Donghwan Kim

Ahmet Alacaoglu, Donghwan Kim, Stephen J. Wright

We focus on constrained, $L$-smooth, potentially stochastic and nonconvex-nonconcave min-max problems either satisfying $ρ$-cohypomonotonicity or admitting a solution to the $ρ$-weakly Minty Variational Inequality (MVI), where larger values of the parameter $ρ>0$ correspond to a greater degree of nonconvexity. These problem classes include examples in two player reinforcement learning, interaction dominant min-max problems, and certain synthetic test problems on which classical min-max algorithms fail. It has been conjectured that first-order methods can tolerate a value of $ρ$ no larger than $\frac{1}{L}$, but existing results in the literature have stagnated at the tighter requirement $ρ< \frac{1}{2L}$. With a simple argument, we obtain optimal or best-known complexity guarantees with cohypomonotonicity or weak MVI conditions for $ρ< \frac{1}{L}$. First main insight for the improvements in the convergence analyses is to harness the recently proposed $\textit{conic nonexpansiveness}$ property of operators. Second, we provide a refined analysis for inexact Halpern iteration that relaxes the required inexactness level to improve some state-of-the-art complexity results even for constrained stochastic convex-concave min-max problems. Third, we analyze a stochastic inexact Krasnosel'skiĭ-Mann iteration with a multilevel Monte Carlo estimator when the assumptions only hold with respect to a solution.

SangHun Im, Gibaeg Kim, Heung-Seon Oh et al.

Hierarchical text classification (HTC) is essential for various real applications. However, HTC models are challenging to develop because they often require processing a large volume of documents and labels with hierarchical taxonomy. Recent HTC models based on deep learning have attempted to incorporate hierarchy information into a model structure. Consequently, these models are challenging to implement when the model parameters increase for a large-scale hierarchy because the model structure depends on the hierarchy size. To solve this problem, we formulate HTC as a sub-hierarchy sequence generation to incorporate hierarchy information into a target label sequence instead of the model structure. Subsequently, we propose the Hierarchy DECoder (HiDEC), which decodes a text sequence into a sub-hierarchy sequence using recursive hierarchy decoding, classifying all parents at the same level into children at once. In addition, HiDEC is trained to use hierarchical path information from a root to each leaf in a sub-hierarchy composed of the labels of a target document via an attention mechanism and hierarchy-aware masking. HiDEC achieved state-of-the-art performance with significantly fewer model parameters than existing models on benchmark datasets, such as RCV1-v2, NYT, and EURLEX57K.