Author name cluster

Bartolomeo Stellato

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7 papers

1 author row

TMLR Journal 2026 Journal Article

On the (linear) convergence of Generalized Newton Inexact ADMM

Zachary Frangella
Theo Diamandis
Bartolomeo Stellato
Madeleine Udell

This paper presents GeNI-ADMM, a framework for large-scale composite convex optimization that facilitates theoretical analysis of both existing and new approximate ADMM schemes. GeNI-ADMM encompasses any ADMM algorithm that solves a first- or second-order approximation to the ADMM subproblem inexactly. GeNI-ADMM exhibits the usual O(1/t)-convergence rate under standard hypotheses and converges linearly under additional hypotheses such as strong convexity. Further, the GeNI-ADMM framework provides explicit convergence rates for ADMM variants accelerated with randomized linear algebra, such as NysADMM and sketch-and-solve ADMM, resolving an important open question on the convergence of these methods. This analysis quantifies the benefit of improved approximations and can aid in the design of new ADMM variants with faster convergence.

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NeurIPS Conference 2025 Conference Paper

AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?

Ori Press
Brandon Amos
Haoyu Zhao
Yikai Wu
Samuel Ainsworth
Dominik Krupke
Patrick Kidger
Touqir Sajed

Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming (SWE-Bench) and mathematics (FrontierMath). We therefore propose testing models' ability to design and implement algorithms in an open-ended benchmark: We task LMs with writing code that efficiently solves computationally challenging problems in computer science, physics, and mathematics. Our AlgoTune benchmark consists of 120 tasks collected from domain experts and a framework for validating and timing LM-synthesized solution code, which is compared to reference implementations from popular open-source packages. In addition, we develop a baseline LM agent, AlgoTuner, and evaluate its performance across a suite of frontier models. AlgoTuner achieves an average 1. 58x speedup against reference solvers, including methods from packages such as SciPy, scikit-learn and CVXPY. However, we find that current models fail to discover algorithmic innovations, instead preferring surface-level optimizations. We hope that AlgoTune catalyzes the development of LM agents exhibiting creative problem solving beyond state-of-the-art human performance.

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JMLR Journal 2025 Journal Article

Data-Driven Performance Guarantees for Classical and Learned Optimizers

Rajiv Sambharya
Bartolomeo Stellato

We introduce a data-driven approach to analyze the performance of continuous optimization algorithms using generalization guarantees from statistical learning theory. We study classical and learned optimizers to solve families of parametric optimization problems. We build generalization guarantees for classical optimizers, using a sample convergence bound, and for learned optimizers, using the Probably Approximately Correct (PAC)-Bayes framework. To train learned optimizers, we use a gradient-based algorithm to directly minimize the PAC-Bayes upper bound. Numerical experiments in signal processing, control, and meta-learning showcase the ability of our framework to provide strong generalization guarantees for both classical and learned optimizers given a fixed budget of iterations. For classical optimizers, our bounds which hold with high probability are much tighter than those that worst-case guarantees provide. For learned optimizers, our bounds outperform the empirical outcomes observed in their non-learned counterparts. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2025. ( edit, beta )

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JMLR Journal 2024 Journal Article

Learning to Warm-Start Fixed-Point Optimization Algorithms

Rajiv Sambharya
Georgina Hall
Brandon Amos
Bartolomeo Stellato

We introduce a machine-learning framework to warm-start fixed-point optimization algorithms. Our architecture consists of a neural network mapping problem parameters to warm starts, followed by a predefined number of fixed-point iterations. We propose two loss functions designed to either minimize the fixed-point residual or the distance to a ground truth solution. In this way, the neural network predicts warm starts with the end-to-end goal of minimizing the downstream loss. An important feature of our architecture is its flexibility, in that it can predict a warm start for fixed-point algorithms run for any number of steps, without being limited to the number of steps it has been trained on. We provide PAC-Bayes generalization bounds on unseen data for common classes of fixed-point operators: contractive, linearly convergent, and averaged. Applying this framework to well-known applications in control, statistics, and signal processing, we observe a significant reduction in the number of iterations and solution time required to solve these problems, through learned warm starts. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

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NeurIPS Conference 2021 Conference Paper

Accelerating Quadratic Optimization with Reinforcement Learning

Jeffrey Ichnowski
Paras Jain
Bartolomeo Stellato
Goran Banjac
Michael Luo
Francesco Borrelli
Joseph E. Gonzalez
Ion Stoica

First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges: manual hyperparameter tuning and convergence time to high-accuracy solutions. To address these, we explore how Reinforcement Learning (RL) can learn a policy to tune parameters to accelerate convergence. In experiments with well-known QP benchmarks we find that our RL policy, RLQP, significantly outperforms state-of-the-art QP solvers by up to 3x. RLQP generalizes surprisingly well to previously unseen problems with varying dimension and structure from different applications, including the QPLIB, Netlib LP and Maros-M{\'e}sz{\'a}ros problems. Code, models, and videos are available at https: //berkeleyautomation. github. io/rlqp/.

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NeurIPS Conference 2021 Conference Paper

Is Bang-Bang Control All You Need? Solving Continuous Control with Bernoulli Policies

Tim Seyde
Igor Gilitschenski
Wilko Schwarting
Bartolomeo Stellato
Martin Riedmiller
Markus Wulfmeier
Daniela Rus

Reinforcement learning (RL) for continuous control typically employs distributions whose support covers the entire action space. In this work, we investigate the colloquially known phenomenon that trained agents often prefer actions at the boundaries of that space. We draw theoretical connections to the emergence of bang-bang behavior in optimal control, and provide extensive empirical evaluation across a variety of recent RL algorithms. We replace the normal Gaussian by a Bernoulli distribution that solely considers the extremes along each action dimension - a bang-bang controller. Surprisingly, this achieves state-of-the-art performance on several continuous control benchmarks - in contrast to robotic hardware, where energy and maintenance cost affect controller choices. Since exploration, learning, and the final solution are entangled in RL, we provide additional imitation learning experiments to reduce the impact of exploration on our analysis. Finally, we show that our observations generalize to environments that aim to model real-world challenges and evaluate factors to mitigate the emergence of bang-bang solutions. Our findings emphasise challenges for benchmarking continuous control algorithms, particularly in light of potential real-world applications.

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JBHI Journal 2021 Journal Article

Machine Learning for Real-Time Heart Disease Prediction

Dimitris Bertsimas
Luca Mingardi
Bartolomeo Stellato

Heart-related anomalies are among the most common causes of death worldwide. Patients are often asymptomatic until a fatal event happens, and even when they are under observation, trained personnel is needed in order to identify a heart anomaly. In the last decades, there has been increasing evidence of how Machine Learning can be leveraged to detect such anomalies, thanks to the availability of Electrocardiograms (ECG) in digital format. New developments in technology have allowed to exploit such data to build models able to analyze the patterns in the occurrence of heart beats, and spot anomalies from them. In this work, we propose a novel methodology to extract ECG-related features and predict the type of ECG recorded in real time (less than 30 milliseconds). Our models leverage a collection of almost 40 thousand ECGs labeled by expert cardiologists across different hospitals and countries, and are able to detect 7 types of signals: Normal, AF, Tachycardia, Bradycardia, Arrhythmia, Other or Noisy. We exploit the XGBoost algorithm, a leading machine learning method, to train models achieving out of sample F1 Scores in the range 0. 93 - 0. 99. To our knowledge, this is the first work reporting high performance across hospitals, countries and recording standards.

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