I am a 5th year Ph.D. student in the Statistics Department at the University of Michigan advised by Ambuj Tewari. Previously, I studied Computer Science and Chemical Engineering also at UM where I worked with Mahdi Cheraghchi, Sindhu Kutty, and Andrej Lenert.
My research interests lie in the Foundations of Machine Learning and Generative AI. In the past, I worked on online learning/bandits, adversarial robustness, and beyond-worst-case analysis for learning algorithms, among other things. Currently, I am interested in all aspects of post-training for LLMs. In particular, I've worked on inference-time methods, differential privacy, and synthetic data generation, and currently thinking about efficient reasoning.
During the summer of 2024, I interned at Apple with Kunal Talwar and Hilal Asi working on differentially private online learning. In early 2025, I went back to Apple working on test-time alignment and efficient missing mass estimation with Kunal Talwar, Hilal Asi, and Satyen Kale. In the summer of 2025, I was a research intern at Google Research working on differential privacy, LLM evaluation, and synthetic data generation with Matthew Joseph, Travis Dick, and Umar Syed!
I am grateful to be supported by the National Science Foundation Graduate Research Fellowship (NSF GRFP) and the 2025 Apple Scholars in AI/ML PhD Fellowship.
Click here to see my CV. Feel free to reach out to me at vkraman [at] umich.edu.
I am on the industry job market. Please reach out if you think I might be a good fit!
Preprints
- Estimating the (Un)seen: Sample-dependent Mass Estimation
with Vitaly Feldman, Satyen Kale, Kunal Talwar, and Ambuj Tewari
Preprint, 2025. - Online Boosting for Multilabel Ranking with Top-k Feedback
with Daniel T. Zhang, Young Hun Jung, Ambuj Tewari
Preprint, 2020.
In Submission
- Optimal Stopping vs Best-of-N for Inference Time Optimization
with Yusuf Kalayci , Shaddin Dughmi
In Submission, 2025. - Transductive and Learning-Augmented Online Regression
with Shenghao Xie , Samson Zhou
In Submission, 2025. - Missing Mass for DIfferentially Private Domain Discovery
with Matthew Joseph , Travis Dick
In Submission, 2025. - AdaBoN: Adaptive Best-of-N Alignment
with Hilal Asi , Satyen Kale
In Submission, 2025.
Publications
Language Generation
Learning to Choose or Choosing to Learn: Best-of-N vs. Supervised Fine-Tuning for Bit String Generation
with Seamus Somerstep , Unique Subedi , Yuekai Sun
Conference on the Mathematical Theory of Deep Neural Networks (DeepMath), 2025.Generation through the lens of learning theory
with Jiaxun Li , Ambuj Tewari
Conference on Learning Theory (COLT), 2025.Representative Language Generation
with Charlotte Peale , Omer Reingold
International Conference on Machine Learning (ICML), 2025.Generation from Noisy Examples
with Ananth Raman
International Conference on Machine Learning (ICML), 2025.
Differential Privacy
Tracking the Best Expert Privately
with Hilal Asi , Aadirupa Saha
International Conference on Machine Learning (ICML), 2025.Faster Rates for Private Adversarial Bandits
with Hilal Asi, Kunal Talwar
International Conference on Machine Learning (ICML), 2025.
Beyond Worst-case Guarantees for Learning
Online Classification with Predictions
with Ambuj Tewari
Conference on Neural Information Processing Systems (NeurIPS), 2024.Smoothed Online Classification can be Harder than Batch Classification
with Unique Subedi, Ambuj Tewari
Conference on Neural Information Processing Systems (NeurIPS), 2024.Multiclass Transductive Online Learning
with Steve Hanneke, Amirreza Shaeiri, Unique Subedi
Conference on Neural Information Processing Systems (NeurIPS), 2024. Spotlight.On Proper Learnability between Average- and Worst-case Robustness
with Unique Subedi, Ambuj Tewari
Conference on Neural Information Processing Systems (NeurIPS), 2023.
