Related papers: Maximum Principle Based Algorithms for Deep Learni…
In this paper, we adopt a probability distribution estimation perspective to explore the optimization mechanisms of supervised classification using deep neural networks. We demonstrate that, when employing the Fenchel-Young loss, despite…
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we…
We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…
We consider the challenge of finding a deterministic policy for a Markov decision process that uniformly (in all states) maximizes one reward subject to a probabilistic constraint over a different reward. Existing solutions do not fully…
This paper highlights a parallel between the forward backward sweeping method for optimal control and deep learning training procedures. We reformulate a classical optimal control problem, constrained by a differential equation system, into…
The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to…
Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align…
A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based…
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…
Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…
This paper is concerned with devising the nonlinear optimal guidance for intercepting a stationary target with a fixed impact time. According to Pontryagin's Maximum Principle (PMP), some optimality conditions for the solutions of the…
In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…
Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly.…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
In this paper, we propose an efficient implementation of deep policy gradient method (PGM) for optimal control problems in continuous time. The proposed method has the ability to manage the allocation of computational resources, number of…
Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…
In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control.…
We study a continuous time stochastic optimal control problem under partial observations that are available only at discrete time instants. This hybrid setting, with continuous dynamics and intermittent noisy measurements, arises in…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…