arXiv subjects

Alexandre d'Aspremont

Publications and source records attributed to Alexandre d'Aspremont.

At least 19 recordsLinked to original sources

arXiv2026

Restart and Adaptive Acceleration in Stochastic Gradient Methods

We study restart schemes in stochastic optimization problems for non-smooth and weakly convex that satisfy a Kurdyka-\L ojasiewicz inequality. We show that using restarts allows us to leverage the K{\L} inequalities to achieve improved rates of convergence, with acceleration depending explicitly on the K{\L} exponent. Furthermore, optimal restart schedules lead to learning-rates akin to Polyak steps for SGD. While regularity constants such as the K{\L} exponent are typically unknown in practice, we prove that restart schemes are robust to a significant misspecification of these constants, hence nearly adaptive. We detail numerical experiments on both toy problems, where the K{\L} exponent is controlled, and training of Large Language Models (LLMs).

math.OC↗

arXiv2025

FORMSpoT: Revealing Fine-Scale Forest Disturbances from Nation-Wide 1.5 m Forest Canopy Height Time Series

Current large-scale satellite-based forest disturbance monitoring systems operate at 10-30~m resolution, too coarse to detect changes at the scale of individual trees and resulting in a systematic underestimation of forest disturbances. Here, we introduce FORMSpoT (Forest Mapping with SPOT Time series), a decade-long (2014-2024), country-scale mapping of forest canopy height at 1.5 m resolution over France, together with FORMSpoT-$\Delta$, annual disturbance polygons derived from height differences in the FORMSpoT time series. Canopy heights were derived from annual SPOT-6/7 composites using a hierarchical transformer model (PVTv2) trained on high-resolution airborne laser scanning (ALS) data. To enable robust change detection, we developed a post-processing pipeline combining co-registration and spatio-temporal total variation denoising. We find that (1) the French disturbance regime is dominated by small events. Sub-100 m$^{2}$ disturbances alone represent 72% of all events, and disturbances below 0.1 ha account for 97% of events and 39% of the disturbed area. These events are largely missed by Sentinel-1/2 and Landsat-based products. (2) Validated against successive ALS revisits across 19 sites and 5,087 NFI plot revisits, FORMSpoT-$\Delta$ provides reliable detection (F1>0.8) above 100 m$^{2}$ while retaining sensitivity to finer events that coarser products do not capture. (3) At the national scale, FORMSpoT-$\Delta$ resolves contrasted disturbance regimes, from clear-cut-dominated dynamics in maritime pine plantations to diffuse, smaller disturbance events in mountain forests, and captures their temporal dynamics, including the salvage-logging signature of the 2017-2022 bark beetle crisis in northeastern France

cs.CV↗

arXiv2025

Don't Be Greedy, Just Relax! Pruning LLMs via Frank-Wolfe

Pruning is a common technique to reduce the compute and storage requirements of Neural Networks. While conventional approaches typically retrain the model to recover pruning-induced performance degradation, state-of-the-art Large Language Model (LLM) pruning methods operate layer-wise, minimizing the per-layer pruning error on a small calibration dataset to avoid full retraining, which is considered computationally prohibitive for LLMs. However, finding the optimal pruning mask is a hard combinatorial problem and solving it to optimality is intractable. Existing methods hence rely on greedy heuristics that ignore the weight interactions in the pruning objective. In this work, we instead consider the convex relaxation of these combinatorial constraints and solve the resulting problem using the Frank-Wolfe (FW) algorithm. Our method drastically reduces the per-layer pruning error, outperforms strong baselines on state-of-the-art GPT architectures, and remains memory-efficient. We provide theoretical justification by showing that, combined with the convergence guarantees of the FW algorithm, we obtain an approximate solution to the original combinatorial problem upon rounding the relaxed solution to integrality.

cs.LG↗

arXiv2025

DUNIA: Pixel-Sized Embeddings via Cross-Modal Alignment for Earth Observation Applications

Significant efforts have been directed towards adapting self-supervised multimodal learning for Earth observation applications. However, most current methods produce coarse patch-sized embeddings, limiting their effectiveness and integration with other modalities like LiDAR. To close this gap, we present DUNIA, an approach to learn pixel-sized embeddings through cross-modal alignment between images and full-waveform LiDAR data. As the model is trained in a contrastive manner, the embeddings can be directly leveraged in the context of a variety of environmental monitoring tasks in a zero-shot setting. In our experiments, we demonstrate the effectiveness of the embeddings for seven such tasks: canopy height mapping, fractional canopy cover, land cover mapping, tree species identification, plant area index, crop type classification, and per-pixel waveform-based vertical structure mapping. The results show that the embeddings, along with zero-shot classifiers, often outperform specialized supervised models, even in low-data regimes. In the fine-tuning setting, we show strong performances near or better than the state-of-the-art on five out of six tasks.

