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Anh Tuan Nguyen

Publications and source records attributed to Anh Tuan Nguyen.

At least 19 recordsLinked to original sources
arXiv2026

Tight Bounds for Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function

Data-driven algorithm design frames hyperparameter tuning as a statistical learning problem, but establishing generalization guarantees remains challenging due to the implicit, non-smooth dependence of model performance on hyperparameters. Existing multi-dimensional bounds under piecewise-polynomial assumptions remain theoretically loose and lack comprehensive lower bounds. We resolve this by establishing tight pseudo-dimension bounds for multi-dimensional data-driven tuning. First, we refine the learning-theoretic upper bound using real algebraic geometry; by analyzing invariant connected sign cells during block elimination rather than isolated sign vectors, we avoid topological over-counting to derive strictly sharper sample complexities. Second, we present a multi-regime lower-bound framework that disentangles combinatorial and algebraic capacities. By constructing shattered problem instances across distinct regimes, we prove our upper bounds are tightly saturated. Finally, we extend our topological framework to accommodate general bi-level validation-loss tuning and broader semi-algebraic applications.

cs.LG↗
arXiv2026

Oranits: Mission Assignment and Task Offloading in Open RAN-based ITS using Metaheuristic and Deep Reinforcement Learning

In this paper, we explore mission assignment and task offloading in an Open Radio Access Network (Open RAN)-based intelligent transportation system (ITS), where autonomous vehicles leverage mobile edge computing for efficient processing. Existing studies often overlook the intricate interdependencies between missions and the costs associated with offloading tasks to edge servers, leading to suboptimal decision-making. To bridge this gap, we introduce Oranits, a novel system model that explicitly accounts for mission dependencies and offloading costs while optimizing performance through vehicle cooperation. To achieve this, we propose a twofold optimization approach. First, we develop a metaheuristic-based evolutionary computing algorithm, namely the Chaotic Gaussian-based Global ARO (CGG-ARO), serving as a baseline for one-slot optimization. Second, we design an enhanced reward-based deep reinforcement learning (DRL) framework, referred to as the Multi-agent Double Deep Q-Network (MA-DDQN), that integrates both multi-agent coordination and multi-action selection mechanisms, significantly reducing mission assignment time and improving adaptability over baseline methods. Extensive simulations reveal that CGG-ARO improves the number of completed missions and overall benefit by approximately 7.1% and 7.7%, respectively. Meanwhile, MA-DDQN achieves even greater improvements of 11.0% in terms of mission completions and 12.5% in terms of the overall benefit. These results highlight the effectiveness of Oranits in enabling faster, more adaptive, and more efficient task processing in dynamic ITS environments.

cs.DC↗
arXiv2026

Provably Data-driven Lagrangian Relaxation for Mixed Integer Linear Programming

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the coupling constraints, LR enables parallel subproblem solving and often yields tighter dual bounds than standard linear programming relaxations, which is crucial for efficient branch-and-bound pruning. While recent empirical work has shown promising results using machine learning to predict these multipliers, a theoretical understanding of such methods remains an open question. In this work, we bridge this gap by analyzing the problem of learning LR through the lens of Data-driven Algorithm Design, i.e., a statistical learning problem over a distribution of problem instances. Our contributions are as follows: first, we derive a generalization bound of $\mathcal{O}(s^{1.5}/\sqrt{N})$ for the learned multipliers, where $s$ is the number of coupling constraints and $N$ is the sample size. Second, we provide a minimax lower-bound of $Ω(s/\sqrt{N})$, proving that a linear dependency is unavoidable. Third, we constructively close this theoretical gap by proving that Stochastic Gradient Ascent (SGA) with averaging achieves the minimax optimal rate $Θ(s/\sqrt{N})$. Finally, we extend our framework to the learning-to-warm-start setting, proving that it achieves a fast, minimax-optimal rate of $Θ(s/N)$ and establishing a theoretical advantage over direct multiplier prediction.

stat.ML↗
arXiv2026

Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function

Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the simple case of a one-dimensional (scalar) hyperparameter. This leaves the practically important, multi-dimensional hyperparameter tuning setting unresolved. We address this open question by establishing the first general framework for establishing generalization guarantees for tuning multi-dimensional hyperparameters in data-driven settings. Our approach strengthens the generalization guarantee framework for semi-algebraic function classes by exploiting tools from real algebraic geometry, yielding sharper, more broadly applicable guarantees. For completeness, we also instantiate the first lower bound for this general setting. We further extend the analysis to hyperparameter tuning using the validation loss under minimal assumptions, and derive improved bounds when additional structure is available. Finally, we demonstrate the scope of the framework with new learnability results, including data-driven weighted group lasso and weighted fused lasso.

