@article{RouxPokuttaWirthetal., author = {Roux, Christophe and Pokutta, Sebastian and Wirth, Elias and Kerdreux, Thomas}, title = {Efficient Online-Bandit Strategies for Minimax Learning Problems}, abstract = {Several learning problems involve solving min-max problems, e.g., empirical distributional robust learning [Namkoong and Duchi, 2016, Curi et al., 2020] or learning with non-standard aggregated losses [Shalev- Shwartz and Wexler, 2016, Fan et al., 2017]. More specifically, these problems are convex-linear problems where the minimization is carried out over the model parameters w ∈ W and the maximization over the empirical distribution p ∈ K of the training set indexes, where K is the simplex or a subset of it. To design efficient methods, we let an online learning algorithm play against a (combinatorial) bandit algorithm. We argue that the efficiency of such approaches critically depends on the structure of K and propose two properties of K that facilitate designing efficient algorithms. We focus on a specific family of sets Sn,k encompassing various learning applications and provide high-probability convergence guarantees to the minimax values.}, language = {en} } @article{KerdreuxRouxd'Aspremontetal., author = {Kerdreux, Thomas and Roux, Christophe and d'Aspremont, Alexandre and Pokutta, Sebastian}, title = {Linear Bandits on Uniformly Convex Sets}, series = {Journal of Machine Learning Research}, volume = {22}, journal = {Journal of Machine Learning Research}, number = {284}, pages = {1 -- 23}, 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} } @inproceedings{MartinezRubioRouxCriscitielloetal., author = {Mart{\´i}nez-Rubio, David and Roux, Christophe and Criscitiello, Christopher and Pokutta, Sebastian}, title = {Accelerated Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties}, series = {Proceedings of Optimization for Machine Learning (NeurIPS Workshop OPT 2023)}, booktitle = {Proceedings of Optimization for Machine Learning (NeurIPS Workshop OPT 2023)}, language = {en} }