arXiv subjects

Miaolan Xie

Publications and source records attributed to Miaolan Xie.

11 recordsLinked to original sources

arXiv2026

PoseShield: Neural Collision Fields for Human Self-Collision Resolution

Self-collision remains a persistent challenge in SMPL-based human pose estimation and motion generation. Under extreme articulations or stochastic motion synthesis, generated meshes frequently exhibit self-penetrations, leading to physically implausible results. We propose PoseShield, a neural collision constraint defined directly in SMPL pose space. We formulate collision correction as a constrained optimization problem and connect the learned constraint with the Eikonal equation. Enforcing Eikonal regularization ensures non-vanishing gradients near the collision boundary, improving numerical stability and robustness of the optimization process. Unlike prior methods that operate in the mesh space or rely on heuristic penalties, our approach operates directly in the low-dimensional space of human poses and is theoretically grounded. The same learned constraint extends to human motion sequences, providing a generator-agnostic post-hoc collision corrector without retraining the underlying motion model. Experiments on a newly constructed SMPL pose benchmark show that our method achieves a 95.8% success rate and outperforms state-of-the-art baselines.

cs.CV↗

arXiv2026

An Adaptive Proximal Framework for Stochastic Weakly Convex Optimization

Many nonsmooth, nonconvex objectives in learning and signal recovery are $ρ$-weakly convex. We minimize such a function when the weak-convexity parameter $ρ$ is unknown and only stochastic candidate and function-difference information is available. We propose the Adaptive Prox-Guided Scheme (APS), a single-trial framework that adapts the proximal parameter online and bidirectionally through a noisy descent test. APS attains a high-probability $O(\varepsilon^{-2})$ iteration bound for Moreau-envelope stationarity. The result allows biased, heavy-tailed function-difference estimates, while the candidate oracle need only be sufficiently accurate with constant probability when the proximal parameter is small and may be arbitrary otherwise. APS does not need to identify which case applies. A model-based extension covers adaptive proximal-point, prox-linear, and proximal-gradient methods. When the oracles are exact, the same analysis yields a deterministic $O(\varepsilon^{-2})$ bound and, for the proximal-point instance, an $\varepsilon$-subgradient stationary point.

math.OC↗

arXiv2026

Optimizing Treatment Allocation to Maximize the Health of a Population

Recent shifts in global health priorities have positioned Population Health Management (PHM) as a central area of focus. However, optimizing PHM strategies presents several challenges: managing high-dimensional patient covariates, tracking their evolution and long-term response to interventions, and accounting for the inflow and outflow of individuals within the population. In this paper, we propose a novel approach based on Measurized MDPs that integrates these components. We consider a setting in which a treatment with population-level benefits is available but scarce, and model an MDP that optimizes the long-term distribution of the healthcare population under expected capacity constraints. This formulation allows us to bypass both the dimensionality and practical challenges of handling and tracking individual patient covariates across the population. To ensure ethical compliance, we introduce a non-maleficence constraint that limits the allowable mortality rate. To solve the resulting infinite-dimensional problem, we use ADP and reduce the task to identifying a finite set of high-performing treated and untreated patients. Despite the complexity of the underlying structure, our approach yields a simple, clinically implementable index policy: a patient is selected for treatment if their adjusted impactability exceeds a specified threshold. The adjusted impactability captures the long-term consequences of receiving or not receiving treatment. While straightforward to apply, the policy remains flexible and can incorporate general machine learning models. Using CMS data, we show that our policy yields a statistically significant improvement over a myopic benchmark. This advantage increases with the time horizon, consistent with the forward-looking nature of our policy. At the longest horizon tested, this corresponds to over 1,500 additional home days annually per 1,000 patients.

math.OC↗

arXiv2025

Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis

We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed noise. This setting captures challenging scenarios where both gradient and function value estimates can be unreliable, making it applicable to many real-world problems, which can have outliers and data anomalies. We introduce an algorithmic and analytical framework that provides high-probability bounds on iteration complexity for this setting. The analysis offers a unified approach, encompassing methods such as line search and trust region.

math.OC↗

arXiv2025

First- and Second-Order Stochastic Adaptive Regularization with Cubics: High Probability Iteration and Sample Complexity

We present high-probability (and expectation) complexity bounds for two versions of stochastic adaptive regularization methods with cubics (SARC), also known as regularized Newton methods. The first algorithm aims to find first-order stationary points, while the second targets second-order optimality conditions. Both methods employ stochastic zeroth-, first-, and second-order oracles with specific accuracy and reliability requirements. These oracles, which have been previously used with other stochastic adaptive methods like trust-region and line-search algorithms, are applicable to various optimization settings including expected risk minimization and simulation optimization. In this paper, we establish the first high-probability iteration and sample complexity bounds for both first- and second-order SARC algorithms. Our analysis demonstrates that as in the deterministic case, they outperform other stochastic adaptive methods.

