I am working towards my PhD in Electrical Engineering department at Arizona State University. Currently, I am working with Prof. Gautam Dasarathy on the intersection between graphs and optimization.
Previously, I was holding the position of Systems Engineer at Netradyne . I was working on using sensor information from Mobile devices/IMU chips to draw out statistics on the general driving behavior of an individual to develop better driver safety features.
I have dual degree (B.Tech + M.Tech) from Electrical Department at IIT Madras. I did my Senior thesis under the guidance of Dr. Radha Krishna Ganti on the broad topic Rank Preserving optimization using Factored Gradient Descent. My thesis work can be found here
PhD in Electrical Engineering, 2022
Arizona State University
M.Tech in Communication, 2016
Indian Institute of Technology, Madras
B.Tech in Electrical Engineering, 2015
Indian Institute of Technology, Madras
We consider the problem of recovering a complex vector from m quadratic measurements. This problem, known as quadratic feasibility, encompasses the well known phase retrieval problem and has applications in a wide range of important areas including power system state estimation and x-ray crystallography. In general, not only is the the quadratic feasibility problem NP-hard to solve, but it may in fact be unidentifiable. In this paper, we establish conditions under which this problem becomes identifiable, and further prove isometry properties in the case when the matrices are Hermitian matrices sampled from a complex Gaussian distribution. Moreover, we explore a nonconvex optimization formulation of this problem, and establish salient features of the associated optimization landscape that enables gradient algorithms with an arbitrary initialization to converge to a globally optimal point with a high probability. Our results also reveal sample complexity requirements for successfully identifying a feasible solution in these contexts.
Recently, due to the increasing size of the data matrices, it has become more and more computationally expensive to operate of such matrices. We suggest some additional thoughts as to how to reduce this computational complexity. First, we suggest the possibility of cutting down on the number of projection operation in a normal constrained optimization setting and thereby cutting down on some of the vary taxing operations on matrices. We also indicate the benefits of limitations of this approach Second, we more to a specific notorious constraint i.e. rank constraint. We study the minimization of function $f(X)$ over the set of all $n * m$ matrices when we are supposed to satisfy a constraint rank=r. We propose a algorithm on the lines of Factored Gradient descent (FGD) and show its theoretical convergence and simulation results.
Motivated by applications in competitive WiFi sensing, and competition to grab user attention in social networks, the problem of when to arrive at/sample a shared resource/server platform with multiple players is considered. Server activity is intermittent, with the server switching between between ON and OFF periods alternatively. Each player spends a certain cost to sample the server state, and due of competition, the per-player service rate is inversely proportional to the number of connected/ arrived players. The objective of each player is to arrive/ sample the server as soon as any ON period begins while incurring minimal sensing cost and to avoid having many other players overlap in time with itself. For this competition model, we propose a distributed randomized learning algorithm (strategy to sample the server) for each player, which is shown to converge to a unique non-trivial fixed point. The fixed point is moreover shown to be a Nash equilibrium of a sensing game, where each player’s utility function is demonstrated to possess all the required selfishness tradeoffs