Research
Some of the links below are under a paywall, but most of my publications are freely available on ArXiv.
Submitted/In Preparation
Tracking Solutions of Time-Varying Variational Inequalities (with S. Sachs and H. Hadiji), 2024
Optimization on a Finer Scale: Local Subgradient Variation Perspective (with J. Diakonikolas), 2024
Accepted/Published
Public Data-Assisted Private Stochastic Optimization: Power and Limitations (with E. Ullah, M. Menart, R. Bassily and R. Arora). Accepted in 2024
Differentially-Private Optimization with Sparse Gradients (with B. Ghazi, P. Kamath, R. Kumar and P. Manurangsi). Accepted in NeurIPS 2024
Private Algorithms for Stochastic Saddle Points and Variational Inequalities: Beyond Euclidean Geometry (with R. Bassily and M. Menart). Accepted on NeurIPS 2024
Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems (with T. González and C. Paquette). COLT 2024
Differentially-Private Non-Convex Optimization Under the KL Condition with Optimal Rates (with M. Menart, E. Ullah, R. Bassily and R. Arora). ALT 2024
Complementary Composite Minimization, Small Gradients in General Norms, and Applications (with J. Diakonikolas). Mathematical Programming Series A, 2024
Optimal Algorithms for Stochastic Complementary Composite Optimization (with A. d'Aspremont and C. Lezane). SIAM J. on Optimization, 2024
Differentially Private Algorithms for the Stochastic Saddle Point Problem with Optimal Rates for the Strong Gap (with R. Bassily & M. Menart). COLT 2023
Faster Rates of Convergence to Stationary Points in Differentially Private Optimization (with R. Arora, R. Bassily, T. González, M. Menart & E. Ullah). ICML 2023
Optimal Algorithms for Differentially Private Stochastic Monotone Variational Inequalities and Saddle-Point Problems (with D. Boob). Mathematical Programming Series A, 2023
Differentially Private Generalized Linear Models Revisited (with R. Arora, R. Bassily, M. Menart & E. Ullah). NeurIPS 2022
A Stochastic Halpern Iteration with Variance Reduction for Stochastic Monotone Inclusion Problems (with X. Cai, C. Song & J. Diakonikolas). NeurIPS 2022
Between Stochastic and Adversarial Online Convex Optimization: Improved Regret Bounds via Smoothness (with S. Sachs, H. Hadiji & T. van Erven). NeurIPS 2022
A Sequential Stackelberg Game for Dynamic Inspection Problems (with J. Riffo, C. Telha & M. Van Vyve). European Journal of Operations Research, 2021
Differentially Private Stochastic Optimization: New Results in Convex and Nonconvex Settings (with R. Bassily and M. Menart). NeurIPS 2021
Best-Case Lower Bounds in Online Learning (with N. Mehta and A. Mortazavi). NeurIPS 2021
An Optimal Algorithm for Strict Circular Seriation (with S. Armstrong and C. Sing-Long). SIAM Journal on Mathematics of Data Science. Code available here
Non-Euclidean Differentially Private Stochastic Convex Optimization (with R. Bassily & A. Nandi). COLT 2021
The Complexity of Nonconvex-Strongly-Concave Minimax Optimization (with S. Zhang, J. Yang, N. Kiyavash & N. He). UAI 2021
Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses (with R. Bassily, V. Feldman and K. Talwar), NeurIPS 2020 (spotlight presentation)
Lower Bounds for Parallel and Randomized Convex Optimization (with J. Diakonikolas), COLT 2019 (full version published at JMLR)
Optimal Affine Invariant Smooth Minimization Algorithms (with A. d’Aspremont and M. Jaggi), SIAM J. Optim., 28(3), pp. 2384-2405, 2018.
Network Pricing: How to Induce Optimal Flows Under Strategic Link Operators (with J. Correa, T. Lianeas, E. Nikolova and M. Schröder). EC '18 (full version accepted in Operations Research)
Fast, Deterministic and Sparse Dimensionality Reduction (with D. Dadush and N. Olver). SODA 2018
Statistical Query Algorithms for Mean Vector Estimation and Stochastic Convex Optimization (with V. Feldman and S. Vempala). SODA 2017 (full version accepted in Math of OR)
New Upper Bounds on the Density of Translative Packings of Three-Dimensional Convex Bodies with Tetrahedral Symmetry (with M. Dostert, F.M. de Oliveira Filho and F. Vallentin). Discrete and Computational Geometry, 58(2), pp.449-481, 2017
Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization via Information Theory (with G. Braun and S. Pokutta). IEEE Transactions on Information Theory, 63(7), pp. 4709 - 4724, 2017
On Lower Complexity Bounds for Large-Scale Smooth Convex Optimization (with A. Nemirovski). Journal of Complexity, 31(1), pp. 1-14, 2015
Network Congestion Control with Markovian Multipath Routing (with R. Cominetti). NETGCOOP 2011 (full version in Mathematical Programming, Series A , 147, pp. 231-251, 2014)
Theses
Information, Complexity and Structure in Convex Optimization. Ph.D. Thesis, Georgia Inst. of Technology, 2015
Un Modelo de Equilibrio para Ruteo y Control de Flujo en Redes de Comunicaciones (in Spanish). Mathematical Engineering thesis, Universidad de Chile, 2010
Others
Open Problem: The Oracle Complexity of Convex Optimization in Nonstandard Settings. COLT 2015 Proceedings
Congested Roads and Traffic Congestion Models (with P. Kleer). Introductory articles for The Network Pages, 2015
Collaborators
I have been extremely fortunate to work with the following colleagues:
Santiago Armstrong, Raman Arora, Alexandre d’Aspremont, Raef Bassily, Digvijay Boob, Gábor Braun, Xufeng Cai, Roberto Cominetti, José Correa, Daniel Dadush, Jelena Diakonikolas, Maria Dostert, Tim van Erven, Vitaly Feldman, Badih Ghazi, Tomás González, Hédi Hadiji, Niao He, Martin Jaggi, Pritish Kamath, Ravi Kumar, Clément Lezane, Thanasis Lianeas, Pasin Manurangsi, Nishant Mehta, Michael Menart, Ali Mortazavi, Anupama Nandi, Arkadi Nemirovski, Evdokia Nikolova, Fernando M. de Oliveira Filho, Neil Olver, Courtney Paquette, Sebastian Pokutta, Javiera Riffo, Sarah Sachs, Marc Schröder, Carlos Sing-Long, Chaobing Song, Kunal Talwar, Claudio Telha, Enayat Ullah, Frank Vallentin, Santosh Vempala, Mathieu Van Vyve, Junchi Yang and Siqi Zhang