stat.ML↗
arXiv2026

COBOLAssist: Analyzing and Fixing Compilation Errors for LLM-Powered COBOL Code Generation

Legacy programming languages such as COBOL (Common Business-Oriented Language) remain critical in business computing. However, maintaining legacy COBOL systems is increasingly challenging due to a declining pool of skilled developers and the persistence of COBOL errors that require deep domain expertise to resolve. This paper investigates the challenges of COBOL compilation errors and introduces a framework leveraging large language models (LLMs) to address these issues. We first categorize the common compilation errors in LLM-generated COBOL code into three groups: incomplete code errors, syntax errors, and type-related errors. We further propose COBOLAssist, a technique to enhance code correctness through iterative repairs guided by compilation feedback. Our evaluation using five LLMs including GPT variants and mAInframer, shows a high prevalence of incorrect program structures and function usage in COBOL programs and demonstrates the effectiveness of COBOLAssist, with the compilation success rates increasing from 29.5\% to 64.38\% for GPT-4o-mini and from 41.8\% to 95.89\% for GPT-4o. It also improves pass@1 significantly, for example from 9.1 to 22.6 for GPT-4. Notably, while mAInframer-34B achieves the highest compilation success rate, its functional correctness remains limited. This research not only highlights the limitations in current LLMs for COBOL but also demonstrates a practical path forward for automated debugging in legacy systems.

cs.SE↗
arXiv2026

COBOL-Coder: Domain-Adapted Large Language Models for COBOL Code Generation and Translation

COBOL remains a critical language for mainframe systems, yet existing large language models (LLMs) struggle to generate and translate COBOL code correctly. This paper reports our experience in developing and evaluating domain-adapted LLMs for COBOL and mainframe software engineering. We introduce (1) an automated data curation pipeline that combines compiler-guided validation with multi-stage similarity-based filtering to construct high-quality COBOL training data, and (2) COBOL-Coder, a COBOL-specialized LLM fine-tuned on the curated COBOL domain data. We evaluate COBOL-Coder on two tasks: code generation (on COBOLEval and COBOLCodeBench) and code translation (on COBOL-JavaTrans, our proposed benchmark for bidirectional COBOL-Java translation). In our experiments, COBOL-Coder achieves up to a 73.95 percent compilation success rate and 49.33 Pass-1 on COBOLEval, compared to 41.8 percent and 16.4 for GPT-4o, while most open-source baselines (e.g., CodeGemma, CodeLlama, StarCoder2) fail to produce compilable programs. For Java-to-COBOL translation, COBOL-Coder reaches 34.93 Pass-1, whereas general-purpose LLMs achieve near-zero scores. To assess the usability of LLM-generated code in real-world settings, we conduct a survey with experienced COBOL developers. Participants consistently report that COBOL-Coder exhibits stronger COBOL awareness, has more reliable program structure, and is better aligned with enterprise practices than general-purpose LLMs.

cs.SE↗
arXiv2026

Hyperbolicity of Fermat-type curves and their complements

In this paper, by using the generalized Borel theorems in $\mathbb{CP}^2$, we show the hyperbolicity of Fermat type curves and their complement in $\mathbb{CP}^2$. This improves Noguchi-Shirosaki's and Demailly-El Goul's degree bounds.

math.AG↗
arXiv2025

Provably data-driven projection method for quadratic programming

Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the projection matrix is learned from observed problem instances drawn from an application-specific distribution of problems. We analyze the generalization guarantee for the data-driven projection matrix learning for convex quadratic programs (QPs). Unlike in LPs, the optimal solutions of convex QPs are not confined to the vertices of the feasible polyhedron, and this complicates the analysis of the optimal value function. To overcome this challenge, we demonstrate that the solutions of convex QPs can be localized within a feasible region corresponding to a special active set, utilizing Caratheodory's theorem. Building on such observation, we propose the unrolled active set method, which models the computation of the optimal value as a Goldberg-Jerrum (GJ) algorithm with bounded complexities, thereby establishing learning guarantees. We then further extend our analysis to other settings, including learning to match the optimal solution and input-aware setting, where we learn a mapping from QP problem instances to projection matrices.

math.OC↗
arXiv2025

PatchSeeker: Mapping NVD Records to their Vulnerability-fixing Commits with LLM Generated Commits and Embeddings

