We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One re...

The Waterfall model has dominated software development for many years, but iteration of processes is catching in. There is now a number of well-established iterative development process models that can be classified according to the levels where iteration is applied. Iteration can improve validation and verification by allowing earlier quality feedback. Moreover, there seems to be a secret marr...

A key problem in reinforcement learning for control with general function approximators (such as deep neural networks and other nonlinear functions) is that, for many algorithms employed in practice, updates to the policy or Q-function may fail to improve performance—or worse, actually cause the policy performance to degrade. Prior work has addressed this for policy iteration by deriving tight ...

Policy Iteration (PI) is a widely-used family of algorithms for computing an optimal policy for a given Markov Decision Problem (MDP). Starting with an arbitrary initial policy, PI repeatedly updates to a dominating policy until an optimal policy is found. The update step involves switching the actions corresponding to a set of “improvable” states, which are easily identified. Whereas progress ...

We propose a unified approach to disk-based search for deterministic, non-deterministic, and probabilistic (MDP) settings. We provide the design of an external Value Iteration algorithm that performs at most O(lG · scan(|E|) + tmax · sort(|E|)) I/Os, where lG is the length of the largest back-edge in the breadth-first search graph G having |E| edges, tmax is the maximum number of iterations, an...

Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital computers. We prove that under a certain generic assumption the proposed algorithm converges. We also estimate the error after N iterations and the running ...

Programming by demonstration (PBD) utilizes a human teacher to train a computer system to perform tasks within that system. This technique effectively improves productivity for many tasks, in many domains. Many tasks are repetitive in nature; these can be learned by PBD by recognizing the repetitions and generalizing these to iterative programs. We present a domain-independent approach to itera...

We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point iteration. Important applications are the Picard iteration and partitioned fluid structure interaction. We prove that the iteration converges irrespective of ho...

In this paper we demonstrate that a number of fixed point iteration problems can be solved using a modified Krasnoselskij iteration process, which is much simpler to use than the other iteration schemes that have been defined. 2008 Elsevier Inc. All rights reserved. For maps with a slow enough growth rate, the Banach contraction principle provides the existence and uniqueness of the fixed point...