Highlighted projects

A selection of research and side projects spanning distributed learning, formalized mathematics, coding theory, and space communications.

Decentralized online learning without learning rates

Tuning learning rates is a major pain point in online learning. In the decentralized setting, the problem is harder because nodes must coordinate with one another and may have different optimal learning rates.

In this work, we proposed a decentralized online learning method that does not require learning rates and achieves sublinear network regret bounds. To do this, we extended the parameter-free framework from Francesco Orabona and Dávid Pál with a gossip consensus scheme. We also developed a new betting-function framework that is easier to analyze and that we believe is of independent interest.

Our analysis requires a linear gossip schedule—in learning round t, we perform t rounds of gossip—to achieve sublinear regret bounds, which is impractical. In every experiment, however, a constant number of gossip rounds works well. We conjecture that the linear schedule is an artifact of our analysis and that a constant schedule is sufficient, but proving this remains an open problem.

The code for this project is available on GitHub.

Decentralized learning. Each node can communicate only with its neighbors; there is no central server.

Privacy-preserving error feedback for distributed learning

Practical distributed learning often uses aggressive, biased compression for communication from clients to the server. Guaranteeing convergence, however, typically requires client-specific control variates for error feedback.

Per-client control variates undermine privacy guarantees and scale poorly with the number of clients. To address this, we proposed a framework that uses previous aggregated client updates for feedback. This permits highly aggressive compression without the privacy and scaling problems of client-specific control variates. The open-source code is available on GitHub.

Compressed aggregate error feedback block diagram.

Truly decentralized learning on directed graphs

Decentralized optimization algorithms typically require bidirectional communication between nodes.

For directed networks and non-convex losses, existing algorithms required each node to know how many listeners it had—its out-degree. We proposed a line of work that avoids this requirement.

The framework also naturally accommodates network delays: we can add imaginary nodes to model delayed communication and use the same analysis to obtain convergence guarantees.

An example of a directed graph with delays. The imaginary nodes (dashed) model communication delays.

Asynchronous federated learning meets compression

In 2021, Meta announced FedBuff, a system for asynchronous federated learning with buffered aggregation. In plain terms, the server waits for a certain number of client updates and then averages the updates in the buffer.

Its analysis did not consider communication compression, a key component of practical federated learning systems. We proposed an algorithm with a similar buffered asynchronous structure and a hidden-state feedback mechanism that supports highly aggressive communication compression.

We proved that the algorithm behaves nicely with respect to the compression parameter: the asynchrony and compression error cross-terms are negligible in the convergence rate.

Our analysis also revealed and fixed a bug in the original FedBuff convergence proof, without requiring its bounded-gradient assumption. Independently, Mohammad Taha Toghani and César A. Uribe proposed another fix, though without considering compression.

Logistic regression with our proposed algorithm. As in the synchronous regime, more local steps mean faster convergence to a more suboptimal point.

Proving stuff with Lean

On the side, I enjoy theorem proving with Lean and would like to formalize more of my proofs with it. I used to organize a group for people in the greater Los Angeles area to learn how to write mathematical proofs in Lean. I have contributed to Compfiles, Sphere-Packing, and OrderedSemigroups, among other projects.

Error-correcting codes from generalized quadrangles

Together with Simeon Ball, we developed a method to construct point-line incidence matrices for several families of generalized quadrangles in polynomial time. The running times have degrees 4, 6, and 11 depending on the family—high, but still an improvement over existing exponential methods.

Using these constructions, we built what is, to our knowledge, the largest repository of point-line incidence matrices for generalized quadrangles. The matrices are also quasi-cyclic, a desirable property when constructing error-correcting codes from generalized quadrangles. The repository includes matrices in the .alist format for running LDPC simulations.

Visualization of GQ(2,2).

Maintaining communication while entering the Martian atmosphere

During the Entry, Descent, and Landing phase of rover missions to Mars, communication is lost because of the large Doppler shift caused by the spacecraft’s rapid deceleration in the Martian atmosphere. During my time at JPL, we proposed a system that tracks this Doppler shift to maintain communications throughout the phase.

This system will be implemented in the next generation of NASA’s spacecraft radios.

As part of this work, we also derived an analytical approximation for the frequency-error standard deviation of phase-locked loops, which is of independent interest.

Mars Entry, Descent, and Landing. Our system helps most during peak deceleration.

Just for fun

I also built a Snake game in Java.

If you’re an NBA nerd, check out Hardwood Heuristics, where I look at whether common basketball tropes are backed by data.