Software vulnerabilities pose serious risks to modern software ecosystems. While the National Vulnerability Database (NVD) is the authoritative source for cataloging these vulnerabilities, it often lacks explicit links to the corresponding Vulnerability-Fixing Commits (VFCs). VFCs encode precise code changes, enabling vulnerability localization, patch analysis, and dataset construction. Automatically mapping NVD records to their true VFCs is therefore critical. Existing approaches have limitations as they rely on sparse, often noisy commit messages and fail to capture the deep semantics in the vulnerability descriptions. To address this gap, we introduce PatchSeeker, a novel method that leverages large language models to create rich semantic links between vulnerability descriptions and their VFCs. PatchSeeker generates embeddings from NVD descriptions and enhances commit messages by synthesizing detailed summaries for those that are short or uninformative. These generated messages act as a semantic bridge, effectively closing the information gap between natural language reports and low-level code changes. Our approach PatchSeeker achieves 59.3% higher MRR and 27.9% higher Recall@10 than the best-performing baseline, Prospector, on the benchmark dataset. The extended evaluation on recent CVEs further confirms PatchSeeker's effectiveness. Ablation study shows that both the commit message generation method and the selection of backbone LLMs make a positive contribution to PatchSeeker. We also discuss limitations and open challenges to guide future work.

cs.SE↗
arXiv2025

Deadline-Aware Joint Task Scheduling and Offloading in Mobile Edge Computing Systems

The demand for stringent interactive quality-of-service has intensified in both mobile edge computing (MEC) and cloud systems, driven by the imperative to improve user experiences. As a result, the processing of computation-intensive tasks in these systems necessitates adherence to specific deadlines or achieving extremely low latency. To optimize task scheduling performance, existing research has mainly focused on reducing the number of late jobs whose deadlines are not met. However, the primary challenge with these methods lies in the total search time and scheduling efficiency. In this paper, we present the optimal job scheduling algorithm designed to determine the optimal task order for a given set of tasks. In addition, users are enabled to make informed decisions for offloading tasks based on the information provided by servers. The details of performance analysis are provided to show its optimality and low complexity with the linearithmic time O(nlogn), where $n$ is the number of tasks. To tackle the uncertainty of the randomly arriving tasks, we further develop an online approach with fast outage detection that achieves rapid acceptance times with time complexity of O(n). Extensive numerical results are provided to demonstrate the effectiveness of the proposed algorithm in terms of the service ratio and scheduling cost.

cs.DC↗
arXiv2025

Algorithm Configuration for Structured Pfaffian Settings

Data-driven algorithm design automatically adapts algorithms to specific application domains, achieving better performance. In the context of parameterized algorithms, this approach involves tuning the algorithm's hyperparameters using problem instances drawn from the problem distribution of the target application domain. This can be achieved by maximizing empirical utilities that measure the algorithms' performance as a function of their hyperparameters, using problem instances. While empirical evidence supports the effectiveness of data-driven algorithm design, providing theoretical guarantees for several parameterized families remains challenging. This is due to the intricate behaviors of their corresponding utility functions, which typically admit piecewise discontinuous structures. In this work, we present refined frameworks for providing learning guarantees for parameterized data-driven algorithm design problems in both distributional and online learning settings. For the distributional learning setting, we introduce the \textit{Pfaffian GJ framework}, an extension of the classical \textit{GJ framework}, that is capable of providing learning guarantees for function classes for which the computation involves Pfaffian functions. Unlike the GJ framework, which is limited to function classes with computation characterized by rational functions, our proposed framework can deal with function classes involving Pfaffian functions, which are much more general and widely applicable. We then show that for many parameterized algorithms of interest, their utility function possesses a \textit{refined piecewise structure}, which automatically translates to learning guarantees using our proposed framework.

cs.LG↗
arXiv2025

Sample complexity of data-driven tuning of model hyperparameters in neural networks with structured parameter-dependent dual function

Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search based approaches to automating this laborious and compute intensive task, the fundamental learning theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data driven setting. We assume that we have a series of deep learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter; our analysis relies on subtle concepts including tools from differential/algebraic geometry and constrained optimization. This can be used to show that the learning theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.

cs.LG↗
arXiv2025

Model-Free Counterfactual Subset Selection at Scale

Ensuring transparency in AI decision-making requires interpretable explanations, particularly at the instance level. Counterfactual explanations are a powerful tool for this purpose, but existing techniques frequently depend on synthetic examples, introducing biases from unrealistic assumptions, flawed models, or skewed data. Many methods also assume full dataset availability, an impractical constraint in real-time environments where data flows continuously. In contrast, streaming explanations offer adaptive, real-time insights without requiring persistent storage of the entire dataset. This work introduces a scalable, model-free approach to selecting diverse and relevant counterfactual examples directly from observed data. Our algorithm operates efficiently in streaming settings, maintaining $O(\log k)$ update complexity per item while ensuring high-quality counterfactual selection. Empirical evaluations on both real-world and synthetic datasets demonstrate superior performance over baseline methods, with robust behavior even under adversarial conditions.

