Related papers: Dynamic Programming in Topological Spaces
This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from…
This book is about dynamic programming and its applications in economics, finance, and adjacent fields. It brings together recent innovations in the theory of dynamic programming and provides applications and code that can help readers…
Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming…
Stochastic Programming is a framework for modelling and solving problems of decision making under uncertainty. Stochastic Dynamic Programming is a branch of Stochastic Programming that takes a "functional equation" approach to the discovery…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
In logic programming, dynamic scheduling refers to a situation where the selection of the atom in each resolution (computation) step is determined at runtime, as opposed to a fixed selection rule such as the left-to-right one of Prolog.…
A model of a geometric algorithm is introduced and methodology of its operation is presented for the dynamic partitioning of data spaces.
We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
Differential Dynamic Programming is an optimal control technique often used for trajectory generation. Many variations of this algorithm have been developed in the literature, including algorithms for stochastic dynamics or state and input…
We incorporate safety specifications into dynamic programming. Explicitly, we address the minimization problem of a Markov decision process up to a stopping time with safety constraints. To incorporate safety into dynamic programming, we…
Adaptive dynamic programming is a collective term for a variety of approaches to infinite-horizon optimal control. Common to all approaches is approximation of the infinite-horizon cost function based on dynamic programming philosophy.…
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…
This paper concerns a theoretical approach that combines topological data analysis (TDA) and sheaf theory. Topological data analysis, a rising field in mathematics and computer science, concerns the shape of the data and has been proven…
Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation, in order to open up a new line of attack. Our paper studies this…
We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…