math.OC↗

arXiv2024

A Sequential Quadratic Programming Method with High Probability Complexity Bounds for Nonlinear Equality Constrained Stochastic Optimization

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic approximations of the objective function and its associated derivatives can be computed via inexact probabilistic zeroth- and first-order oracles. Under reasonable assumptions, a high-probability bound on the iteration complexity of the algorithm to approximate first-order stationarity is derived. Numerical results on standard nonlinear optimization test problems illustrate the advantages and limitations of our proposed method.

math.OC↗

arXiv2024

A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers

We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an expectation, and hence one can design a quasi-Newton method to exploit common random numbers. In contrast, and motivated by problems in variational quantum algorithms, we assume that function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles and no common random numbers can be exploited. Our algorithmic framework -- based on prior work on the SASS algorithm -- is general and does not assume common random numbers. We derive a high-probability tail bound on the iteration complexity of the algorithm for nonconvex and strongly convex functions. We present numerical results demonstrating the empirical benefits of augmenting SASS with our quasi-Newton updating scheme, both on synthetic problems and on real problems in quantum chemistry.

math.OC↗

arXiv2023

High Probability Complexity Bounds for Adaptive Step Search Based on Stochastic Oracles

We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient method and its many variants, the algorithm does not use a pre-specified sequence of step sizes but increases or decreases the step size adaptively according to the estimated progress of the algorithm. These oracles capture multiple standard settings including expected loss minimization and zeroth-order optimization. Moreover, our framework is very general and allows the function and gradient estimates to be biased. The proposed algorithm is simple to describe and easy to implement. Under fairly general conditions on the oracles, we derive a high probability tail bound on the iteration complexity of the algorithm when it is applied to non-convex, convex, and strongly convex (more generally, those satisfying the PL condition) functions. Our analysis strengthens and extends prior results for stochastic step and line search methods.

math.OC↗

arXiv2023

Sample Complexity Analysis for Adaptive Optimization Algorithms with Stochastic Oracles

Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic oracles. Unlike the majority of stochastic methods, these methods do not use a pre-specified sequence of step size parameters, but adapt the step size parameter according to the estimated progress of the algorithm and use it to dictate the accuracy required from the stochastic approximations. The requirements on stochastic approximations are, thus, also adaptive and the oracle costs can vary from iteration to iteration. The step size parameters in these methods can increase and decrease based on the perceived progress, but unlike the deterministic case they are not bounded away from zero due to possible oracle failures, and bounds on the step size parameter have not been previously derived. This creates obstacles in the total complexity analysis of such methods, because the oracle costs are typically decreasing in the step size parameter, and could be arbitrarily large as the step size parameter goes to 0. Thus, until now only the total iteration complexity of these methods has been analyzed. In this paper, we derive a lower bound on the step size parameter that holds with high probability for a large class of adaptive stochastic methods. We then use this lower bound to derive a framework for analyzing the expected and high probability total oracle complexity of any method in this class. Finally, we apply this framework to analyze the total sample complexity of two particular algorithms, STORM and SASS, in the expected risk minimization problem.

math.OC↗

arXiv2022

ControlBurn: Nonlinear Feature Selection with Sparse Tree Ensembles

ControlBurn is a Python package to construct feature-sparse tree ensembles that support nonlinear feature selection and interpretable machine learning. The algorithms in this package first build large tree ensembles that prioritize basis functions with few features and then select a feature-sparse subset of these basis functions using a weighted lasso optimization criterion. The package includes visualizations to analyze the features selected by the ensemble and their impact on predictions. Hence ControlBurn offers the accuracy and flexibility of tree-ensemble models and the interpretability of sparse generalized additive models. ControlBurn is scalable and flexible: for example, it can use warm-start continuation to compute the regularization path (prediction error for any number of selected features) for a dataset with tens of thousands of samples and hundreds of features in seconds. For larger datasets, the runtime scales linearly in the number of samples and features (up to a log factor), and the package support acceleration using sketching. Moreover, the ControlBurn framework accommodates feature costs, feature groupings, and $\ell_0$-based regularizers. The package is user-friendly and open-source: its documentation and source code appear on https://pypi.org/project/ControlBurn/ and https://github.com/udellgroup/controlburn/.

stat.ML↗

arXiv2021

ControlBurn: Feature Selection by Sparse Forests

Tree ensembles distribute feature importance evenly amongst groups of correlated features. The average feature ranking of the correlated group is suppressed, which reduces interpretability and complicates feature selection. In this paper we present ControlBurn, a feature selection algorithm that uses a weighted LASSO-based feature selection method to prune unnecessary features from tree ensembles, just as low-intensity fire reduces overgrown vegetation. Like the linear LASSO, ControlBurn assigns all the feature importance of a correlated group of features to a single feature. Moreover, the algorithm is efficient and only requires a single training iteration to run, unlike iterative wrapper-based feature selection methods. We show that ControlBurn performs substantially better than feature selection methods with comparable computational costs on datasets with correlated features.

cs.LG↗