About

Yu-Jui Huang is an Associate Professor in the Department of Applied Mathematics at the University of Colorado Boulder, CO 80309, USA. The provided page includes his profile, research, teaching, and miscellaneous information, but does not contain detailed biographical or research-specific content. Therefore, no further biographical details are available from the given text.

Research topics

• Computer Science
• Mathematical economics
• Mathematics
• Economics
• Mathematical analysis
• Applied mathematics
• Pure mathematics
• Finance
• Mathematical optimization

Selected publications

• Policy Iteration Achieves Regularized Equilibrium under Time Inconsistency

  Open MIND · 2026-03-06

  preprint1st authorCorresponding

  For a general entropy-regularized time-inconsistent stochastic control problem, we propose a policy iteration algorithm (PIA) and establish its convergence to an equilibrium policy with an exponential convergence rate. The design of the PIA is based on a coupled system of non-local partial differential equations, called the exploratory equilibrium Hamilton--Jacobi--Bellman (EEHJB) equation. As opposed to the standard time-consistent case, policy improvement fails in general and the target value function (now an equilibrium value function) is not even known to exist a priori. To overcome these, we prove that the value functions generated by the PIA form a Cauchy sequence in a specialized Banach space, hence admit a limit, and the rate of convergence is exponential, on the strength of the Bismut--Elworthy--Li formula of stochastic representation. The limiting value function is shown to fulfill the EEHJB equation, which induces an equilibrium policy in a Gibbs form. Such convergence in value additionally implies uniform convergence of the generated policies to the equilibrium policy, again with an exponential rate. As a byproduct, the PIA gives a constructive proof of the global existence and uniqueness of a classical solution to our general EEHJB equation, whose well-posedness has not been explored in the literature.

  DOI

• Policy Iteration Achieves Regularized Equilibrium under Time Inconsistency

  ArXiv.org · 2026-03-06

  articleOpen access1st authorCorresponding

  For a general entropy-regularized time-inconsistent stochastic control problem, we propose a policy iteration algorithm (PIA) and establish its convergence to an equilibrium policy with an exponential convergence rate. The design of the PIA is based on a coupled system of non-local partial differential equations, called the exploratory equilibrium Hamilton--Jacobi--Bellman (EEHJB) equation. As opposed to the standard time-consistent case, policy improvement fails in general and the target value function (now an equilibrium value function) is not even known to exist a priori. To overcome these, we prove that the value functions generated by the PIA form a Cauchy sequence in a specialized Banach space, hence admit a limit, and the rate of convergence is exponential, on the strength of the Bismut--Elworthy--Li formula of stochastic representation. The limiting value function is shown to fulfill the EEHJB equation, which induces an equilibrium policy in a Gibbs form. Such convergence in value additionally implies uniform convergence of the generated policies to the equilibrium policy, again with an exponential rate. As a byproduct, the PIA gives a constructive proof of the global existence and uniqueness of a classical solution to our general EEHJB equation, whose well-posedness has not been explored in the literature.

  PublisherOA PDF

• Convergence of Policy Iteration for Entropy-Regularized Stochastic Control Problems

  SIAM Journal on Control and Optimization · 2025-03-17 · 4 citations

  article1st authorCorresponding
  PublisherDOI

• On optimal solutions of classical and sliced Wasserstein GANs with non-Gaussian data

  ArXiv.org · 2025-09-08

  preprintOpen access1st authorCorresponding

  The generative adversarial network (GAN) aims to approximate an unknown distribution via a parameterized neural network (NN). While GANs have been widely applied in reinforcement and semi-supervised learning as well as computer vision tasks, selecting their parameters often needs an exhaustive search, and only a few selection methods have been proven to be theoretically optimal. One of the most promising GAN variants is the Wasserstein GAN (WGAN). Prior work on optimal parameters for population WGAN is limited to the linear-quadratic-Gaussian (LQG) setting, where the generator NN is linear, and the data is Gaussian. In this paper, we focus on the characterization of optimal solutions of population WGAN beyond the LQG setting. As a basic result, closed-form optimal parameters for one-dimensional WGAN are derived when the NN has non-linear activation functions, and the data is non-Gaussian. For high-dimensional data, we adopt the sliced Wasserstein framework and show that the linear generator can be asymptotically optimal. Moreover, the original sliced WGAN only constrains the projected data marginal instead of the whole one in classical WGAN, and thus, we propose another new unprojected sliced WGAN and identify its asymptotic optimality. Empirical studies show that compared to the celebrated r-principal component analysis (r-PCA) solution, which has cubic complexity to the data dimension, our generator for sliced WGAN can achieve better performance with only linear complexity.

