Planning in partially-observable dynamical systems (such as POMDPs and PSRs) is a computationally challenging task. Popular approximation techniques that have proved successful are point-based planning methods including pointbased value iteration (PBVI), which works by approximating the solution at a finite set of points. These point-based methods typically are anytime algorithms, whereby an in...

In this paper, we establish a fixed point theorem for multi-valued operators in a complete b−metric space using the concept of Berinde and Berinde [9] on multi-valued weak contractions for the Picard iteration in a metric space. Our main result generalizes, extends and improves some of the recent results of Berinde and Berinde [9] as well as those of Daffer and Kaneko [17] and also unifies seve...

Constrained partially observable Markov decision processes (CPOMDPs) extend the standard POMDPs by allowing the specification of constraints on some aspects of the policy in addition to the optimality objective for the value function. CPOMDPs have many practical advantages over standard POMDPs since they naturally model problems involving limited resource or multiple objectives. In this paper, ...

We propose a novel approach to optimize Partially Observable Markov Decisions Processes (POMDPs) defined on continuous spaces. To date, most algorithms for model-based POMDPs are restricted to discrete states, actions, and observations, but many real-world problems such as, for instance, robot navigation, are naturally defined on continuous spaces. In this work, we demonstrate that the value fu...

How to make decisions while the future is full of uncertainties is a major problem shared virtually by every human being including housewives, firm managers, as well as politicians. In this paper we introduce a mathematical programming resolution to the problem, namely multi-stage stochastic programming. An advantage of that approach is obviously that we will be working with a precise, tangible...

Fixed point iteration is a technique that is used in order to compute function for fixed points; fixed point can be given by many different theorems of fixed point iteration. Problems that occur in the field of nonlinear and linear address by the techniques of fixed point iteration. This paper tells about the fixed point iteration techniques and its applicability in different field of engineeri...