Assistant Professor of math and data science @NYU_Courant and @NYUDataScience | Former PhD @stanford_ee, postdoc @SimonsInstitute @mit | views are my own
New York, NY
Joined September 2020
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Great to join @Nived_Rajaraman in pushing lower bounds for bandit convex optimization!
For n-round regret of d-dim convex 1-Lip:
• d^{4/3}√n for n>d^{10/3}, closer to d^{3/2}√n UB
• √d n^{3/4} for d²<n<d^{10/3}: the 20-year-old FKM bound is optimal!
arxiv.org/pdf/2607.18652
I have reformulated Ling’s proof of Samuels’ conjecture using a cap move operation. Check out the note!
yanjunhan2021.github.io/pape…
Preprint by Zhi Ling arxiv.org/abs/2608.18392 claims to prove the more general Samuels conjecture, a strict strengthening of Feige’s conjecture!
Two AI-assisted arXiv preprints today:
arxiv.org/abs/2607.23836: New inequalities on ESPs of centered vectors and matrices, strengthening my recent AOS paper tinyurl.com/h6ft5bra.
arxiv.org/abs/2607.23980: Feige's 1/e conjecture resolved. See my previous post for details!
A super fun weekend project with friends back at Stanford!
TL;DR: With GPT-5.6, we resolved Feige's 1/e conjecture based on a recent calibration result of Vlassis and Thomas, and convex geometry!
Paper link: arxiv.org/abs/2607.23980
My friend Zhengqing used GPT-5.6 to solve a beautiful well-known conjecture in probability.
Feige's 1/e conjecture: for independent nonnegative X_1,…,X_n with E[X_i] ≤ 1 and S_n = X_1+⋯+X_n, we have P(S_n ≤ E[S_n] + 1) ≥ 1/e.
Exciting to see a problem we used to kick around over lunch and dinner get solved! 1/2
Coincidentally, some other teams found it too:
arxiv.org/abs/2607.24528
zenodo.org/records/21622951
An interesting competition in the AI era!
Yanjun Han retweeted
The Price of Hidden Curvature: An widetildeΩ (d⁵/⁴ √T) Lower Bound for Bandit Convex Optimization
Nived Rajaraman
arxiv.org/abs/2607.18652 [𝚜𝚝𝚊𝚝.𝙼𝙻 𝚌𝚜.𝙸𝚃 𝚌𝚜.𝙻𝙶]
ALT We establish a widetildeΩ(d⁵/⁴√ T) lower bound on the minimax expected regret of stochastic bandit convex optimization of 1-Lipschitz functions on the Euclidean ball. This presents the first nontrivial regret lower bound that grows faster than d√T for this problem, establishing that stochastic bandit convex optimization is fundamentally harder than linear bandits. The hard class of convex functions we construct takes the following form in dimension 2d: for an action a = (a¹,a²) ∈ B²ᵈ₂, each function is the scaled soft maximum of a "tube", r⁻¹ ‖W⋆ a¹ - r/8ε a² ‖₂ (hyperparameterized by ε,r), and a squared distance function, ¹⁄₂ ‖a¹ - u⋆ ‖₂² - ¹⁄₂ ‖u⋆ ‖₂². Here, W⋆ ∈ ℝᵈˣᵈ is an unknown linear transformation, and u⋆ ∈ ℝᵈ is an unknown vector which must be learned to minimize the function. Observations are informative about u⋆ only when the learner's action lies near the tube determined by W⋆, satisfying a² ≈ 8ε/r W⋆ a¹: thus the learner must either find this tube without knowing W⋆, or sp
Here are the slides from a recent talk at CDS! yanjunhan2021.github.io/slid…
CDS Asst. Prof. Yanjun Han (@yanjun_han) and colleagues at NYU and MIT explains why transformers trained on synthetic data excel at empirical Bayes (EB) problems.