  PublisherOA PDFDOI

• Mean-Field Langevin Diffusions with Density-dependent Temperature

  ArXiv.org · 2025-07-28

  preprintOpen access1st authorCorresponding

  In the context of non-convex optimization, we let the temperature of a Langevin diffusion to depend on the diffusion's own density function. The rationale is that the induced density captures to some extent the landscape imposed by the non-convex function to be minimized, such that a density-dependent temperature provides location-wise random perturbation that may better react to, for instance, the location and depth of local minimizers. As the Langevin dynamics is now self-regulated by its own density, it forms a mean-field stochastic differential equation (SDE) of the Nemytskii type, distinct from the standard McKean-Vlasov equations. Relying on Wasserstein subdifferential calculus, we first show that the corresponding (nonlinear) Fokker-Planck equation has a unique solution. Next, a weak solution to the SDE is constructed from the solution to the Fokker-Planck equation, by Trevisan's superposition principle. As time goes to infinity, we further show that the induced density converges to an invariant distribution, which admits an explicit formula in terms of the Lambert $W$ function. A numerical example suggests that the density-dependent temperature can simultaneously improve the accuracy of and rate of convergence to the estimate of global minimizers.

  PublisherOA PDFDOI

• Incidence of Physical Health Conditions in Autistic Children Within 5 Years After Their Autism Diagnosis

  Autism Research · 2025-08-15 · 1 citations

  article

  This study aimed to investigate the incidence of physical illnesses of autistic young children compared with children in the general population. This population-based study included children (aged ≤ 5 years) with newly diagnosed autism (autism group), followed up for 5 years after their autism diagnoses. Data were collected from Taiwan's National Health Insurance Research Database in the period of 2000-2019. Autistic children (n = 45,680) were matched (1:20; by age and sex [assigned at birth]) with a comparison group from the general population (n = 913,600). We calculated incidence rate ratios (IRRs) for physical illnesses diagnosed within 5 years after autism diagnoses. Data were analyzed using Poisson regression models adjusted for person-time and stratified by sex and the presence/absence of intellectual disabilities. The prevalence of almost all illnesses across major organ systems after 1 year of autism diagnosis was higher in the autism group than in the comparison group. The autism group exhibited significantly elevated incidence of cardiovascular disorders, cerebrovascular disorders, and endocrine diseases within 1 year after autism diagnosis (IRR 2.30-71.42). Although the incidence rates of these illnesses decreased over the 5-year follow-up period in the autism group, they remained higher than those in the comparison group, with most IRRs exceeding 2 in the fifth year after autism diagnosis. The IRRs were significant in both autistic male and female children and those with and without intellectual disabilities, although those with intellectual disabilities displayed descriptively larger IRRs. Autistic young children have heightened risks of being diagnosed with physical illnesses soon after their autism diagnoses. Future research should understand the etiological associations between autism and physical illnesses to offer tailored care from early in life.

  PublisherDOI

• Application of Convolutional Neural Networks in an Automatic Judgment System for Tooth Impaction Based on Dental Panoramic Radiography

  Diagnostics · 2025-05-28 · 1 citations

  articleOpen access

  Background/Objectives: Panoramic radiography (PANO) is widely utilized for routine dental examinations, as a single PANO image captures most anatomical structures and clinical findings, enabling an initial assessment of overall dental health. Dentists rely on PANO images to enhance clinical diagnosis and inform treatment planning. With the advancement of artificial intelligence (AI), the integration of clinical data and AI-driven analysis presents significant potential for supporting medical applications. Methods: The proposed method focuses on the segmentation and localization of impacted third molars in PANO images, incorporating Sobel edge detection and enhancement methods to improve feature extraction. A convolutional neural network (CNN) was subsequently trained to develop an automated impacted tooth detection system. Results: Experimental results demonstrated that the trained CNN achieved an accuracy of 84.48% without image preprocessing and enhancement. Following the application of the proposed preprocessing and enhancement methods, the detection accuracy improved significantly to 98.66%. This substantial increase confirmed the effectiveness of the image preprocessing and enhancement strategies proposed in this study. Compared to existing methods, which achieve approximately 90% accuracy, the proposed approach represents a notable improvement. Furthermore, the entire process, from inputting a raw PANO image to completing the detection, takes only 4.4 s. Conclusions: This system serves as a clinical decision support system for dentists and medical professionals, allowing them to focus more effectively on patient care and treatment planning.