cs.CV↗

arXiv2024

Open-Canopy: Towards Very High Resolution Forest Monitoring

Estimating canopy height and its changes at meter resolution from satellite imagery is a significant challenge in computer vision with critical environmental applications. However, the lack of open-access datasets at this resolution hinders the reproducibility and evaluation of models. We introduce Open-Canopy, the first open-access, country-scale benchmark for very high-resolution (1.5 m) canopy height estimation, covering over 87,000 km$^2$ across France with 1.5 m resolution satellite imagery and aerial LiDAR data. Additionally, we present Open-Canopy-$\Delta$, a benchmark for canopy height change detection between images from different years at tree level-a challenging task for current computer vision models. We evaluate state-of-the-art architectures on these benchmarks, highlighting significant challenges and opportunities for improvement. Our datasets and code are publicly available at https://github.com/fajwel/Open-Canopy.

cs.CV↗

arXiv2024

Frank-Wolfe meets Shapley-Folkman: a systematic approach for solving nonconvex separable problems with linear constraints

We consider separable nonconvex optimization problems under affine constraints. For these problems, the Shapley-Folkman theorem provides an upper bound on the duality gap as a function of the nonconvexity of the objective functions, but does not provide a systematic way to construct primal solutions satisfying that bound. In this work, we develop a two-stage approach to do so. The first stage approximates the optimal dual value with a large set of primal feasible solutions. In the second stage, this set is trimmed down to a primal solution by computing (approximate) Caratheodory representations. The main computational requirement of our method is tractability of the Fenchel conjugates of the component functions and their (sub)gradients. When the function domains are convex, the method recovers the classical duality gap bounds obtained via Shapley-Folkman. When the function domains are nonconvex, the method also recovers classical duality gap bounds from the literature, based on a more general notion of nonconvexity.

math.OC↗

arXiv2024

Modeling Methane Intensity of Oil and Gas Upstream Activities by Production Profile

We propose a methodology for modelling methane intensities of Oil and Gas upstream activities for different production profiles with diverse combinations of region of operation and production volumes associated. This methodology leverages different data sources, including satellite measurements and public estimates of methane emissions but also country-level oil and gas production data and company reporting. The obtained methane intensity models are compared to the reference companies' own reporting in order to better understand methane emissions for different types of companies. The results show that regions of operation within the different production profiles have a significant impact on the value of modelled methane intensities, especially for operators located in a single or few countries, such as national and medium-sized international operators. This paper also shows that methane intensities reported by the companies tend to be on average 16.1 times smaller than that obtained using the methodology presented here, and cannot account for total methane emissions that are estimated for upstream operations in the different regions observed.

cs.CE↗

arXiv2024

Optimal Algorithms for Stochastic Complementary Composite Minimization

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed with a stochastic first-order oracle, and a structured uniformly convex (possibly nonsmooth and non-Lipschitz) regularization term. Despite intensive work on closely related settings, prior to our work no complexity bounds for this problem were known. We close this gap by providing novel excess risk bounds, both in expectation and with high probability. Our algorithms are nearly optimal, which we prove via novel lower complexity bounds for this class of problems. We conclude by providing numerical results comparing our methods to the state of the art.

cs.LG↗

arXiv2024

Iteratively Reweighted Least Squares for Phase Unwrapping

The 2D phase unwrapping problem seeks to recover a phase image from its observation modulo 2$π$, and is a crucial step in a variety of imaging applications. In particular, it is one of the most time-consuming steps in the interferometric synthetic aperture radar (InSAR) pipeline. In this work we tackle the $L^1$-norm phase unwrapping problem. In optimization terms, this is a simple sparsity-inducing problem, albeit in very large dimension. To solve this high-dimensional problem, we iteratively solve a series of numerically simpler weighted least squares problems, which are themselves solved using a preconditioned conjugate gradient method. Our algorithm guarantees a sublinear rate of convergence in function values, is simple to implement and can easily be ported to GPUs, where it significantly outperforms state of the art phase unwrapping methods.

