Optimization & Variational Methods

Optimal Mixing Time for Log-Concave Sampling

KLS Conjecture (Kannan–Lovász–Simonovits)

Posed by Ravi Kannan, László Lovász, Miklós Simonovits (1995)

Multiple Risk Control Beyond Sequential Order: Graph-Structured Dependencies

Posed by Joshi, Sun, Hassani, and Dobriban (2025)

Smoothed Complexity of the Simplex Method

Posed by Spielman & Teng (implicit) (2004)

Minimax Rate for Wasserstein Distance Estimation in High Dimensions

Does the score-matched optimal convex estimator attain the full semiparametric efficiency bound?

Sourced from the work of Oliver Y. Feng, Yu-Chun Kao, Min Xu, Richard J. Samworth

Quantify and characterize the efficiency gap induced by convex-loss restriction for non-log-concave errors

Sourced from the work of Oliver Y. Feng, Yu-Chun Kao, Min Xu, Richard J. Samworth

Optimal Break-Point Estimation Rate in Grouped Time-Varying Network VAR

Sourced from the work of Degui Li, Bin Peng, Songqiao Tang, Wei Biao Wu

Full Multiple-Break Theory for Latent Group Structure and Coefficients

Sourced from the work of Degui Li, Bin Peng, Songqiao Tang, Wei Biao Wu

Asymptotic Normality of Spectrum-Aware Debiasing Beyond Right-Rotationally Invariant Designs

Sourced from the work of Yufan Li, Pragya Sur

Theory for Debiased PCR Under General Covariate Models

Sourced from the work of Yufan Li, Pragya Sur

Overparameterized optimal subsample size for infinite-ensemble subagging

Sourced from the work of Takuya Koriyama, Pratik Patil, Jin-Hong Du, Kai Tan, Pierre C. Bellec

Nonasymptotic guarantees for bagged regularized M-estimators

Sourced from the work of Takuya Koriyama, Pratik Patil, Jin-Hong Du, Kai Tan, Pierre C. Bellec

Extension beyond convex differentiable-loss framework

Sourced from the work of Takuya Koriyama, Pratik Patil, Jin-Hong Du, Kai Tan, Pierre C. Bellec

State evolution for gradient descent beyond the mean-field scaling

Sourced from the work of Qiyang Han, Xiaocong Xu

Sharp characterization of misspecification robustness for debiased GD inference

Sourced from the work of Qiyang Han, Xiaocong Xu

Generalization-error estimation beyond Gaussian designs

Sourced from the work of Pierre C Bellec, Kai Tan

Early-stopping optimality without a U-shape risk assumption

Sourced from the work of Pierre C Bellec, Kai Tan

Critical SNR for outlier emergence at fixed summary statistics

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Small-SNR no-outlier regime and monotonicity in SNR

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Sharp dynamic emergence thresholds for XOR/multilayer GMM classification

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Outlier theory beyond non-degeneracy/invertibility assumptions (ReLU and zero diagonal entries)

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Outlier characterization for unbounded link functions (e.g., phase retrieval)

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Regret Minimization in Heavy-Tailed Bandits with Unknown Distributional Parameters

Posed by Gianmarco Genalti et al. (2025)

What is the Complexity of Joint Differential Privacy in Linear Contextual Bandits?

Posed by Achraf Azize et al. (2024)

Black-Box Reductions and Adaptive Gradient Methods for Nonconvex Optimization

Posed by Xinyi Chen et al. (2024)

Optimal Rates for Stochastic Decision-Theoretic Online Learning Under Differentially Privacy

Posed by Bingshan Hu et al. (2024)

Anytime Convergence Rate of Gradient Descent

Posed by Guy Kornowski et al. (2024)

Order Optimal Regret Bounds for Kernel-Based Reinforcement Learning

Posed by Sattar Vakili (2024)

Convergence of single-timescale mean-field Langevin descent-ascent for two-player zero-sum games

Posed by Guillaume Wang et al. (2024)

Polynomial linearly-convergent method for g-convex optimization?

Posed by Christopher Criscitiello et al. (2023)

Regret Bounds for Noise-Free Kernel-Based Bandits

Posed by Sattar Vakili (2022)

Do you pay for Privacy in Online learning?

Posed by Amartya Sanyal et al. (2022)

Finite-Time Instance Dependent Optimality for Stochastic Online Learning with Feedback Graphs

Posed by Teodor Vanislavov Marinov et al. (2022)

Is There an Online Learning Algorithm That Learns Whenever Online Learning Is Possible?

Posed by Steve Hanneke (2021)

Tight Online Confidence Intervals for RKHS Elements

Posed by Sattar Vakili et al. (2021)

Can Single-Shuffle SGD be Better than Reshuffling SGD and GD?

Posed by Chulhee Yun et al. (2021)

Model Selection for Contextual Bandits

Posed by Dylan J. Foster et al. (2020)

Tight Convergence of SGD in Constant Dimension

Posed by Tomer Koren et al. (2020)

Fast and Optimal Online Portfolio Selection

Posed by Tim Van Erven et al. (2020)

Risk of Ruin in Multiarmed Bandits

Posed by Filipo S. Perotto et al. (2019)

The Oracle Complexity of Convex Optimization with Limited Memory

Posed by Blake Woodworth et al. (2019)