources, and can be effortlessly integrated into conventional generalization strategies to further elevate model generalization.

This paper investigates a constrained inverse kinematic (IK) problem that seeks a feasible configuration of an articulated robot under various constraints such as joint limits and obstacle collision avoidance. Due to the high-dimensionality and complex constraints, this problem is often solved numerically via iterative local optimization. Classic local optimization methods take joint angles as the decision variable, which suffers from non-linearity caused by the trigonometric constraints. Recently, distance-based IK methods have been developed as an alternative approach that formulates IK as an optimization over the distances among points attached to the robot and the obstacles. Although distance-based methods have demonstrated unique advantages, they still suffer from low computational efficiency, since these approaches usually ignore the chain structure in the kinematics of serial robots. This paper proposes a new method called propagative distance optimization for constrained inverse kinematics (PDO-IK), which captures and leverages the chain structure in the distance-based formulation and expedites the optimization by computing forward kinematics and the Jacobian propagatively along the kinematic chain. Test results show that PDO-IK runs up to two orders of magnitude faster than the existing distance-based methods under joint limits constraints and obstacle avoidance constraints. It also achieves up to three times higher success rates than the conventional joint-angle-based optimization methods for IK problems. The high runtime efficiency of PDO-IK allows the real-time computation (10$-$1500 Hz) and enables a simulated humanoid robot with 19 degrees of freedom (DoFs) to avoid moving obstacles, which is otherwise hard to achieve with the baselines.

Numerous recent techniques for text style transfer characterize their approaches as variants of reinforcement learning and preference optimization. In this work, we consider the relationship between these approaches and a class of optimization approaches developed primarily for (non-neural) statistical machine translation, formerly known as 'tuning'. Inspired by these techniques from the past, we improve upon established preference optimization approaches, incorporating multiple iterations of exploration and optimization, and choosing contrastive examples by following a 'hope' vs 'fear' sampling strategy. Cognizant of the difference between machine translation and style transfer, however, we further tailor our framework with a new pseudo-parallel generation method and a dynamic weighted reward aggregation method to tackle the lack of parallel data and the need for a multi-objective reward. We evaluate our model on two commonly used text style transfer datasets. Through automatic and human evaluation results we show the effectiveness and the superiority of our model compared to state-of-the-art baselines.

Language Model Programs, i.e. sophisticated pipelines of modular language model (LM) calls, are increasingly advancing NLP tasks, but they require crafting prompts that are jointly effective for all modules. We study prompt optimization for LM programs, i.e. how to update these prompts to maximize a downstream metric without access to module-level labels or gradients. To make this tractable, we factorize our problem into optimizing the free-form instructions and few-shot demonstrations of every module and introduce several strategies to craft task-grounded instructions and navigate credit assignment across modules. Our strategies include (i) program- and data-aware techniques for proposing effective instructions, (ii) a stochastic mini-batch evaluation function for learning a surrogate model of our objective, and (iii) a meta-optimization procedure in which we refine how LMs construct proposals over time. Using these insights we develop MIPRO, a novel optimizer that outperforms baselines on five of six diverse LM programs using a best-in-class open-source model (Llama-3-8B), by as high as 12.9% accuracy. We will release our new optimizers and benchmark in DSPy at https://github.com/stanfordnlp/dspy

As we push the boundaries of performance in various vision tasks, the models grow in size correspondingly. To keep up with this growth, we need very aggressive pruning techniques for efficient inference and deployment on edge devices. Existing pruning approaches are limited to channel pruning and struggle with aggressive parameter reductions. In this paper, we propose a novel multi-dimensional pruning framework that jointly optimizes pruning across channels, layers, and blocks while adhering to latency constraints. We develop a latency modeling technique that accurately captures model-wide latency variations during pruning, which is crucial for achieving an optimal latency-accuracy trade-offs at high pruning ratio. We reformulate pruning as a Mixed-Integer Nonlinear Program (MINLP) to efficiently determine the optimal pruned structure with only a single pass. Our extensive results demonstrate substantial improvements over previous methods, particularly at large pruning ratios. In classification, our method significantly outperforms prior art HALP with a Top-1 accuracy of 70.0(v.s. 68.6) and an FPS of 5262 im/s(v.s. 4101 im/s). In 3D object detection, we establish a new state-of-the-art by pruning StreamPETR at a 45% pruning ratio, achieving higher FPS (37.3 vs. 31.7) and mAP (0.451 vs. 0.449) than the dense baseline.