  PublisherOA PDFDOI

• Partial Information in a Mean‐Variance Portfolio Selection Game

  Mathematical Finance · 2025-09-22 · 1 citations

  article1st authorCorresponding

  ABSTRACT This paper considers finitely many investors who perform mean‐variance portfolio selection under relative performance criteria. That is, each investor is concerned about not only her terminal wealth, but how it compares to the average terminal wealth of all investors. At the inter‐personal level, each investor selects a trading strategy in response to others' strategies. This selected strategy additionally needs to yield an equilibrium intra‐personally , so as to resolve time inconsistency among the investor's current and future selves (triggered by the mean‐variance objective). A Nash equilibrium we look for is thus a tuple of trading strategies under which every investor achieves her intra‐personal equilibrium simultaneously. We derive such a Nash equilibrium explicitly in the idealized case of full information (i.e., the dynamics of the underlying stock is perfectly known) and semi‐explicitly in the realistic case of partial information (i.e., the stock evolution is observed, but the expected return of the stock is not precisely known). The formula under partial information consists of the myopic trading and intertemporal hedging terms, both of which depend on an additional state process that serves to filter the true expected return and whose influence on trading is captured by a degenerate Cauchy problem. Our results identify that relative performance criteria can induce downward self‐reinforcement of investors' wealth—if every investor suffers a wealth decline simultaneously, then everyone's wealth tends to decline further. This phenomenon, as numerical examples show, is negligible under full information but pronounced under partial information.

  PublisherDOI

• Oxidative stress associated with indicators of endothelial dysfunction in bipolar disorder

  Psychiatry and Clinical Neurosciences · 2025-05-03

  letterOpen access
  PublisherOA PDFDOI

• Extended-release ketamine tablets for treatment-resistant depression: a randomized placebo-controlled phase 2 trial

  Nature Medicine · 2024-06-24 · 51 citations

  articleOpen accessSenior author

  Ketamine has rapid-onset antidepressant activity in patients with treatment-resistant major depression (TRD). The safety and tolerability of racemic ketamine may be improved if given orally, as an extended-release tablet (R-107), compared with other routes of administration. In this phase 2 multicenter clinical trial, male and female adult patients with TRD and Montgomery-Asberg Depression Rating Scale (MADRS) scores ≥20 received open-label R-107 tablets 120 mg per day for 5 days and were assessed on day 8 (enrichment phase). On day 8, responders (MADRS scores ≤12 and reduction ≥50%) were randomized on a 1:1:1:1:1 basis to receive double-blind R-107 doses of 30, 60, 120 or 180 mg, or placebo, twice weekly for a further 12 weeks. Nonresponders on day 8 exited the study. The primary endpoint was least square mean change in MADRS for each active treatment compared with placebo at 13 weeks, starting with the 180 mg dose, using a fixed sequence step-down closed test procedure. Between May 2019 and August 2021, 329 individuals were screened for eligibility, 231 entered the open-label enrichment phase (days 1-8) and 168 responders were randomized to double-blind treatment. The primary objective was met; the least square mean difference of MADRS score for the 180 mg tablet group and placebo was -6.1 (95% confidence interval 1.0 to 11.16, P = 0.019) at 13 weeks. Relapse rates during double-blind treatment showed a dose response from 70.6% for placebo to 42.9% for 180 mg. Tolerability was excellent, with no changes in blood pressure, minimal reports of sedation and minimal dissociation. The most common adverse events were headache, dizziness and anxiety. During the randomized phase of the study, most patient dosing occurred at home. R-107 tablets were effective, safe and well tolerated in a patient population with TRD, enriched for initial response to R-107 tablets. ClinicalTrials.gov registration: ACTRN12618001042235 .

  PublisherOA PDFDOI

Recent grants

• Topics in Stochastic Control: Finance, Epidemics, and Machine Learning

  NSF · $273k · 2021–2025

• Stochastic Games for Intergenerational Equity in Mathematical Finance

  NSF · $186k · 2017–2021

Frequent coauthors

• Erhan Bayraktar

  Ceva Animal Health (United Kingdom)

  21 shared

• Paolo Guasoni

  10 shared

• Joshua Aurand

  Verus Research (United States)

  9 shared

• Qingshuo Song

  9 shared

• Zhou Zhou

  Sichuan University

  9 shared

• Saeed Khalili

  Fort Lewis College

  9 shared

• Adrien Nguyen‐Huu

  8 shared

• Chin‐Ti Chen

  Institute of Chemistry, Academia Sinica

  7 shared

Education

• Ph.D., Mathematics

  University of California, Los Angeles

  2009

• M.S., Mathematics

  University of California, Los Angeles

  2006

• B.S., Mathematics

  National Tsinghua University

  2004