math.OC↗

arXiv2023

Strong Convexity of Sets in Riemannian Manifolds

Curvature properties of convex objects, such as strong convexity, are important in designing and analyzing convex optimization algorithms in the Hilbertian or Riemannian settings. In the case of the Hilbertian setting, strongly convex sets are well studied. Herein, we propose various definitions of strong convexity for uniquely geodesic sets in a Riemannian manifold. We study their relationship, propose tools to determine the geodesic strongly convex nature of sets, and analyze the convergence of optimization algorithms over those sets. In particular, we demonstrate that the Riemannian Frank-Wolfe algorithm enjoys a global linear convergence rate when the Riemannian scaling inequalities hold.

math.OC↗

arXiv2023

Oblivious Stochastic Composite Optimization

In stochastic convex optimization problems, most existing adaptive methods rely on prior knowledge about the diameter bound $D$ when the smoothness or the Lipschitz constant is unknown. This often significantly affects performance as only a rough approximation of $D$ is usually known in practice. Here, we bypass this limitation by combining mirror descent with dual averaging techniques and we show that, under oblivious step-sizes regime, our algorithms converge without any prior knowledge on the parameters of the problem. We introduce three oblivious stochastic algorithms to address different settings. The first algorithm is designed for objectives in relative scale, the second one is an accelerated version tailored for smooth objectives, whereas the last one is for relatively-smooth objectives. All three algorithms work without prior knowledge of the diameter of the feasible set, the Lipschitz constant or smoothness of the objective function. We use these results to revisit the problem of solving large-scale semidefinite programs using randomized first-order methods and stochastic smoothing. We extend our framework to relative scale and demonstrate the efficiency and robustness of our methods on large-scale semidefinite programs.

math.OC↗

arXiv2023

Vision Transformers, a new approach for high-resolution and large-scale mapping of canopy heights

Accurate and timely monitoring of forest canopy heights is critical for assessing forest dynamics, biodiversity, carbon sequestration as well as forest degradation and deforestation. Recent advances in deep learning techniques, coupled with the vast amount of spaceborne remote sensing data offer an unprecedented opportunity to map canopy height at high spatial and temporal resolutions. Current techniques for wall-to-wall canopy height mapping correlate remotely sensed 2D information from optical and radar sensors to the vertical structure of trees using LiDAR measurements. While studies using deep learning algorithms have shown promising performances for the accurate mapping of canopy heights, they have limitations due to the type of architectures and loss functions employed. Moreover, mapping canopy heights over tropical forests remains poorly studied, and the accurate height estimation of tall canopies is a challenge due to signal saturation from optical and radar sensors, persistent cloud covers and sometimes the limited penetration capabilities of LiDARs. Here, we map heights at 10 m resolution across the diverse landscape of Ghana with a new vision transformer (ViT) model optimized concurrently with a classification (discrete) and a regression (continuous) loss function. This model achieves better accuracy than previously used convolutional based approaches (ConvNets) optimized with only a continuous loss function. The ViT model results show that our proposed discrete/continuous loss significantly increases the sensitivity for very tall trees (i.e., > 35m), for which other approaches show saturation effects. The height maps generated by the ViT also have better ground sampling distance and better sensitivity to sparse vegetation in comparison to a convolutional model. Our ViT model has a RMSE of 3.12m in comparison to a reference dataset while the ConvNet model has a RMSE of 4.3m.

cs.CV↗

arXiv2022

Global Tracking and Quantification of Oil and Gas Methane Emissions from Recurrent Sentinel-2 Imagery

Methane (CH4) emissions estimates from top-down studies over oil and gas basins have revealed systematic under-estimation of CH4 emissions in current national inventories. Sparse but extremely large amounts of CH4 from oil and gas production activities have been detected across the globe, resulting in a significant increase of the overall O&G contribution. However, attribution to specific facilities remains a major challenge unless high-resolution images provide the sufficient granularity within O&G basin. In this paper, we monitor known oil-and-gas infrastructures across the globe using recurrent Sentinel-2 imagery to detect and quantify more than 800 CH4 emissions. In combination with emissions estimates from airborne and Sentinel-5P measurements, we demonstrate the robustness of the fit to a power law from 0.1 tCH4/hr to 600 tCH4/hr. We conclude here that the prevalence of ultra-emitters (> 25tCH4/hr) detected globally by Sentinel-5P directly relates to emission occurrences below its detection threshold. Similar power law coefficients arise from several major oil and gas producers but noticeable differences in emissions magnitudes suggest large differences in maintenance practices and infrastructures across countries.

