| Publications about 'artificial intelligence' |
| Books and proceedings |
| Textbook on Artificial Intelligence. Scanned 2005. The complete pdf file is 16 Megabytes. (Libro de texto con introduccion a la inteligencia artificial. El pdf file completo tiene 16 Megabytes.) |
| Articles in journal or book chapters |
| Solutions of optimization problems, including policy optimization in reinforcement learning, typically rely upon some variant of gradient descent. There has been much recent work in the machine learning, control, and optimization communities applying the Polyak-Łojasiewicz Inequality (PLI) to such problems in order to establish an exponential rate of convergence (a.k.a. ``linear convergence'' in the local-iteration language of numerical analysis) of loss functions to their minima under the gradient flow. Often, as is the case of policy iteration for the continuous-time LQR problem, this rate vanishes for large initial conditions, resulting in a mixed globally linear / locally exponential behavior. This is in sharp contrast with the discrete-time LQR problem, where there is global exponential convergence. That gap between CT and DT behaviors motivates the search for various generalized PLI-like conditions, and this paper addresses that topic. Moreover, these generalizations are key to understanding the transient and asymptotic effects of errors in the estimation of the gradient, errors which might arise from adversarial attacks, wrong evaluation by an oracle, early stopping of a simulation, inaccurate and very approximate digital twins, stochastic computations (algorithm ``reproducibility''), or learning by sampling from limited data. We describe an ``input to state stability'' (ISS) analysis of this issue. We also discuss convergence and PLI-like properties of ``linear feedforward neural networks'' in feedback control. Much of the work described here was done in collaboration with Arthur Castello B. de Oliveira, Leilei Cui, Zhong-Ping Jiang, and Milad Siami. This is a short paper summarizing the slides presented at my keynote at the 2025 L4DC (Learning for Dynamics \& Control Conference) in Ann Arbor, Michigan, 05 June 2025. A partial bibliography has been added. |
| Motivated by the growing use of Artificial Intelligence (AI) tools in control design, this paper takes the first steps towards bridging the gap between results from Direct Gradient methods for the Linear Quadratic Regulator (LQR), and neural networks. More specifically, it looks into the case where one wants to find a Linear Feed-Forward Neural Network (LFFNN) feedback that minimizes a LQR cost. This paper starts by computing the gradient formulas for the parameters of each layer, which are used to derive a key conservation law of the system. This conservation law is then leveraged to prove boundedness and global convergence of solutions to critical points, and invariance of the set of stabilizing networks under the training dynamics. This is followed by an analysis of the case where the LFFNN has a single hidden layer. For this case, the paper proves that the training converges not only to critical points but to the optimal feedback control law for all but a set of measure-zero of the initializations. These theoretical results are followed by an extensive analysis of a simple version of the problem (the ``vector case''), proving the theoretical properties of accelerated convergence and robustness for this simpler example. Finally, the paper presents numerical evidence of faster convergence of the training of general LFFNNs when compared to traditional direct gradient methods, showing that the acceleration of the solution is observable even when the gradient is not explicitly computed but estimated from evaluations of the cost function. |
| Conference articles |
| Motivated by the current interest in using Artificial intelligence (AI) tools in control design, this paper takes the first steps towards bridging results from gradient methods for solving the LQR control problem, and neural networks. More specifically, it looks into the case where one wants to find a Linear Feed-Forward Neural Network (LFFNN) that minimizes the Linear Quadratic Regulator (LQR) cost. This work develops gradient formulas that can be used to implement the training of LFFNNs to solve the LQR problem, and derives an important conservation law of the system. This conservation law is then leveraged to prove global convergence of solutions and invariance of the set of stabilizing networks under the training dynamics. These theoretical results are then followed by and extensive analysis of the simplest version of the problem (the ``scalar case'') and by numerical evidence of faster convergence of the training of general LFFNNs when compared to traditional direct gradient methods. These results not only serve as indication of the theoretical value of studying such a problem, but also of the practical value of LFFNNs as design tools for data-driven control applications. |
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