By using universal priors, these models adapt to new data through posterior contraction.
arxiv.org/abs/2602.15136
Yanjun Han retweeted
Just posted a preprint on arXiv (with P. Durcik, J. Roos, X. Xie) settling the Kahn–Park conjecture on the Hamming cube:
arxiv.org/abs/2602.20462
I first learned about the problem through Gil Kalai’s (@GilKalaiblog) blog:
gilkalai.wordpress.com/2019/…
(I should also add that I was asking about related question "Sharp L1 Poincare inequality for boolean functions" 8-9 years ago
mathoverflow.net/questions/2… and now the preprint solves both of them though these two problems do not imply each other but they are connected).
In addition, it confirms the low-noise limit for balanced functions predicted by the Hellinger conjecture on noisy Boolean channels in information theory.
The paper shows C_{11b}=0.5 in our GitHub repo: github.com/teorth/optimizati…
and answers my recent experimental AI challenge:
nitter.cf/PI010101/status/202618…
(For the record: I received many interesting submissions -- all incorrect, often due to surprisingly simple mistakes. I still don’t know whether there is a proof avoiding the argument in our paper.) But AI did correctly identify the bottleneck that one needs to show C_{11b}=0.5 which is (now was) an open problem.
Finally, many thanks to @AIMathematics -- this project began at our SQuaREs program in San Jose supported by AIM. Without AIM, this would not have happened 🙏
RT @zhun_deng: 🔥 The key isn’t more compute — it’s better allocation.
Test-time self-consistency improves reasoning by sampling multiple t…
New paper alert: arxiv.org/abs/2602.15136
Why do pretrained transformers succeed at empirical Bayes? Rather than analyzing architecture or training dynamics, we ask a statistical question: how can a fixed training prior perform well under arbitrary test distributions? [1/2]
New preprint out: arxiv.org/abs/2509.07355!
For the good old problem of distribution estimation, we use empirical Bayes and nonparametric MLE, two cornerstones of 20th century statistics, to propose a new, efficient, parameter-free, and competitively optimal estimator. [1/3]
Technically, we resolved a decade-old competitive gap in papers.nips.cc/paper/by-sour…, an award-winning paper in NeurIPS 2015. Yihong Wu brought this question to me years ago, and we are so happy to solve it along with two amazing collaborators Jon Niles-Weed and Yandi Shen! [2/3]
A key technical challenge is to show a quantitative mean-field approximation of the best permutation-invariant decision rule by a simple rule. We managed to apply the tools we developed last year arxiv.org/abs/2408.09341 to give tight results in Gaussian and Poisson models! [3/3]
Yanjun Han retweeted

The Fall 2025 CDS PhD Program application is now open! Apply now: cds.nyu.edu/phd-admissions-r…
Information on our Fall 2025 PhD Admissions Information Sessions is coming soon!
#datascience #ai #artificialintelligence #machinelearning
Yanjun Han retweeted
there are surprisingly many open problems when it comes to theory/methods in causal inference
check out this talk by Siva Balakrishnan for an excellent & comprehensive summary of the state of the art
youtube.com/live/Mnum0Ox1f_o…
stat.cmu.edu/~siva/
I haven’t enjoyed the mathematics in a paper this much in a long time: arxiv.org/abs/2408.09341
Summary: an example of performing method-of-moment type analysis for high-dimensional mixtures.
Joint work with my amazing colleague Jonathan Niles-Weed.
Excited for the new journey!
Yanjun Han (@yanjun_han) will be joining CDS this fall as an Assistant Professor of Mathematics and Data Science. Read about Yanjun and his work on the mathematics of data science on the CDS blog!
nyudatascience.medium.com/me…
Apply and work with me if you are interested in the math of data!
Applications for the NYU Data Science PhD program are now open! To apply/find more information, please visit our PhD Admissions page: cds.nyu.edu/phd-admissions-r…. We're excited to welcome the next cohort of leading researchers in data science! #datascience
