Reinforcement learning algorithms need to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces. This is known as the curse of dimensionality. By projecting the agent’s state onto a low-dimensional manifold, we can represent the state space in a smaller and more efficient representation. By using this representation during learning, the...

We analyze a diffuse interface type approximation, known as the diffuse domain approach, of a linear coupled bulk-surface elliptic PDE system. The well-posedness of the diffuse domain approximation is shown using weighted Sobolev spaces and we prove that the solution to the diffuse domain approximation converges weakly to the solution of the coupled bulk-surface elliptic system as the approxima...

(3) { zn = βnxn + (1− βn)Txn, xn+1 = αnxn + (1− αn)Tzn, n ≥ 0, where the initial guess x0 is taken arbitrarily and {αn}n=0 and {βn} are sequences in the interval [0, 1]. In general not much has been known regarding the convergence of the iteration processes (1)-(3) unless the underlying space X has nice properties which we briefly mention here. The iteration process (1) has been proved to be st...

Convergence rates results for Tikhonov regularization of nonlinear ill-posed operator equations in abstract function spaces require the handling of both smoothness conditions imposed on the solution and structural conditions expressing the character of nonlinearity. Recently, the distinguished role of variational inequalities holding on some level sets was outlined for obtaining convergence rat...

Waveform relaxation algorithms for partial diierential equations (PDEs) are traditionally obtained by discretizing the PDE in space and then splitting the discrete operator using matrix splittings. For the semidiscrete heat equation one can show linear convergence on unbounded time intervals and superlinear convergence on bounded time intervals by this approach. However the bounds depend in gen...

This paper presents a new stochastic approach for solving combinatorial optimization problems by using a new selection method, i.e. SA-selection, in genetic algorithm (GA). This approach combines GA with simulated annealing (SA) to improve the performance of GA. GA and SA have complementary strengths and weaknesses. While GA explores the search space by means of population of search points, it ...

In this paper, we investigate sparsity regularization for electrical impedance tomography (EIT). Here, we combine sparsity regularization with the energy functional approach. The main results of our paper is the well-posedness and convergence rates of the sparsity regularization method.

A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence struct...

While significant theoretical and experimental progress has been made in the development of neural networkbased systems for the autonomous identification and control of space platforms, there remain important unresolved issues associated with the reliable prediction of convergence speed and the avoidance of inordinately slow convergence. Focusing here on autonomous identification of lightly dam...