Related papers: Computing Fixpoints of Learned Functions: Chaotic …
Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…
In this work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…
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…
We propose a conversion scheme that turns regret minimizing algorithms into fixed point iterations, with convergence guarantees following from regret bounds. The resulting iterations can be seen as a grand extension of the classical…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…
The Halpern algorithm is a powerful fixed point approximation method for finding the closest point in the fixed point set of a nonexpansive mapping to the initial point. However, in practice, it is not necessarily true that this algorithm…
We analyze the oracle complexity of the stochastic Halpern iteration with minibatch, where we aim to approximate fixed-points of nonexpansive and contractive operators in a normed finite-dimensional space. We show that if the underlying…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
Simple stochastic games can be solved by value iteration (VI), which yields a sequence of under-approximations of the value of the game. This sequence is guaranteed to converge to the value only in the limit. Since no stopping criterion is…
Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…