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We prove local convergence of several notable gradient descent algorithms used in machine learning, for which standard stochastic gradient descent theory does not apply directly. This includes, first, online algorithms for recurrent models…

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

Existing end-to-end autonomous driving (AD) algorithms typically follow the Imitation Learning (IL) paradigm, which faces challenges such as causal confusion and an open-loop gap. In this work, we propose RAD, a 3DGS-based closed-loop…

Randomized neural networks (RaNNs) are attractive for partial differential equations (PDEs) because they replace expensive end-to-end training with a linear least-squares solve over randomized hidden features. Their practical performance,…

It is known that the standard stochastic gradient descent (SGD) optimization method, as well as accelerated and adaptive SGD optimization methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (as,…

We develop provably safe and convergent reinforcement learning (RL) algorithms for control of nonlinear dynamical systems, bridging the gap between the hard safety guarantees of control theory and the convergence guarantees of RL theory.…

The learning rate warmup heuristic achieves remarkable success in stabilizing training, accelerating convergence and improving generalization for adaptive stochastic optimization algorithms like RMSprop and Adam. Here, we study its…

Adaptive optimization methods have been widely used in deep learning. They scale the learning rates adaptively according to the past gradient, which has been shown to be effective to accelerate the convergence. However, they suffer from…

Within the current sphere of deep learning research, despite the extensive application of optimization algorithms such as Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), there remains a pronounced inadequacy in…

In this paper, we present a Deep Reinforcement Learning (RL)-driven Adaptive Stochastic Nonlinear Model Predictive Control (SNMPC) to optimize uncertainty handling, constraints robustification, feasibility, and closed-loop performance. To…

Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. There is an emerging literature on tackling this problem by…

The pursuit of energy-efficient and adaptive artificial intelligence (AI) has positioned neuromorphic computing as a promising alternative to conventional computing. However, achieving learning on these platforms requires techniques that…

In this paper, we consider reinforcement learning of nonlinear systems with continuous state and action spaces. We present an episodic learning algorithm, where we for each episode use convex optimization to find a two-layer neural network…

RMSProp and ADAM continue to be extremely popular algorithms for training neural nets but their theoretical convergence properties have remained unclear. Further, recent work has seemed to suggest that these algorithms have worse…

Adaptive gradient methods, such as AdaGrad, have become fundamental tools in deep learning. Despite their widespread use, the asymptotic convergence of AdaGrad remains poorly understood in non-convex scenarios. In this work, we present the…

Offline reinforcement learning (RL) enables agents to learn policies from fixed datasets, avoiding costly or unsafe environment interactions. However, its effectiveness is often limited by dataset sparsity and the lack of transition overlap…

The use of Reinforcement Learning (RL) agents in practical applications requires the consideration of suboptimal outcomes, depending on the familiarity of the agent with its environment. This is especially important in safety-critical…

In reinforcement learning (RL), it is common to apply techniques used broadly in machine learning such as neural network function approximators and momentum-based optimizers. However, such tools were largely developed for supervised…

We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…

The success of deep learning can be attributed to various factors such as increase in computational power, large datasets, deep convolutional neural networks, optimizers etc. Particularly, the choice of optimizer affects the generalization,…