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Enea Monzio Compagnoni

6 accepted papers

2026

Adaptive Methods Are Preferable in High Privacy Settings: An SDE Perspective

Enea Monzio Compagnoni, Alessandro Stanghellini, Rustem Islamov, Aurelien Lucchi, Anastasia Koloskova
ICLR 2026poster

Differential Privacy (DP) is becoming central to large-scale training as privacy regulations tighten. We revisit how DP noise interacts with *adaptivity* in optimization through the lens of *stochastic differential equations*, providing the first SDE-based analysis of private optimizers. Focusing on…

Cited by 0Source ↗code ↗Scholar ↗
2026

On the Interaction of Batch Noise, Adaptivity, and Compression, under $(L_0,L_1)$-Smoothness: An SDE Approach

Enea Monzio Compagnoni, Rustem Islamov, Frank Proske, Aurelien Lucchi, Antonio Orvieto, Eduard Gorbunov
ICML 2026poster

Distributed stochastic optimization intertwines (i) stochastic gradient noise, (ii) communication compression, and (iii) adaptive/normalized updates. While each factor has been studied in isolation, their joint effect under realistic assumptions remains poorly understood. In this work, we develop a …

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2025

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise

Enea Monzio Compagnoni, Tianlin Liu, Rustem Islamov, Frank Norbert Proske, Antonio Orvieto, Aurelien Lucchi
ICLR 2025poster

Despite the vast empirical evidence supporting the efficacy of adaptive optimization methods in deep learning, their theoretical understanding is far from complete. This work introduces novel SDEs for commonly used adaptive optimizers: SignSGD, RMSprop(W), and Adam(W). These SDEs offer a quantitativ…

Cited by 2Source ↗PDF ↗Scholar ↗
2025

Unbiased and Sign Compression in Distributed Learning: Comparing Noise Resilience via SDEs

Enea Monzio Compagnoni, Rustem Islamov, Frank Norbert Proske, Aurelien Lucchi
AISTATS 2025oral

Distributed methods are essential for handling machine learning pipelines comprising large-scale models and datasets. However, their benefits often come at the cost of increased communication overhead between the central server and agents, which can become the main bottleneck, making training costly…

Cited by 0Source ↗Scholar ↗
2024

SDEs for Minimax Optimization

Enea Monzio Compagnoni, Antonio Orvieto, Hans Kersting, Frank Proske, Aurelien Lucchi
AISTATS 2024poster

Minimax optimization problems have attracted a lot of attention over the past few years, with applications ranging from economics to machine learning. While advanced optimization methods exist for such problems, characterizing their dynamics in stochastic scenarios remains notably challenging. In th…

Cited by 4Source ↗PDF ↗code ↗Scholar ↗
2023

An SDE for Modeling SAM: Theory and Insights

Enea Monzio Compagnoni, Luca Biggio, Antonio Orvieto, Frank Norbert Proske, Hans Kersting, Aurelien Lucchi
ICML 2023poster

We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic gradient descent. Our main contribution is the derivation of continuous-time models (in the form of SDEs) for SAM and t…

Cited by 26Source ↗PDF ↗Scholar ↗