Related papers: Approximating Fixpoints of Approximated Functions
The need for recognition/approximation of functions in terms of elementary functions/operations emerges in many areas of experimental mathematics, numerical analysis, computer algebra systems, model building, machine learning, approximation…
We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by "controlled" Markov noise. In particular, the faster and slower recursions have non-additive controlled Markov noise…
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e.\ operators whose range are sets…
The use of approximation is fundamental in computational science. Almost all computational methods adopt approximations in some form in order to obtain a favourable cost/accuracy trade-off and there are usually many approximations that…
We study fixpoints of operators on lattices. To this end we introduce the notion of an approximation of an operator. We order approximations by means of a precision ordering. We show that each lattice operator O has a unique most precise or…
Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When…
This paper studies systematic exploration for reinforcement learning with rich observations and function approximation. We introduce a new model called contextual decision processes, that unifies and generalizes most prior settings. Our…
A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that…
We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
We study a stochastically perturbed version of the well-known Krasnoselski--Mann iteration for computing fixed points of nonexpansive maps in finite dimensional normed spaces. We discuss sufficient conditions on the stochastic noise and…
Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable…
Nonnegative matrix factorization (NMF), which is the approximation of a data matrix as the product of two nonnegative matrices, is a key issue in machine learning and data analysis. One approach to NMF is to formulate the problem as a…