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We present $\textit{Learn2Aggregate}$, a machine learning (ML) framework for optimizing the generation of Chv\'atal-Gomory (CG) cuts in mixed integer linear programming (MILP). The framework trains a graph neural network to classify useful constraints for aggregation in CG cut generation. The ML-driven CG separator selectively focuses on a small set of impactful constraints, improving runtimes without compromising the strength of the generated cuts. Key to our approach is the formulation of a constraint classification task which favours sparse aggregation of constraints, consistent with empirical findings. This, in conjunction with a careful constraint labeling scheme and a hybrid of deep learning and feature engineering, results in enhanced CG cut generation across five diverse MILP benchmarks. On the largest test sets, our method closes roughly $\textit{twice}$ as much of the integrality gap as the standard CG method while running 40$% faster. This performance improvement is due to our method eliminating 75% of the constraints prior to aggregation., Comment: 12 pages, 8 figures

While in-context Learning (ICL) has proven to be an effective technique to improve the performance of Large Language Models (LLMs) in a variety of complex tasks, notably in translating natural language questions into Structured Query Language (NL2SQL), the question of how to select the most beneficial demonstration examples remains an open research problem. While prior works often adapted off-the-shelf encoders to retrieve examples dynamically, an inherent discrepancy exists in the representational capacities between the external retrievers and the LLMs. Further, optimizing the selection of examples is a non-trivial task, since there are no straightforward methods to assess the relative benefits of examples without performing pairwise inference. To address these shortcomings, we propose DeTriever, a novel demonstration retrieval framework that learns a weighted combination of LLM hidden states, where rich semantic information is encoded. To train the model, we propose a proxy score that estimates the relative benefits of examples based on the similarities between output queries. Experiments on two popular NL2SQL benchmarks demonstrate that our method significantly outperforms the state-of-the-art baselines on one-shot NL2SQL tasks.

Detecting structural similarity between queries is essential for selecting examples in in-context learning models. However, assessing structural similarity based solely on the natural language expressions of queries, without considering SQL queries, presents a significant challenge. This paper explores the significance of this similarity metric and proposes a model for accurately estimating it. To achieve this, we leverage a dataset comprising 170k question pairs, meticulously curated to train a similarity prediction model. Our comprehensive evaluation demonstrates that the proposed model adeptly captures the structural similarity between questions, as evidenced by improvements in Kendall-Tau distance and precision@k metrics. Notably, our model outperforms strong competitive embedding models from OpenAI and Cohere. Furthermore, compared to these competitive models, our proposed encoder enhances the downstream performance of NL2SQL models in 1-shot in-context learning scenarios by 1-2\% for GPT-3.5-turbo, 4-8\% for CodeLlama-7B, and 2-3\% for CodeLlama-13B.

In an era of digital ubiquity, efficient resource management and decision-making are paramount across numerous industries. To this end, we present a comprehensive study on the integration of machine learning (ML) techniques into Huawei Cloud's OptVerse AI Solver, which aims to mitigate the scarcity of real-world mathematical programming instances, and to surpass the capabilities of traditional optimization techniques. We showcase our methods for generating complex SAT and MILP instances utilizing generative models that mirror multifaceted structures of real-world problem. Furthermore, we introduce a training framework leveraging augmentation policies to maintain solvers' utility in dynamic environments. Besides the data generation and augmentation, our proposed approaches also include novel ML-driven policies for personalized solver strategies, with an emphasis on applications like graph convolutional networks for initial basis selection and reinforcement learning for advanced presolving and cut selection. Additionally, we detail the incorporation of state-of-the-art parameter tuning algorithms which markedly elevate solver performance. Compared with traditional solvers such as Cplex and SCIP, our ML-augmented OptVerse AI Solver demonstrates superior speed and precision across both established benchmarks and real-world scenarios, reinforcing the practical imperative and effectiveness of machine learning techniques in mathematical programming solvers.

The rapid advancement of artificial intelligence (AI) techniques has opened up new opportunities to revolutionize various fields, including operations research (OR). This survey paper explores the integration of AI within the OR process (AI4OR) to enhance its effectiveness and efficiency across multiple stages, such as parameter generation, model formulation, and model optimization. By providing a comprehensive overview of the state-of-the-art and examining the potential of AI to transform OR, this paper aims to inspire further research and innovation in the development of AI-enhanced OR methods and tools. The synergy between AI and OR is poised to drive significant advancements and novel solutions in a multitude of domains, ultimately leading to more effective and efficient decision-making.

Federated learning is an emerging technique for training models from decentralized data sets. In many applications, data owners participating in the federated learning system hold not only the data but also a set of domain knowledge. Such knowledge includes human know-how and craftsmanship that can be extremely helpful to the federated learning task. In this work, we propose a federated learning framework that allows the injection of participants' domain knowledge, where the key idea is to refine the global model with knowledge locally. The scenario we consider is motivated by a real industry-level application, and we demonstrate the effectiveness of our approach to this application.

