Publications

First-order Methods Almost Always Avoid Saddle Points (with Jason D. Lee, Georgios Piliouras, Max Simchowitz, Michael I. Jordan and Benjamin Recht). [Arxiv] / Have a look at this nice exposition about our work! Accepted at Math. Programming

Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization (with Costis Daskalakis). ITCS 2019 [Arxiv]

The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization (with Costis Daskalakis). NIPS 2018 [Arxiv]

Cycles in Zero Sum Differential Games and Biological Diversity (with Tung Mai, Milena Mihail, Will Ratcliff, Vijay V. Vazirani and Peter Yunker). EC 2018 [Arxiv], [slides]

Multiplicative Weights Update with Constant step-size in Congestion Games: Convergence, Limit Cycles and Chaos (with Gerasimos Palaiopanos and Georgios Piliouras). NIPS 2017 (spotlight) [Arxiv], [Poster], [Video] 

Opinion Dynamics in Networks: Convergence, Stability and Lack of Explosion (with Tung Mai and Vijay V. Vazirani).
ICALP 2017 [Arxiv], [slides]

Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions (with Georgios Piliouras). 
ITCS 2017 [Arxiv], [slides], [video

Mutation, Sexual Reproduction and Survival in Dynamic Environments (with Ruta Mehta, Georgios Piliouras, Prasad Tetali and Vijay V. Vazirani). 
ITCS 2017 [Arxiv]

The Computational Complexity of Genetic Diversity (with Ruta Mehta, Georgios Piliouras and Sadra Yazdanbod). 
ESA 2016 [Arxiv], [slides]

Average Case Performance of Replicator Dynamics in Potential Games via Computing Regions of Attraction (with Georgios Piliouras). 
EC 2016 [Arxiv]

Mixing Time of Markov Chains, Dynamical Systems and Evolution (with Nisheeth K. Vishnoi). 
ICALP 2016 [Pdf]

Evolutionary Dynamics in finite populations mix rapidly (with Piyush Srivastava and Nisheeth K. Vishnoi). 
SODA 2016 [Pdf],[slides]

Natural Selection as an Inhibitor of Genetic Diversity: Multiplicative Weights Updates Algorithm and a Conjecture of Haploid Genetics (with Ruta Mehta and Georgios Piliouras). 
ITCS 2015 [Arxiv],[slides]

Support-theoretic subgraph preconditioners for large-scale SLAM (with Yong-Dian Jian, Doru Balcan, Prasad Tetali, Frank Dellaert). 
IROS 2013 [Pdf]

Manuscripts
Regression from Dependent Observations (with Costis Daskalakis and Nishanth Dikkala). [Coming soon]

Multiplicative Weights Updates as a distributed constrained optimization algorithm: Convergence to second-order stationary points almost always (with Georgios Piliouras and Xiao Wang). [Arxiv]

Thesis