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A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The method explicitly determines an affine…

Reinforcement Learning with Verifiable Rewards (RLVR), which uses simple binary feedback to post-train large language models, has found significant empirical success. However, a principled understanding of why it works is lacking. This…

Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…

Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing…

Recently, reinforcement learning (RL) is receiving more and more attentions due to its successful demonstrations outperforming human performance in certain challenging tasks. In our recent paper `primal-dual Q-learning framework for LQR…

The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…

Motivated by recent advances of reinforcement learning and direct data-driven control, we propose policy gradient adaptive control (PGAC) for the linear quadratic regulator (LQR), which uses online closed-loop data to improve the control…

We consider solutions to the linear quadratic Gaussian (LQG) regulator problem via policy gradient (PG) methods. Although PG methods have demonstrated strong theoretical guarantees in solving the linear quadratic regulator (LQR) problem,…

Recent work on data-driven control and reinforcement learning has renewed interest in a relative old field in control theory: model-free optimal control approaches which work directly with a cost function and do not rely upon perfect…

Online safe reinforcement learning (RL) involves training a policy that maximizes task efficiency while satisfying constraints via interacting with the environments. In this paper, our focus lies in addressing the complex challenges…

The field of artificial neural network (ANN) training has garnered significant attention in recent years, with researchers exploring various mathematical techniques for optimizing the training process. In particular, this paper focuses on…

State-of-the-art results in large language models (LLMs) often rely on scale, which becomes computationally expensive. This has sparked a research agenda to reduce these models' parameter counts and computational costs without significantly…

The importance of Reinforcement Learning from Human Feedback (RLHF) in aligning large language models (LLMs) with human values cannot be overstated. RLHF is a three-stage process that includes supervised fine-tuning (SFT), reward learning,…

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all…

Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rules of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the…

In recent years, artificial neural networks have developed into a powerful tool for addressing a multitude of problems for which classical solution approaches reach their limits. However, it is still unclear why gradient descent…

Transient energy growth of flow perturbations is an important mechanism for laminar-to-turbulent transition that can be mitigated with feedback control. Linear quadratic optimal control strategies have shown some success in reducing…

This paper is concerned with the design of algorithms based on systems of interacting particles to represent, approximate, and learn the optimal control law for reinforcement learning (RL). The primary contribution is that convergence rates…

In this paper, we propose a geometric framework to analyze the convergence properties of gradient descent trajectories in the context of linear neural networks. We translate a well-known empirical observation of linear neural nets into a…

Optimal control theory and machine learning techniques are combined to formulate and solve in closed form an optimal control formulation of online learning from supervised examples with regularization of the updates. The connections with…