Hello! I'm Qiran.
I am a Ph.D. student of Industrial Engineering & Operations Research at University of California, Berkeley. My current research interest lies in the field of parametric optimization and stochastic gradient methods.
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Qiran Dong
GitHub:
@Cumberkid
Email:
Address:
450 Sutardja Dai Hall
University of California
Berkeley, CA 94720
RESEARCH & PROJECTS
2022 - Present
Ph.D.
UNIVERSITY OF CALIFORNIA, BERKELEY
Working paper: ``Beyond Descretization: Learning the Optimal Solution Path,'' with Paul Grigas and Vishal Gupta, submitted to International Conference on Machine Learning (ICML) 2024.
We developed a novel and flexible first-order method to solve the entire solution path in a parametrized optimization problem by prescribing a set of basis functions and using stochastic gradient descent (SGD) with randomized hyperparameters. We proved substantial complexity improvements for our algorithm over traditional grid search methods using probability bounds. Specifically, our method requires O(log(1/ε)) and O(1/ε) gradient calls for exact and noisy gradient oracle models respectively, compared to the best-known grid search schemes which require ~O(ε^(-1/2)) and O(ε^(-3/2))$ gradient calls. In the paper, We demonstrate our method's effectiveness on a weighted logistic regression problem with an imbalanced dataset using PyTorch NN Modules.
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May 2019
Individual Project
AMHERST COLLEGE
I discussed the topological and algebraic construction of Hopf fibration in a joint final project for my Lie algebra and topology class. In this paper, I also gave a visualization of Hopf fibration implemented to a classical homotopy problem, i.e. mapping a 3-sphere to a 2-sphere.
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Jun - Aug 2018
Summer Research
UNIVERSITY OF MARYLAND
I participated in an REU program: Combinatorics and Algorithms for Real Problems (REU-CAAR) where I worked with three colleagues to attack the Hadwiger-Nelson problem. We advanced a probabilistic method initially developed by the Polymath16 project and improved bound for some cases.
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Jun - Aug 2017
Summer Research
MOUNT HOLYOKE COLLEGE
I worked under the mentorship of Professor Timothy Chumley to create a model for a sphere randomly bombarded by air molecules on a horizontal plane using RStudio. I studied how the process is affected by changes in environmental factors such as temperature and sphere mass, and showed the sphere’s behavior was characterized by Brownian motion.
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EDUCATION
2021-Present
Doctor of Philosophy(Ph.D.) in IEOR
UNIVERSITY OF CALIFORNIA, BERKELEY
2019-2021
Master of Science(MS) in Mathematics
NEW YORK UNIVERSITY COURANT INSTITUTE
Relevant coursework during my degree includes Probability Theory, Random Matrix Theory, Differential Geometry, Linear Algebra, Real Variables, Multivariable Analysis, and Complex Variables.
2015-2019
Bachelor of Arts(BA) in Mathematics
Magna Cum Laude
MOUNT HOLYOKE COLLEGE
Relevant coursework during my degree included Probabilistic Combinatorics, Scientific Computing, Stochastic Process, Algorithms, Data Structure, Topology, Lie Algebra, Galois Theory, and Differential Equations.
2017-2018
Graduated with High Honors
BUDAPEST SEMESTERS IN MATHEMATICS
Relevant coursework during my degree included Number Theory, Functional Analysis, Advanced Combinatorics, Graph Theory, Theory of Computing, and Combinatorial Optimization.
EXTRACURRICULUM
MUSIC
Sonata for Two Pianos in F minor, Op.34 by Johannes Brahms, performed with my friend and classmate, Wenfan Jiang, in 2019, at Mount Holyoke College.
DRAWING
I am a fan of DC Comics superheroes and a lover of cats and horses. They appear in most of my drawings.
PHOTOGRAPHY
Taken with iPhone.