@article{Kerdreuxd'AspremontPokutta2021, author = {Kerdreux, Thomas and d'Aspremont, Alexandre and Pokutta, Sebastian}, title = {Local and Global Uniform Convexity Conditions}, year = {2021}, abstract = {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 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.}, language = {en} } @inproceedings{FayadZimmerSchwartzetal.2025, author = {Fayad, Ibrahim and Zimmer, Max and Schwartz, Martin and Ciais, Philippe and Gieseke, Fabian and Belouze, Gabriel and Brood, Sarah and De Truchis, Aurelien and d'Aspremont, Alexandre}, title = {DUNIA: Pixel-Sized Embeddings via Cross-Modal Alignment for Earth Observation Applications}, volume = {267}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, arxiv = {http://arxiv.org/abs/2502.17066}, pages = {16375 -- 16406}, year = {2025}, language = {en} } @article{Kerdreuxd'AspremontPokutta2022, author = {Kerdreux, Thomas and d'Aspremont, Alexandre and Pokutta, Sebastian}, title = {Restarting Frank-Wolfe: Faster Rates under H{\"o}lderian Error Bounds}, journal = {Journal of Optimization Theory and Applications}, year = {2022}, language = {en} } @inproceedings{Kerdreuxd'AspremontPokutta2020, author = {Kerdreux, Thomas and d'Aspremont, Alexandre and Pokutta, Sebastian}, title = {Projection-Free Optimization on Uniformly Convex Sets}, booktitle = {To Appear in Proceedings of AISTATS}, year = {2020}, language = {en} } @article{KerdreuxRouxd'Aspremontetal.2021, author = {Kerdreux, Thomas and Roux, Christophe and d'Aspremont, Alexandre and Pokutta, Sebastian}, title = {Linear Bandits on Uniformly Convex Sets}, volume = {22}, journal = {Journal of Machine Learning Research}, number = {284}, pages = {1 -- 23}, year = {2021}, abstract = {Linear bandit algorithms yield O~(n√T) pseudo-regret bounds on compact convex action sets K⊂Rn and two types of structural assumptions lead to better pseudo-regret bounds. When K is the simplex or an ℓp ball with p∈]1,2], there exist bandits algorithms with O~(√n√T) pseudo-regret bounds. Here, we derive bandit algorithms for some strongly convex sets beyond ℓp balls that enjoy pseudo-regret bounds of O~(√n√T), which answers an open question from [BCB12, \S5.5.]. Interestingly, when the action set is uniformly convex but not necessarily strongly convex, we obtain pseudo-regret bounds with a dimension dependency smaller than O(√n). However, this comes at the expense of asymptotic rates in T varying between O(√T) and O(T).}, language = {en} }