In this work we propose a general framework for the structured perturbation analysis of several classes of structured matrix polynomials in homogeneous form, including complex symmetric, skew-symmetric, even and odd matrix polynomials. We introduce structured backward errors for approximate eigenvalues and eigenvectors and we construct minimal structured perturbations such that an approximate e...

Dec-POMDPs are a powerful framework for planning in multiagent systems, but are provably intractable to solve. Despite recent work on scaling to more agents by exploiting weak couplings in factored models, scalability for unrestricted subclasses remains limited. This paper proposes a factored forward-sweep policy computation method that tackles the stages of the problem one by one, exploiting w...

A weakness of classical Markov decision processes is that they scale very poorly due to the flat state-space representation. Factored MDPs address this representational problem by exploiting problem structure to specify the transition and reward functions of an MDP in a compact manner. However, in general, solutions to factored MDPs do not retain the structure and compactness of the problem rep...

We are interested in the problem of planning for factored POMDPs. Building on the recent results of Kearns, Mansour and Ng, we provide a planning algorithm for fac-tored POMDPs that exploits the accuracy-eeciency tradeoo in the belief state simplii-cation introduced by Boyen and Koller.

Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to compute for large models, and most approximations either require an expensive iterative procedure or make crude approximations to the curvature. We present K...

Approximate linear programming (ALP) is as one of the most promising methods for solving complex factored MDPs. The method was applied first to tackle problems with discrete state variables. More recently the ALP methods that can solve MDPs with continuous and hybrid (both continuous and discrete) variables have emerged. This paper briefly reviews the work on ALP methods for such problems.

We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach. We formulate the problem as an infinite-dimensional linear programming (LP) problem on measures and its dual on continuous functions. Then we approximate the LP by a hierarchy of finitedimensional semidefinite programming (SDP) programs on moments of...

on the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. the convergence of vn to the analytical solution is also proved. ...

We survey recent papers on the problem of backward dynamics in economics, providing along the way a glimpse at the economics perspective, a discussion of the economic models and mathematical tools involved, and a list of applicable literature in both mathematics and economics. Lı́mites inversos, Economı́a y Dinámica Regresiva Resumen. Examinamos artı́culos recientes sobre el problema de la dinámic...