arXiv subjects

Mohammad Mahdi Ahmadi

Publications and source records attributed to Mohammad Mahdi Ahmadi.

7 recordsLinked to original sources

arXiv2026

Stochastic Dynamic Barrier Perturbed Gradient Methods for Nonconvex Simple Bilevel Optimization

We study stochastic simple bilevel optimization with smooth, possibly nonconvex upper- and lower-level objectives accessed only through stochastic gradient oracles. A key challenge is that the dual multiplier induced by the lower-level constraint may become unbounded near lower-level stationary points, invalidating bounded-dual analyses and destabilizing stochastic gradient estimates. To address this, we propose \emph{Stochastic Dynamic Barrier Perturbed Gradient} (SDBPG), a single-loop method that adaptively perturbs the dual formulation to regularize this degeneracy. The perturbation stabilizes the multiplier and yields controlled bias and variance even near the lower-level stationarity region. Under a rare-visit assumption governed by a parameter $δ\in (0, \tfrac{1}{2}]$, SDBPG finds an $(ε, ε)$-stationary point in $\mathcal{O}(ε^{-1/δ})$ iterations, with sample gradient complexities $\mathcal{O}(ε^{-2/δ})$ and $\mathcal{O}(ε^{-3/δ})$ for the upper- and lower-level objectives, where larger $δ$ corresponds to rarer visits to the bad region describing the negative alignment between the two objectives when the lower-level gradient is small. We further develop PR-SDBPG, a penalty-regularized variant that eliminates the rare-visit assumption, and VR-PR-SDBPG, which improves the resulting sample complexities entirely through variance reduction. To our knowledge, these are the first explicit $(ε_f,ε_g)$-stationarity guarantees for stochastic nonconvex-nonconvex simple bilevel optimization.

math.OC↗

arXiv2026

Memory-Augmented LSTM Autoencoder for Unsupervised Activity Recognition with IMU Sensor Fusion

HAR using Inertial Measurement Unit (IMU) sensors is vital for healthcare monitoring and rehabilitation. Despite deep learning advancements, major challenges remain: reliance on labeled data, multi-sensor fusion complexity, and the limited ability of unsupervised methods to capture spatiotemporal dependencies. These issues are pronounced in real-world scenarios with noisy data, overlapping activities, and missing labels. We propose a fully unsupervised spatiotemporal feature fusion framework using a memory-augmented autoencoder. It enhances activity representations via short temporal windows of multi-sensor IMU data, enabling real-time applications. Our framework extracts hierarchical static features via a Stacked Autoencoder, fusing them within and across sensors. A sequence-to-sequence LSTM Autoencoder then temporally refines these features, incorporating historical motion patterns without labels. We analyze key hyperparameters to identify configurations that maximize feature separability under short-window constraints. Evaluated on DaLiAc and PAMAP2 using realistic inter-class window segmentation, our method achieves 96.6% and 98.4% accuracy, respectively, surpassing supervised baselines and unsupervised approaches. Our method improves feature separability by up to 9% despite shorter temporal windows. While our realistic inter-class segmentation reduces accuracy by ~7%, it was intentionally adopted to better reflect real-world activity transitions and practical relevance.

cs.CV↗

arXiv2026

On the Analysis of Misspecified Variational Inequalities with Nonlinear Constraints

In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods typically follow a decoupled learn-then-optimize scheme, causing the approximation error from the learning to propagate the main decision-making problem and hinder convergence. We instead consider a simultaneous approach that jointly solves the main and secondary VIs. To efficiently handle nonlinear constraints with parameter misspecification, we propose a single-loop inexact Augmented Lagrangian method that simultaneously updates the primal decision variables, dual multipliers, and the misspecified parameter. The method combines a forward-reflected-backward step with an Augmented Lagrangian penalty, and explicitly handles misspecification on both the operator and constraint functions. Moreover, we introduce a relaxed performance metric based on the Minty VI gap combined with an aggregated infeasibility metric. By proving boundedness of the dual iterates, we establish $\mathcal{O}(1/K)$ ergodic convergence rates for these metrics. Numerical Experiments are provided to showcase the superior performance of our algorithm compared to state-of-the-art methods.

