Bhavya Agrawalla

I am Bhavya Agrawalla, senior in Mathematics (Course 18) and AI and Decision Making (Course 6-4) at the Massachusetts Institute of Technology. I did my first year of undergraduate at the Indian Institute of Science (IISc) Bangalore, after which I transferred to MIT.

My research interests span machine learning (ML) theory, algorithms, and its applications in real-world problems. I will be starting a ML PhD at Carnegie Mellon University School of Computer Science in Fall 2024!

At MIT, I have been extremely lucky to work with-

• Prof. Haynes Miller from the MIT Math Department on homological algebra,
• Prof. Promit Ghosal from Brandeis Math and Prof. Krishnakumar Balasubramaniam from UC Davis Statistics on learning theory, statistics and optimisation,
• Prof. Ramesh Raskar's Camera Culture Group on using reinforcement learning to automate imaging system design,
• Prof. Pulkit Agrawal's Improbable AI lab on reinforcement learning algorithms.

During high school, I represented India at the International Mathematical Olympiad 2019 and won a silver medal. In free time, I like to play badminton and read books.

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Publications and Preprints

Much progress has been made in the last two decades toward understanding the iteration complexity of SGD (in expectation and high-probability) in the learning theory and optimization literature. However, using SGD for high-stakes applications requires careful quantification of the associated uncertainty. Toward that end, in this work, we establish high-dimensional Central Limit Theorems (CLTs) for linear functionals of online least-squares SGD iterates under a Gaussian design assumption. Our main result shows that a CLT holds even when the dimensionality is of order exponential in the number of iterations of the online SGD, thereby enabling high-dimensional inference with online SGD. Our proof technique involves leveraging Berry-Esseen bounds developed for martingale difference sequences and carefully evaluating the required moment and quadratic variation terms through recent advances in concentration inequalities for product random matrices. We also provide an online approach for estimating the variance appearing in the CLT (required for constructing confidence intervals in practice) and establish consistency results in the high-dimensional setting.

Imaging systems consist of cameras to encode visual information about the world and perception models to interpret this encoding. Cameras contain (1) illumination sources, (2) optical elements, and (3) sensors, while perception models use (4) algorithms. Directly searching over all combinations of these four building blocks to design an imaging system is challenging due to the size of the search space. Moreover, cameras and perception models are often designed independently, leading to sub-optimal task performance. In this paper, we formulate these four building blocks of imaging systems as a context-free grammar (CFG), which can be automatically searched over with a learned camera designer to jointly optimize the imaging system with task-specific perception models. By transforming the CFG to a state-action space, we then show how the camera designer can be implemented with reinforcement learning to intelligently search over the combinatorial space of possible imaging system configurations. We demonstrate our approach on two tasks, depth estimation and camera rig design for autonomous vehicles, showing that our method yields rigs that outperform industry-wide standards. We believe that our proposed approach is an important step towards automating imaging system design.

We observe that Beck modules for a commutative monoid are exactly modules over a graded commutative ring associated to the monoid. Under this identification, the Quillen cohomology of commutative monoids is a special case of Andre-Quillen cohomology for graded commutative rings, generalizing a result of Kurdiani and Pirashvili. To verify this we develop the necessary grading formalism. The partial cochain complex developed by Pierre Grillet appears as the start of a modification of the Harrison cochain complex suggested by Michael Barr. We show that Harrison and Quillen cohomology coincide rationally, and thereby establish a cochain complex computing the rational cohomology of a commutative monoid.