I am a research scientist at Google. My current focus is designing and analyzing optimization methods for federated learning. I actively contribute to TensorFlow Federated, Google’s open-source framework for federated learning experimentation, and Federated Research, Google’s open-source repository for federated learning research.

I received a Ph.D. in applied mathematics from the University of Wisconsin-Madison, and went on to do a postdoc with the wonderful Dimitris Papailiopoulos. In my limited free time I often foster dogs and bake. You can find recipes I am fond of in my dissertation (no, really).

## Research

I am generally interested in optimization for machine learning, especially federated learning. I tend to focus on developing holistic understandings of algorithms that incorporate communication-efficiency, robustness, fairness, and practicality. I am particularly interested in reconciling optimization theory with practical machine learning. Much of my work does this by leveraging tools from probability theory and high-dimensional statistics.

## Publications & Preprints

### 2021

**[new!]****Iterated Vector Fields and Conservatism, with Applications to Federated Learning**

Z. Charles, K. Rush.**[new!]****A Field Guide to Federated Optimization**

J. Wang, Z. Charles, Z. Xu, G. Joshi, H. B. McMahan, et al.**[new!]****On Large-Cohort Training for Federated Learning**

Z. Charles, Z. Garrett, Z. Huo, S. Shmulyian, V. Smith.**Local Adaptivity in Federated Learning: Convergence and Consistency**

J. Wang, Z. Xu, Z. Garrett, Z. Charles, L. Liu, G. Joshi.**Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learning**

Z. Charles and J. Konečný. AISTATS 2021.**Adaptive Federated Optimization**

S. Reddi, Z. Charles, M. Zaheer, Z. Garrett, K. Rush, J. Konečný, S. Kumar, H. B. McMahan. ICLR 2021.

### 2020

**Advances and Open Problems in Federated Learning**

P. Kairouz, H. B. McMahan, et al. (including Z. Charles).**On the Outsized Importance of Learning Rates in Local Update Methods**

Z. Charles and J. Konečný.

### 2019

**Convergence and Margin of Adversarial Training on Separable Data**

Z. Charles, S. Rajput, S. Wright, D. Papailiopoulos.**DETOX: A Redundancy-based Framework for Faster and More Robust Gradient Aggregation**(arXiv)

S. Rajput, H. Wang, Z. Charles, D. Papailiopoulos. NeurIPS 2019.**Does Data Augmentation Lead to Positive Margin?**(arXiv)

S. Rajput, Z. Feng, Z. Charles, P. Loh, D. Papailiopoulos. ICML, 2019.**A Geometric Perspective on the Transferability of Adversarial Directions**(arXiv)

Z. Charles, H. Rosenberg, D. Papailiopoulos. AISTATS, 2019.**ErasureHead: Distributed Gradient Descent without Delays Using Approximate Gradient Codes**

H. Wang, Z. Charles, D. Papailiopoulos.

### 2018

**ATOMO: Communication-efficient Learning via Atomic Sparsification**(arXiv)

H. Wang, S. Sievert, Z. Charles, S. Liu, S. Wright, D. Papailiopoulos. NeurIPS, 2018.**Stability and Generalization of Learning Algorithms that Converge to Global Optima**(arXiv)

Z. Charles and D. Papailiopoulos. ICML, 2018.**Approximate Gradient Coding via Sparse Random Graphs**(arXiv)

Z. Charles, D. Papailiopoulos, J. Ellenberg.**DRACO: Robust Distributed Training via Redundant Gradients**(arXiv)

L. Chen, H. Wang, Z. Charles, D. Papailiopoulos. ICML, 2018.**Gradient Coding Using the Stochastic Block Model**(arXiv)

Z. Charles and D. Papailiopoulos. ISIT, 2018.**Subspace Clustering with Missing and Corrupted Data**(arXiv)

Z. Charles, A. Jalali, R. Willett. IEEE Data Science Workshop, 2018.**Exploiting Algebraic Structure in Global Optimization and the Belgian Chocolate Problem**(arXiv)

Z. Charles and N. Boston. Journal of Global Optimization, 2018.**Generating Random Factored Ideals in Number Fields**(arXiv)

Z. Charles. Mathematics of Computation, 2018.

### 2017 and earlier

**Algebraic and Geometric Structure in Machine Learning and Optimization Algorithms**(link)

Z. Charles. Ph.D. Thesis, University of Wisconsin-Madison, Dec 2017.**Efficiently Finding All Power Flow Solutions to Tree Networks**

A. Zachariah and Z. Charles. Allerton, 2017.**Nonpositive Eigenvalues of Hollow, Symmetric, Nonnegative Matrices**(arXiv)

Z. Charles, M. Farber, C. R. Johnson, L. Kennedy-Shaffer. SIAM Journal on Matrix Analysis and Applications, 2013.**Nonpositive Eigenvalues of the Adjacency Matrix and Lower Bounds for Laplacian Eigenvalues**(arXiv)

Z. Charles, M. Farber, C. R. Johnson, L. Kennedy-Shaffer. Discrete Mathematics, 2013.**The Relation Between the Diagonal Entries and the Eigenvalues of a Symmetric Matrix, Based upon the Sign Pattern of its Off-Diagonal Entries**

Z. Charles, M. Farber, C. R. Johnson, L. Kennedy-Shaffer. Linear Algebra and its Applications, 2013.