Constrained optimization problems are pervasive in various fields, and while conventional techniques offer solutions, they often struggle with scalability. Leveraging the power of deep neural networks (DNNs) in optimization, we present a novel learning-based approach, the Constraint Boundary Wandering Framework (CBWF), to address these challenges. Our contributions include introducing a boundary wandering strategy inspired by the active-set method, enhancing equality constraint feasibility, and treating the Lipschitz constant as a learnable parameter. Additionally, we evaluate the regularization term, illustrating that the nonsmooth L2 norm yields superior results. Extensive testing on synthetic datasets and the ACOPT dataset demonstrates CBWF's superiority, outperforming existing deep learning-based solvers in terms of both objective and constraint loss.

Autonomous vehicles have stridden over the budding stage and are stepping into the phase of large-scale commercial deployment. Nonetheless, safety issues of autonomous driving remain to be fully solved. Sensor data provide the observations of the internal status and the driving environment of the autonomous vehicle, and sensor data anomaly detection is indispensable to ensure the safety since the occurrence of sensor data anomalies indicate potential safety risks. Tremendous works has contributed to the sensor data anomaly detection issue but most of them ignore the trustworthiness estimation of the anomaly detection results, leading to difficulties for decision-making in safety-critical systems. Therefore, this work proposes an uncertainty-aware sensor data anomaly detection method to enhance the trustworthiness of anomaly detection results. Specifically, this method includes a Bayesian LSTM prediction network that outputs both the predicted values and the distribution of the predicted values, an anomaly uncertainty quantification method, and an adaptive thresholding method to improve the anomaly detection performance. Anomaly detection is achieved by capturing the predicted values with high uncertainty. The efficacy and robustness of the proposed methodology have been substantiated through empirical field tests conducted with real-world autonomous driving vehicles. The evaluation yielded a recall of 0.893 and an F1-Score of 0.937, which underscores the superior anomaly detection capabilities of the approach within practical autonomous driving contexts.

In federated learning (FL), a cluster of local clients are chaired under the coordination of the global server and cooperatively train one model with privacy protection. Due to the multiple local updates and the isolated non-iid dataset, clients are prone to overfit into their own optima, which extremely deviates from the global objective and significantly undermines the performance. Most previous works only focus on enhancing the consistency between the local and global objectives to alleviate this prejudicial client drifts from the perspective of the optimization view, whose performance would be prominently deteriorated on the high heterogeneity. In this work, we propose a novel and general algorithm FedSMOO by jointly considering the optimization and generalization targets to efficiently improve the performance in FL. Concretely, FedSMOO adopts a dynamic regularizer to guarantee the local optima towards the global objective, which is meanwhile revised by the global Sharpness Aware Minimization (SAM) optimizer to search for the consistent flat minima. Our theoretical analysis indicates that FedSMOO achieves fast $\mathcal{O}(1/T)$ convergence rate with low generalization bound. Extensive numerical studies are conducted on the real-world dataset to verify its peerless efficiency and excellent generality.

Safe reinforcement learning aims to learn the optimal policy while satisfying safety constraints, which is essential in real-world applications. However, current algorithms still struggle for efficient policy updates with hard constraint satisfaction. In this paper, we propose Penalized Proximal Policy Optimization (P3O), which solves the cumbersome constrained policy iteration via a single minimization of an equivalent unconstrained problem. Specifically, P3O utilizes a simple yet effective penalty approach to eliminate cost constraints and removes the trust-region constraint by the clipped surrogate objective. We theoretically prove the exactness of the penalized method with a finite penalty factor and provide a worst-case analysis for approximate error when evaluated on sample trajectories. Moreover, we extend P3O to more challenging multi-constraint and multi-agent scenarios which are less studied in previous work. Extensive experiments show that P3O outperforms state-of-the-art algorithms with respect to both reward improvement and constraint satisfaction on a set of constrained locomotive tasks.

Modern deep neural networks for classification usually jointly learn a backbone for representation and a linear classifier to output the logit of each class. A recent study has shown a phenomenon called neural collapse that the within-class means of features and the classifier vectors converge to the vertices of a simplex equiangular tight frame (ETF) at the terminal phase of training on a balanced dataset. Since the ETF geometric structure maximally separates the pair-wise angles of all classes in the classifier, it is natural to raise the question, why do we spend an effort to learn a classifier when we know its optimal geometric structure? In this paper, we study the potential of learning a neural network for classification with the classifier randomly initialized as an ETF and fixed during training. Our analytical work based on the layer-peeled model indicates that the feature learning with a fixed ETF classifier naturally leads to the neural collapse state even when the dataset is imbalanced among classes. We further show that in this case the cross entropy (CE) loss is not necessary and can be replaced by a simple squared loss that shares the same global optimality but enjoys a better convergence property. Our experimental results show that our method is able to bring significant improvements with faster convergence on multiple imbalanced datasets.

We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local function is associated with one agent and agents communicate with each other over an undirected connected graph. The problem is non-convex as local functions are possibly non-convex (but smooth) and the Steifel manifold is a non-convex set. We present a decentralized Riemannian stochastic gradient method (DRSGD) with the convergence rate of $\mathcal{O}(1/\sqrt{K})$ to a stationary point. To have exact convergence with constant stepsize, we also propose a decentralized Riemannian gradient tracking algorithm (DRGTA) with the convergence rate of $\mathcal{O}(1/K)$ to a stationary point. We use multi-step consensus to preserve the iteration in the local (consensus) region. DRGTA is the first decentralized algorithm with exact convergence for distributed optimization on Stiefel manifold.

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\sqrt{\kappa})$ and thus achieves the optimal rate among first-order methods, where $\kappa$ is the condition number of the problem. Numerical results on linear regression and logistic regression with elastic net regularization show that GeoPG compares favorably with Nesterov's accelerated proximal gradient method, especially when the problem is ill-conditioned.