Research

Some of the links below are under a paywall, but most of my publications are freely available on ArXiv. 

Submitted/In Preparation

• Differentially-Private Optimization with Sparse Gradients (with B. Ghazi, P. Kamath, R. Kumar and P. Manurangsi), 2024

• Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems (with T. González and C. Paquette), 2024

• Public Data-Assisted Private Stochastic Optimization: Power and Limitations (with E. Ullah, M. Menart, R. Bassily and R. Arora), 2024

Accepted/Published

• 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 to Regression Problems (with J. Diakonikolas). Accepted in Mathematical Programming Ser. A

• 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