Main research interest
Learning in games
Reinforcement Learning and MDPs
Nonexpansive maps
Optimization
Stochastic approximation algorithms
Collaborators
I have been fortunate to collaborate and discuss mathematics with many colleagues and friends. Among them,
Michel Benaïm, Sebastian Bervoets, Luis Briceño-Arias, Thierry Champion, Roberto Cominetti, Juan Pablo Contreras, Cristián Cortés, Mathieu Faure, Juan Pablo Flores-Mella, Cristóbal Guzmán, Jongmin Lee, David S. Leslie, Francisco Martínez, Panayotis Mertikopoulos, Laurent Miclo, Miquel Oliu-Barton, Matías Pavez-Signé, David Salas, Bruno Ziliotto.
In preparation
On the Occupation Measure in Evolution Models with Vanishing Mutations. (with Mathieu Faure and Michel Benaïm)
Optimal Halpern Iteration for Lipschitz maps (with Jongmin Lee and Roberto Cominetti)
On the Krasnoselskii--Mann Iteration for Contractions in Banach Spaces (with Roberto Cominetti)
The Unknown Stochastic Game (with Miquel Oliu-Barton)
Papers
Bravo, M., Flores-Mella, J.P., Guzmán, C. Mixing times and privacy analysis for the projected Langevin algorithm under a modulus of continuity (2025). To appear in Journal of Machine Learning Research (ArXiv version).
Lee, J., Bravo, M., Cominetti, R. Near-optimal sample complexity for MDPs via anchoring. In Proceedings of the 42nd International Conference on Machine Learning (ICML), 2025 (pdf)
Bravo, M., Contreras, J.P. Stochastic Halpern iteration and applications to reinforcement learning (2024). Submitted (ArXiv version)
Bravo, M., Cominetti, R. Stochastic fixed-point iterations for nonexpansive maps: Convergence and error bounds . SIAM Journal on Control and Optimization 62(1), 191-219, 2024 (Arxiv version) .
Bravo, M., Champion T., Cominetti, R. Universal bounds for fixed point iterations via transport metrics. Applied Set-Valued Analysis and Optimization 4(3), 293-310, 2022 (ArXiv version)
Bervoets, S., Bravo, M., Faure, M. Learning with minimal information in continuous games. Theoretical Economics, 15(4), 1471-1508, 2020, (online version).
Bravo, M., Cominetti, R., Pavez-Signé, M. Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces. Mathematical Programming, 175(1), 241-262, 2019, (arxiv, online version).
Bravo, M., Leslie, D.S., Mertikopoulos, P. Bandit learning in concave N-person games. In NIPS ’18: Proceedings of the 32nd International Conference on Neural Information Processing Systems, 2018.
Bravo, M., Cominetti, R. Sharp convergence rates for averaged nonexansive maps. Israel Journal of Mathematics, 227(1), 163-188, 2018. (arxiv, online version).
Bravo, M., Mertikopoulos P. On the robustness of learning in games with stochastically perturbed payoff observations. Games and Economic Behavior (Special Issue: John Nash Memorial), 103, 41-66, 2017.(pdf).
Bravo, M. An adjusted payoff-based procedure for normal form games. Mathematics of Operations Research, 41(4), 1469-1483, 2016.(pdf).
Bravo, M., Faure M. Reinforcement learning with restrictions on the action set. SIAM Journal on Control and Optimization, 53(1), 287–312, 2015 (pdf).
Bravo, M., Briceño, L., Cominetti, R., Cortés, C., Martínez, F., An integrated behavioral model of the land-use and transport systems with network congestion and location externalities. Transportation Research Part B : Methodological, 44, 584--596, 2010. (pdf)