physics.ao-ph↗

arXiv2022

Detecting Methane Plumes using PRISMA: Deep Learning Model and Data Augmentation

The new generation of hyperspectral imagers, such as PRISMA, has improved significantly our detection capability of methane (CH4) plumes from space at high spatial resolution (30m). We present here a complete framework to identify CH4 plumes using images from the PRISMA satellite mission and a deep learning model able to detect plumes over large areas. To compensate for the relative scarcity of PRISMA images, we trained our model by transposing high resolution plumes from Sentinel-2 to PRISMA. Our methodology thus avoids computationally expensive synthetic plume generation from Large Eddy Simulations by generating a broad and realistic training database, and paves the way for large-scale detection of methane plumes using future hyperspectral sensors (EnMAP, EMIT, CarbonMapper).

cs.CV↗

arXiv2021

Restarting Frank-Wolfe: Faster Rates Under Hölderian Error Bounds

Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While the vanilla Frank-Wolfe algorithm only ensures a worst-case rate of $\mathcal{O}(1/ε)$, various recent results have shown that for strongly convex functions on polytopes, the method can be slightly modified to achieve linear convergence. However, this still leaves a huge gap between sublinear $\mathcal{O}(1/ε)$ convergence and linear $\mathcal{O}(\log 1/ε)$ convergence to reach an $ε$-approximate solution. Here, we present a new variant of Conditional Gradient algorithms, that can dynamically adapt to the function's geometric properties using restarts and smoothly interpolates between the sublinear and linear regimes. These interpolated convergence rates are obtained when the optimization problem satisfies a new type of error bounds, which we call \textit{strong Wolfe primal bounds}. They combine geometric information on the constraint set with Hölderian Error Bounds on the objective function.

math.OC↗

arXiv2021

Global Assessment of Oil and Gas Methane Ultra-Emitters

Methane emissions from oil and gas (O&G) production and transmission represent a significant contribution to climate change. These emissions comprise sporadic releases of large amounts of methane during maintenance operations or equipment failures not accounted for in current inventory estimates. We collected and analyzed hundreds of very large releases from atmospheric methane images sampled by the TROPOspheric Monitoring Instrument (TROPOMI) over 2019 and 2020 to quantify emissions from O&G ultra-emitters. Ultra-emitters are primarily detected over the largest O&G basins of the world, following a power-law relationship with noticeable variations across countries but similar regression slopes. With a total contribution equivalent to 8-12% of the global O&G production methane emissions, mitigation of ultra-emitters is largely achievable at low costs and would lead to robust net benefits in billions of US dollars for the six major producing countries when incorporating recent estimates of societal costs of methane.

physics.ao-ph↗

arXiv2021

Linear Bandits on Uniformly Convex Sets

Linear bandit algorithms yield $\tilde{\mathcal{O}}(n\sqrt{T})$ pseudo-regret bounds on compact convex action sets $\mathcal{K}\subset\mathbb{R}^n$ and two types of structural assumptions lead to better pseudo-regret bounds. When $\mathcal{K}$ is the simplex or an $\ell_p$ ball with $p\in]1,2]$, there exist bandits algorithms with $\tilde{\mathcal{O}}(\sqrt{nT})$ pseudo-regret bounds. Here, we derive bandit algorithms for some strongly convex sets beyond $\ell_p$ balls that enjoy pseudo-regret bounds of $\tilde{\mathcal{O}}(\sqrt{nT})$, which answers an open question from [BCB12, §5.5.]. Interestingly, when the action set is uniformly convex but not necessarily strongly convex, we obtain pseudo-regret bounds with a dimension dependency smaller than $\mathcal{O}(\sqrt{n})$. However, this comes at the expense of asymptotic rates in $T$ varying between $\tilde{\mathcal{O}}(\sqrt{T})$ and $\tilde{\mathcal{O}}(T)$.

cs.LG↗

arXiv2021

Local and Global Uniform Convexity Conditions

We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the convergence of optimization methods. In particular, we establish local versions of these conditions to provide sharper insights on a recent body of complexity results in learning theory, online learning, or offline optimization, which rely on the strong convexity of the feasible set. While they have a significant impact on complexity, these strong convexity or uniform convexity properties of feasible sets are not exploited as thoroughly as their functional counterparts, and this work is an effort to correct this imbalance. We conclude with some practical examples in optimization and machine learning where leveraging these conditions and localized assumptions lead to new complexity results.

math.OC↗