Related papers: Maximum Principle Based Algorithms for Deep Learni…

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems,…

Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…

Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches…

We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handle uncertainty, can be solved using dynamic…

In this paper, we address the adversarial training of neural ODEs from a robust control perspective. This is an alternative to the classical training via empirical risk minimization, and it is widely used to enforce reliable outcomes for…

We propose a scalable, policy-centric framework for continuous-time multi-asset portfolio-consumption optimization under inequality constraints. Our method integrates neural policies with Pontryagin's Maximum Principle (PMP) and enforces…

We study the problem of building an efficient learning system. Efficient learning processes information in the least time, i.e., building a system that reaches a desired error threshold with the least number of observations. Building upon…

Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…

We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…

Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…

Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…

This paper aims to study the relationship between the maximum principle and the dynamic programming principle for recursive optimal control problem of stochastic evolution equations, where the control domain is not necessarily convex and…

Deep Reinforcement Learning has enabled the control of increasingly complex and high-dimensional problems. However, the need of vast amounts of data before reasonable performance is attained prevents its widespread application. We employ…

In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam)…

In this paper, an eco--driving Pontryagin maximum principle (PMP) algorithm is designed for optimal deceleration and gear shifting in trucks based on switching among a finite set of driving modes. The PMP algorithm is implemented and…

Most artificial intelligence models have limiting ability to solve new tasks faster, without forgetting previously acquired knowledge. The recently emerging paradigm of continual learning aims to solve this issue, in which the model learns…

In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…

Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety…

When deploying machine learning solutions, they must satisfy multiple requirements beyond accuracy, such as fairness, robustness, or safety. These requirements are imposed during training either implicitly, using penalties, or explicitly,…

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…