Related papers: Augmented Lagrangian Multiplier Network for State-…

Navigating urban intersections, especially when interacting with heterogeneous traffic participants, presents a formidable challenge for autonomous vehicles (AVs). In such environments, safety risks arise simultaneously from multiple…

Restless Multi-Armed Bandits (RMABs) are a powerful framework for sequential decision-making, widely applied in resource allocation and intervention optimization challenges in public health. However, traditional RMABs assume independence…

Reinforcement Learning (RL) is essentially a trial-and-error learning procedure which may cause unsafe behavior during the exploration-and-exploitation process. This hinders the application of RL to real-world control problems, especially…

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since…

Regularizing Deep Neural Networks (DNNs) is essential for improving generalizability and preventing overfitting. Fixed penalty methods, though common, lack adaptability and suffer from hyperparameter sensitivity. In this paper, we propose a…

We propose both serial and parallel proximal (linearized) alternating direction method of multipliers (ADMM) algorithms for training residual neural networks. In contrast to backpropagation-based approaches, our methods inherently mitigate…

Artificial neural network training with stochastic gradient descent can be destabilized by "bad batches" with high losses. This is often problematic for training with small batch sizes, high order loss functions or unstably high learning…

During initial iterations of training in most Reinforcement Learning (RL) algorithms, agents perform a significant number of random exploratory steps. In the real world, this can limit the practicality of these algorithms as it can lead to…

Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence…

Advanced Air Mobility (AAM) introduces a new, efficient mode of transportation with the use of vehicle autonomy and electrified aircraft to provide increasingly autonomous transportation between previously underserved markets. Safe and…

The safety constraints commonly used by existing safe reinforcement learning (RL) methods are defined only on expectation of initial states, but allow each certain state to be unsafe, which is unsatisfying for real-world safety-critical…

Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…

Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and…

Safe reinforcement learning (RL) seeks to mitigate unsafe behaviors that arise from exploration during training by reducing constraint violations while maintaining task performance. Existing approaches typically rely on a single policy to…

In this paper, we propose a Robbins-Monro augmented Lagrangian method (RMALM) to solve a class of constrained stochastic convex optimization, which can be regarded as a hybrid of the Robbins-Monro type stochastic approximation method and…

Training large language models (LLMs) typically relies on adaptive optimizers like Adam (Kingma & Ba, 2015) which store additional state information to accelerate convergence but incur significant memory overhead. Recent efforts, such as…

Reinforcement learning (RL) agents are vulnerable to adversarial disturbances, which can deteriorate task performance or compromise safety specifications. Existing methods either address safety requirements under the assumption of no…

A preconditioning strategy for the Powell-Hestenes-Rockafellar Augmented Lagrangian method (ALM) is presented. The scheme exploits the structure of the Augmented Lagrangian Hessian. It is a modular preconditioner consisting of two blocks.…

The rapid advancement of machine learning (ML) has led to its increasing integration into cyber-physical systems (CPS) across diverse domains. While CPS offer powerful capabilities, incorporating ML components introduces significant safety…

In this paper, we adopt the augmented Lagrangian method (ALM) to solve convex quadratic second-order cone programming problems (SOCPs). Fruitful results on the efficiency of the ALM have been established in the literature. Recently, it has…