Online Learning
The Complexity of Sequential Prediction in Dynamical Systems
with Unique Subedi, Ambuj Tewari
Conference on Learning for Dynamics and Control (L4DC), 2025. Oral Presentation.A Unified Theory of Supervised Online Learnability
with Unique Subedi, Ambuj Tewari
Conference on Algorithmic Learning Theory (ALT), 2025. Outstanding Paper Award.Online Learning with Set-Valued Feedback
with Unique Subedi, Ambuj Tewari
Conference on Learning Theory (COLT), 2024.Online Infinite-Dimensional Regression: Learning Linear Operators
with Unique Subedi, Ambuj Tewari
Conference on Algorithmic Learning Theory (ALT), 2024.Multiclass Online Learning and Uniform Convergence
with Steve Hanneke, Shay Moran, Unique Subedi, Ambuj Tewari
Conference on Learning Theory (COLT), 2023.Online Agnostic Multiclass Boosting
with Ambuj Tewari
Conference on Neural Information Processing Systems (NeurIPS), 2022.
Partial Feedback
Apple Tasting: Combinatorial Dimensions and Minimax Rates
with Ananth Raman , Unique Subedi, Ambuj Tewari
Conference on Learning Theory (COLT), 2024.Multiclass Online Learnability under Bandit Feedback
with Ananth Raman , Unique Subedi, Idan Mehalel, Ambuj Tewari
Conference on Algorithmic Learning Theory (ALT), 2024.
Multioutput Learning
A Characterization of Multioutput Learnability
with Unique Subedi, Ambuj Tewari
Journal of Machine Learning Research (JMLR), 2024.On the Learnability of Multilabel Ranking
with Unique Subedi, Ambuj Tewari
Conference on Neural Information Processing Systems (NeurIPS), 2023. Spotlight.
Other
- Design of thermophotovoltaics for tolerance of parasitic absorption
with Tobias Burger, Andrej Lenert
Optics Express, 2019.
Projects
I have also been working on more empirical research, especially towards understanding RL for LLMs and the abilities/limitations of the Transformer architecture. Below are some ongoing projects related to these topics:
Talks
- A Unified Theory of Supervised Online Learnability (ALT 2025)
- Generation through the lens of learning theory (Apple 2025)
- Generation through the lens of learning theory (NEU CS Theory Seminar) [slides]
- Generation through the lens of learning theory (STATS 700 Guest Lecture)
- Trichotomies in Online Learnability (Student ML Research Seminar 2024) [slides]
- Trichotomies in Online Learnability (Apple 2024) [slides]
- Revisiting the Learnability of Apple Tasting (MSSISS 2024)
- Multiclass Online Learnability under Bandit Feedback (ALT 2024)
- Multiclass Online Learning and Uniform Convergence (UM EECS Theory Seminar) [slides]
- On Classification-Calibration of Gamma-Phi Losses (COLT 2023) [slides]
Awards and Fellowships
- Apple Scholars in AI/ML PhD Fellowship (2025)
- ALT Outstanding Paper Award (2025)
- MSSISS Best Oral Presentation (2024)
- Outstanding First-year Ph.D. Student (2022)
- NSF Graduate Research Fellowship (2022)
Teaching
I enjoy teaching. Here are a couple courses and organizations that I have taught for in the past:
- PhD Math Preparation Workshop, Fall 2023
- STATS 507 (Data Science using Python), Fall 2022, Winter 2023
- STATS 315 (Introduction to Deep Learning), Winter 2022
- STATS 250 (Introduction to Statistics), Fall 2021
- InspiritAI, Summer 2021
- AI4ALL, Summer 2021
- ChE 330 (Chemical and Engineering Thermodynamics), Winter 2018
Hobbies
Apart from research, I am a big fan of bodybuilding and actively keep up with the Mr. Olympia.