math.OC↗

arXiv2025

Simultaneous Learning and Optimization via Misspecified Saddle Point Problems

We study a class of misspecified saddle point (SP) problems, where the optimization objective depends on an unknown parameter that must be learned concurrently from data. Unlike existing studies that assume parameters are fully known or pre-estimated, our framework integrates optimization and learning into a unified formulation, enabling a more flexible problem class. To address this setting, we propose two algorithms based on the accelerated primal-dual (APD) by Hamedani & Aybat 2021. In particular, we first analyze the naive extension of the APD method by directly substituting the evolving parameter estimates into the primal-dual updates; then, we design a new learning-aware variant of the APD method that explicitly accounts for parameter dynamics by adjusting the momentum updates. Both methods achieve a provable convergence rate of $\mathcal{O}(\log K / K)$, while the learning-aware approach attains a tighter $\mathcal{O}(1)$ constant and further benefits from an adaptive step-size selection enabled by a backtracking strategy. Furthermore, we extend the framework to problems where the learning problem admits multiple optimal solutions, showing that our modified algorithm for a structured setting achieves an $\mathcal{O}(1/\sqrt{K})$ rate. To demonstrate practical impact, we evaluate our methods on a misspecified portfolio optimization problem and show superior empirical performance compared to state-of-the-art algorithms.

cs.LG↗

arXiv2025

Single-loop Projection-free and Projected Gradient-based Algorithms for Nonconvex-concave Saddle Point Problems with Bilevel Structure

In this paper, we explore a broad class of constrained saddle point problems with a bilevel structure, wherein the upper-level objective function is nonconvex-concave and smooth over compact and convex constraint sets, subject to a strongly convex lower-level objective function. This class of problems finds wide applicability in machine learning, encompassing robust multi-task learning, adversarial learning, and robust meta-learning. Our study extends the current literature in two main directions: (i) We consider a more general setting where the upper-level function is not necessarily strongly concave or linear in the maximization variable. (ii) While existing methods for solving saddle point problems with a bilevel structure are projection-based algorithms, we propose a one-sided projection-free method employing a linear minimization oracle. Specifically, by utilizing regularization and nested approximation techniques, we introduce a novel single-loop one-sided projection-free algorithm, requiring $\cO(ε^{-4})$ iterations to attain an $ε$-stationary solution, moreover, when the objective function in the upper-level is linear in the maximization component, our result improve to $\cO(ε^{-3})$. Subsequently, we develop an efficient single-loop fully projected gradient-based algorithm capable of achieving an $ε$-stationary solution within $\cO(ε^{-5})$ iterations. This result improves to $\cO(ε^{-4})$ when the upper-level objective function is strongly concave in the maximization component. Finally, we tested our proposed methods against the state-of-the-art algorithms for solving a robust multi-task regression problem to showcase the superiority of our algorithms.

math.OC↗

arXiv2025

CNN Autoencoders for Hierarchical Feature Extraction and Fusion in Multi-sensor Human Activity Recognition

Deep learning methods have been widely used for Human Activity Recognition (HAR) using recorded signals from Iner-tial Measurement Units (IMUs) sensors that are installed on various parts of the human body. For this type of HAR, sev-eral challenges exist, the most significant of which is the analysis of multivarious IMU sensors data. Here, we introduce a Hierarchically Unsupervised Fusion (HUF) model designed to extract, and fuse features from IMU sensors data via a hybrid structure of Convolutional Neural Networks (CNN)s and Autoencoders (AE)s. First, we design a stack CNN-AE to embed short-time signals into sets of high dimensional features. Second, we develop another CNN-AE network to locally fuse the extracted features from each sensor unit. Finally, we unify all the sensor features through a third CNN-AE architecture as globally feature fusion to create a unique feature set. Additionally, we analyze the effects of varying the model hyperparameters. The best results are achieved with eight convolutional layers in each AE. Furthermore, it is determined that an overcomplete AE with 256 kernels in the code layer is suitable for feature extraction in the first block of the proposed HUF model; this number reduces to 64 in the last block of the model to customize the size of the applied features to the classifier. The tuned model is applied to the UCI-HAR, DaLiAc, and Parkinson's disease gait da-tasets, achieving the classification accuracies of 97%, 97%, and 88%, respectively, which are nearly 3% better com-pared to the state-of-the-art supervised methods.

cs.LG↗

arXiv2022

Elderly Fall Detection Using CCTV Cameras under Partial Occlusion of the Subjects Body

One of the possible dangers that older people face in their daily lives is falling. Occlusion is one of the biggest challenges of vision-based fall detection systems and degrades their detection performance considerably. To tackle this problem, we synthesize specifically-designed occluded videos for training fall detection systems using existing datasets. Then, by defining a new cost function, we introduce a framework for weighted training of fall detection models using occluded and un-occluded videos, which can be applied to any learnable fall detection system. Finally, we use both a non-deep and deep model to evaluate the effect of the proposed weighted training method. Experiments show that the proposed method can improve the classification accuracy by 36% for a non-deep model and 55% for a deep model in occlusion conditions. Moreover, it is shown that the proposed training framework can also significantly improve the detection performance of a deep network on normal un-occluded samples.

cs.CV↗