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In this paper the infinite horizon optimal regulation problem is solved online for a deterministic control-affine nonlinear dynamical system using the state following (StaF) kernel method to approximate the value function. Unlike…
Artificial neural networks often struggle with catastrophic forgetting when learning multiple tasks sequentially, as training on new tasks degrades the performance on previously learned tasks. Recent theoretical work has addressed this…
This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…
An iterative learning based economic model predictive controller (ILEMPC) is proposed for repetitive tasks in this paper. Compared with existing works, the initial feasible trajectory of the proposed ILEMPC is not restricted to be…
In this work we seek for an approach to integrate safety in the learning process that relies on a partly known state-space model of the system and regards the unknown dynamics as an additive bounded disturbance. We introduce a framework for…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…
Meta learning is a promising solution to few-shot learning problems. However, existing meta learning methods are restricted to the scenarios where training and application tasks share the same out-put structure. To obtain a meta model…
Machine learning is the dominant approach to artificial intelligence, through which computers learn from data and experience. In the framework of supervised learning, a necessity for a computer to learn from data accurately and efficiently…
The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
This paper addresses the study of the hierarchical control for the one-dimensional wave equation in intervals with a moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving. When…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…
Model predictive control can optimally deal with nonlinear systems under consideration of constraints. The control performance depends on the model accuracy and the prediction horizon. Recent advances propose to use reinforcement learning…
A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…
We study a two-player Stackelberg game with incomplete information such that the follower's strategy belongs to a known family of parameterized functions with an unknown parameter vector. We design an adaptive learning approach to…
We study a continuous-time stochastic Stackelberg game in which a leader seeks to accomplish a primary objective while inferring a hidden parameter of a rational follower. The follower solves an entropy-regularized tracking problem and…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach…