相关论文: Dynamic Programming and Linear Programming for Odd…

This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…

We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…

We consider a dynamic programming (DP) approach to approximately solving an infinite-horizon constrained Markov decision process (CMDP) problem with a fixed initial-state for the expected total discounted-reward criterion with a…

Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…

There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both…

The idea of dynamic programming (DP), proposed by Bellman in the 1950s, is one of the most important algorithmic techniques. However, in parallel, many fundamental and sequentially simple problems become more challenging, and open to a…

It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…

This paper provides new conditions for dynamic optimality in discrete time and uses them to establish fundamental dynamic programming results for several commonly used recursive preference specifications. These include Epstein-Zin…

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…

Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…

The rate vs. distance problem is a long-standing open problem in coding theory. Recent papers have suggested a new way to tackle this problem by appealing to a new hierarchy of linear programs. If one can find good dual solutions to these…

Dynamic programming (DP) is a fundamental tool used across many engineering fields. The main goal of DP is to solve Bellman's optimality equations for a given Markov decision process (MDP). Standard methods like policy iteration exploit the…

This paper explores the use of Answer Set Programming (ASP) in solving Distributed Constraint Optimization Problems (DCOPs). The paper provides the following novel contributions: (1) It shows how one can formulate DCOPs as logic programs;…

A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…

Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…

We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the…

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use…

In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered, whose properties are studied in this article, may be used to model the optimal…

This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…