This paper introduces the Point-Based Value Iteration (PBVI) algorithm for POMDP planning. PBVI approximates an exact value iteration solution by selecting a small set of representative belief points, and planning for those only. By using stochastic trajectories to choose belief points, and by maintaining only one value hyperplane per point, it is able to successfully solve large problems, incl...

In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical method calculates successive square roots. In this article, a new algorithm is presented that relies on the computation of successive matrix exponentials. Conver...

In this paper we propose a derivative-free iterative method for the approximate solution of a nonlinear inverse problem Fx = y. In this method the iterations are defined as Gxk+1 = Gxk +(Sy−SFxk), where G is an easily invertible operator and S is an operator from a data space to a solution space. We give general suggestions for the choice of operators G and S and show a practically relevant exa...

We develop a point based method for solving finitely nested interactive POMDPs approximately. Analogously to point based value iteration (PBVI) in POMDPs, we maintain a set of belief points and form value functions composed of only those value vectors that are optimal at these points. However, as we focus on multiagent settings, the beliefs are nested and the computation of the value vectors re...

Recent research on point-based approximation algorithms for POMDPs demonstrated that good solutions to POMDP problems can be obtained without considering the entire belief simplex. For instance, the Point Based Value Iteration (PBVI) algorithm [Pineau et al., 2003] computes the value function only for a small set of belief states and iteratively adds more points to the set as needed. A key comp...

A new general composite implicit random iteration scheme with perturbed mapping is proposed and obtain necessary and sufficient conditions for strong convergence of proposed iteration scheme to random fixed point of a finite family of random nonexpansive mappings are obtained.

Powerdomains are used both when describing the semantics of non-deterministic programming languages and when doing abstract interpretation of deterministic programming languages. In the latter case, the restrictions imposed on sets in the usual powerdomain constructions can lead to less precise results than desired. We show a variant of the Plotkin (convex) powerdomain which impose fewer restri...

For the singular saddle-point problems with nonsymmetric positive definite (1, 1) block, we present a general constraint preconditioning (GCP) iteration method based on a singular constraint preconditioner. Using the properties of the Moore-Penrose inverse, the convergence properties of the GCP iteration method are studied. In particular, for each of the two different choices of the (1, 1) bloc...

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

The power iteration is a classical method for computing the eigenvector associated with the largest eigenvalue of a matrix. The subspace iteration is an extension of the power iteration where the subspace spanned by n largest eigenvectors of a matrix, is determined. The natural power iteration is an exemplary instance of the subspace iteration, providing a general framework for many principal s...