cs.LG↗
arXiv2024

VPI-Mlogs: A web-based machine learning solution for applications in petrophysics

Machine learning is an important part of the data science field. In petrophysics, machine learning algorithms and applications have been widely approached. In this context, Vietnam Petroleum Institute (VPI) has researched and deployed several effective prediction models, namely missing log prediction, fracture zone and fracture density forecast, etc. As one of our solutions, VPI-MLogs is a web-based deployment platform which integrates data preprocessing, exploratory data analysis, visualisation and model execution. Using the most popular data analysis programming language, Python, this approach gives users a powerful tool to deal with the petrophysical logs section. The solution helps to narrow the gap between common knowledge and petrophysics insights. This article will focus on the web-based application which integrates many solutions to grasp petrophysical data.

cs.LG↗
arXiv2024

XMainframe: A Large Language Model for Mainframe Modernization

Mainframe operating systems, despite their inception in the 1940s, continue to support critical sectors like finance and government. However, these systems are often viewed as outdated, requiring extensive maintenance and modernization. Addressing this challenge necessitates innovative tools that can understand and interact with legacy codebases. To this end, we introduce XMainframe, a state-of-the-art large language model (LLM) specifically designed with knowledge of mainframe legacy systems and COBOL codebases. Our solution involves the creation of an extensive data collection pipeline to produce high-quality training datasets, enhancing XMainframe's performance in this specialized domain. Additionally, we present MainframeBench, a comprehensive benchmark for assessing mainframe knowledge, including multiple-choice questions, question answering, and COBOL code summarization. Our empirical evaluations demonstrate that XMainframe consistently outperforms existing state-of-the-art LLMs across these tasks. Specifically, XMainframe achieves 30% higher accuracy than DeepSeek-Coder on multiple-choice questions, doubles the BLEU score of Mixtral-Instruct 8x7B on question answering, and scores six times higher than GPT-3.5 on COBOL summarization. Our work highlights the potential of XMainframe to drive significant advancements in managing and modernizing legacy systems, thereby enhancing productivity and saving time for software developers.

cs.CL↗
arXiv2022

Artificial Intelligence Enables Real-Time and Intuitive Control of Prostheses via Nerve Interface

Objective: The next generation prosthetic hand that moves and feels like a real hand requires a robust neural interconnection between the human minds and machines. Methods: Here we present a neuroprosthetic system to demonstrate that principle by employing an artificial intelligence (AI) agent to translate the amputee's movement intent through a peripheral nerve interface. The AI agent is designed based on the recurrent neural network (RNN) and could simultaneously decode six degree-of-freedom (DOF) from multichannel nerve data in real-time. The decoder's performance is characterized in motor decoding experiments with three human amputees. Results: First, we show the AI agent enables amputees to intuitively control a prosthetic hand with individual finger and wrist movements up to 97-98% accuracy. Second, we demonstrate the AI agent's real-time performance by measuring the reaction time and information throughput in a hand gesture matching task. Third, we investigate the AI agent's long-term uses and show the decoder's robust predictive performance over a 16-month implant duration. Conclusion & significance: Our study demonstrates the potential of AI-enabled nerve technology, underling the next generation of dexterous and intuitive prosthetic hands.

cs.RO↗
arXiv2021

On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative

In this work, we investigate the IVP for a time-fractional fourth-order equation with nonlinear source terms. More specifically, we consider the time-fractional biharmonic with exponential nonlinearity and the time-fractional Cahn-Hilliard equation. By using the Fourier transform concept, the generalized formula for the mild solution as well as the smoothing effects of resolvent operators are proved. For the IVP associated with the first one, by using the Orlicz space with the function $ Ξ(z)=e^{|z|^p}-1$ and some embeddings between it and the usual Lebesgue spaces, we prove that the solution is a global-in-time solution or it shall blow up in a finite time if the initial value is regular. In the case of singular initial data, the local-in-time/global-in-time existence and uniqueness are derived. Also, the regularity of the mild solution is investigated. For the IVP associated with the second one, some modifications to the generalized formula are made to deal with the nonlinear term. We also establish some important estimates for the derivatives of resolvent operators, they are the basis for using the Picard sequence to prove the local-in-time existence of the solution.

math.AP↗