Rishabh Dixit

Email : ridixit@ucsd.edu

Office:
APM 1210,
2985 Muir Lane,
UCSD Math,
La Jolla, CA

I am currently a Stefan E. Warschawski (SEW) Math Fellow in the UCSD Math department. My research interests lie at the intersections of nonconvex optimization, statistical signal processing, dynamical systems and control, as well as decentralized optimization. I have broadly worked on the following research themes:

Online learning proximal point algorithms for centralized and decentralized time-varying optimization
Decentralized robust optimization under time-varying adversarial network attacks
Analysis of gradient descent trajectories around saddle points of Morse functions and sharp exit time estimates of trajectories from such regions
Improved curvature-based perturbation of gradient descent in nonconvex Morse functions for faster saddle escape and second-order convergence
Dynamics of a class of Nesterov-type accelerated gradient methods on smooth nonconvex functions over different state spaces, almost sure saddle escape under momentum, and tradeoffs between saddle escape and local minimum convergence for accelerated methods
Volume estimates of the data forging sets arising in machine unlearning algorithms, and sequential hypothesis testing-based methods for auditing multi-step forging mechanisms in machine unlearning
Riemannian optimization on nonconvex-nonconcave minimax landscapes with connections to distributional robustness over Bures-Wasserstein geometry

Education

Rutgers University
Ph.D., Electrical and Computer Engineering, Oct. 2024
Thesis: Gradient Based Methods for Nonconvex Optimization: A Dynamical Systems Viewpoint
Advisors: Prof. Waheed Bajwa, Prof. Mert Gurbuzbalaban
Rutgers University
M.S., Mathematics, Jan. 2023
Advisor: Prof. Yanyan Li
Indian Institute of Technology (IIT), Kanpur
B.Tech., Electrical Engineering, June 2015

Employment

University of California, San Diego
S.E.W. Math Fellow, July 2024-June 2027
Department of Mathematics
Mentor: Prof. Rayan Saab
Department of Electrical Engineering, IIT Kanpur
Senior Project Associate, Feb 2017-Aug 2018
Supervisor: Prof. Ketan Rajawat
EXL Analytics, Gurugram, India
Data Scientist- Product Development, Aug 2015-Jan 2017

Teaching at the University of California, San Diego

MATH 20D : Intro to Differential Equations, Fall 2024 & 2026, Spring 2026
MATH 170B : Intro to Numerical Analysis - nonlinear equations and approximations, Winter & Spring 2025, 2026
MATH 170C : Intro to Numerical Analysis - ordinary differential equations, Spring 2025
MATH 180A : Intro to Probability, Fall 2025

Journal publications and preprints

You can also visit my Google Scholar page for a complete list.

Riemannian ascent--descent for nonconvex nonconcave minimax landscapes: convergence to basin saddle points and applications to distributionally robust optimization, R. Dixit, P. Upadrashta, A. Cloninger. Submitted to JMLR 2026 [arxiv].
RESIST: Resilient Decentralized Learning Using Consensus Gradient Descent, C. Fang*, R. Dixit*, W.U. Bajwa, M. Gurbuzbalaban, preprint 2025 ("*" denotes equal contribution), Transactions on Machine Learning Research (featured certification), 99 pages.
The Measure of Deception: An Analysis of Data Forging in Machine Unlearning, R. Dixit, Y. Hui, R. Saab, Information and Inference, IMA 2026, 60 pages.
Accelerated gradient methods for nonconvex optimization: Escape trajectories from strict saddle points and convergence to local minima, R. Dixit, M. Gurbuzbalaban, W.U. Bajwa, Foundations of Computational Mathematics (FoCM Journal) 2026, pp. 1-173.
Boundary conditions for linear exit time gradient trajectories around saddle points: Analysis and algorithm, R. Dixit, M. Gurbuzbalaban, W.U. Bajwa, IEEE Transactions on Information Theory 2023, pp. 2556-2602.
Exit time analysis for approximations of gradient descent trajectories around saddle points, R. Dixit, M. Gurbuzbalaban, W.U. Bajwa, Information and Inference, IMA 2023, pp. 714-786.
Online learning over dynamic graphs via distributed proximal gradient algorithm, R. Dixit, A.S. Bedi, K. Rajawat, IEEE Transactions on Automatic Control 2020, pp. 5065-5079.
Online learning with inexact proximal online gradient descent algorithms, R. Dixit, A.S. Bedi, R. Tripathi, K. Rajawat, IEEE Transactions on Signal Processing 2019, pp. 1338-1352.

Conference publications

Distributed online learning over time-varying graphs via proximal gradient descent, 58th IEEE Conference on Decision and Control (CDC), Nice, France, pages 2745-2751, 2019, R. Dixit, A. Bedi, K. Rajawat, A. Koppel.
Time varying optimization via inexact proximal online gradient descent, 52nd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, 2018, R. Dixit, A. Bedi, K. Rajawat.
Second order cone programming based localization method for Internet of Things, 4th International Conference on Control, Decision and Information Technologies (CoDIT), Barcelona, Spain, 2017, S. Kumar, R. Dixit, R. Hegde.

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