We study the federated optimization problem from a dual perspective and propose a new algorithm termed federated dual coordinate descent (FedDCD), which is based on a type of coordinate descent method developed by Necora et al.[Journal of Optimization Theory and Applications, 2017]. Additionally, we enhance the FedDCD method with inexact gradient oracles and Nesterov's acceleration. We demonstrate theoretically that our proposed approach achieves better convergence rates than the state-of-the-art primal federated optimization algorithms under certain situations. Numerical experiments on real-world datasets support our analysis.

Federated learning is a popular technology for training machine learning models on distributed data sources without sharing data. Vertical federated learning or feature-based federated learning applies to the cases that different data sources share the same sample ID space but differ in feature space. To ensure the data owners' long-term engagement, it is critical to objectively assess the contribution from each data source and recompense them accordingly. The Shapley value (SV) is a provably fair contribution valuation metric originated from cooperative game theory. However, computing the SV requires extensively retraining the model on each subset of data sources, which causes prohibitively high communication costs in federated learning. We propose a contribution valuation metric called vertical federated Shapley value (VerFedSV) based on SV. We show that VerFedSV not only satisfies many desirable properties for fairness but is also efficient to compute, and can be adapted to both synchronous and asynchronous vertical federated learning algorithms. Both theoretical analysis and extensive experimental results verify the fairness, efficiency, and adaptability of VerFedSV.

Federated learning is an emerging decentralized machine learning scheme that allows multiple data owners to work collaboratively while ensuring data privacy. The success of federated learning depends largely on the participation of data owners. To sustain and encourage data owners' participation, it is crucial to fairly evaluate the quality of the data provided by the data owners and reward them correspondingly. Federated Shapley value, recently proposed by Wang et al. [Federated Learning, 2020], is a measure for data value under the framework of federated learning that satisfies many desired properties for data valuation. However, there are still factors of potential unfairness in the design of federated Shapley value because two data owners with the same local data may not receive the same evaluation. We propose a new measure called completed federated Shapley value to improve the fairness of federated Shapley value. The design depends on completing a matrix consisting of all the possible contributions by different subsets of the data owners. It is shown under mild conditions that this matrix is approximately low-rank by leveraging concepts and tools from optimization. Both theoretical analysis and empirical evaluation verify that the proposed measure does improve fairness in many circumstances.

Vertical federated learning (VFL) has attracted greater and greater interest since it enables multiple parties possessing non-overlapping features to strengthen their machine learning models without disclosing their private data and model parameters. Similar to other machine learning algorithms, VFL faces demands and challenges of fairness, i.e., the learned model may be unfairly discriminatory over some groups with sensitive attributes. To tackle this problem, we propose a fair VFL framework in this work. First, we systematically formulate the problem of training fair models in VFL, where the learning task is modelled as a constrained optimization problem. To solve it in a federated and privacy-preserving manner, we consider the equivalent dual form of the problem and develop an asynchronous gradient coordinate-descent ascent algorithm, where some active data parties perform multiple parallelized local updates per communication round to effectively reduce the number of communication rounds. The messages that the server sends to passive parties are deliberately designed such that the information necessary for local updates is released without intruding on the privacy of data and sensitive attributes. We rigorously study the convergence of the algorithm when applied to general nonconvex-concave min-max problems. We prove that the algorithm finds a $\delta$-stationary point of the dual objective in $\mathcal{O}(\delta^{-4})$ communication rounds under mild conditions. Finally, the extensive experiments on three benchmark datasets demonstrate the superior performance of our method in training fair models., Comment: 13 pages, 2 figures

A memory-efficient framework is described for the cardinality-constrained structured data-fitting problem. Dual-based atom-identification rules are proposed that reveal the structure of the optimal primal solution from near-optimal dual solutions. These rules allow for a simple and computationally cheap algorithm for translating any feasible dual solution to a primal solution that satisfies the cardinality constraint. Rigorous guarantees are provided for obtaining a near-optimal primal solution given any dual-based method that generates dual iterates converging to an optimal dual solution. Numerical experiments on real-world datasets support confirm the analysis and demonstrate the efficiency of the proposed approach.

The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled observations of the superposition using two convex programs. Probabilistic error bounds are given on the accuracy with which this process approximates the individual signals. The theory of polar convolution of convex sets and gauge functions plays a central role in the analysis and solution process. If the measurements are random and the noise is bounded, this approach stably recovers low-complexity and mutually incoherent signals, with high probability and with near-optimal sample complexity. We develop an efficient algorithm, based on level-set and conditional-gradient methods, that solves the convex optimization problems with sublinear iteration complexity and linear space requirements. Numerical experiments on both real and synthetic data confirm the theory and the efficiency of the approach.

Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple and geometric form of convex duality. This duality correspondence yields a general notion of alignment that leads to an intuitive and complete description of how atoms participate in the final decomposition of the solution. The resulting geometric perspective leads to variations of existing algorithms effective for large-scale problems. We illustrate these ideas with many examples, including applications in matrix completion and morphological component analysis for the separation of mixtures of signals., Comment: 39 pages

The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage discovers the optimal atomic support for the primal problem by solving a sequence of approximations of the dual problem using a bundle-type method. The second stage recovers the approximate primal solution using the atoms discovered in the first stage. The overall approach leads to implementable and efficient algorithms for large problems., Comment: 53rd Annual Asilomar Conference on Signals, Systems, and Computers