A Householder-based algorithm for Hessenberg-triangular reduction

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil $A - \lambda B$ requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations regrouped and accumulated into small dense matrices which are subsequently applied using matrix multiplication routines. A non-vanishing fraction of the total flop count must nevertheless still be performed as sequences of overlapping Givens rotations alternately applied from the left and from the right. The many data dependencies associated with this computational pattern leads to inefficient use of the processor and poor scalability. In this paper, we therefore introduce a fundamentally different approach that relies entirely on (large) Householder reflectors partially accumulated into block reflectors, by using (compact) WY representations. Even though the new algorithm requires more floating point operations than the state of the art algorithm, extensive experiments on both real and synthetic data indicate that it is still competitive, even in a sequential setting. The new algorithm is conjectured to have better parallel scalability, an idea which is partially supported by early small-scale experiments using multi-threaded BLAS. The design and evaluation of a parallel formulation is future work

A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems

In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent years, and significant progress has been made in both the theoretical understanding and efficient implementation of various competing algorithms. There are several goals of this manuscript: first, to gather in one place an overview of different approaches for solving large-scale Riccati equations, and to point to the recent advances in each of them. Second, to analyze and compare the main computational ingredients of these algorithms, to detect their strong points and their potential bottlenecks. And finally, to compare the effective implementations of all methods on a set of relevant benchmark examples, giving an indication of their relative performance

AlphaZero: strojno učenje podrškom bez domenskog znanja

U ovom članku ćemo opisati AlphaZero, algoritam tvrtke DeepMind koji tabula rasa (to jest, bez unaprijed implementirane ikakve strategije igranja osim samih pravila) može postići nadljudski učinak u raznovrsnim izazovnim domenama, poput šaha, shogija (japanskog šaha) i igre Go. Predstavljen u [14], ovaj algoritam je uvjerljivo pobijedio ponajbolje svjetske igrače u navedenim trima igrama, a njegovu su izuzetnost šahovski velemajstori usporedili s igrom kakvu bi prezentirala superiorna vanzemaljska vrsta. Stvaranje algoritma koji tabula rasa stječe nadljudsku vještinu u zahtjevnim domenama bio je dugogodišnji cilj umjetne inteligencije te upravo AlphaZero, svojom sposobnošću prilagođavanja raznolikim pravilima igre, predstavlja njegovo ispunjenje i značajan korak naprijed prema ostvarenju općeg sustava za igranje igara. U članku ćemo izložiti osnovne koncepte algoritma AlphaZero, te demonstrirati rezultate dobivene njegovom implementacijom za igru Connect Four (Četiri u nizu) pomoću programskog jezika Python i njegovih dodatnih biblioteka. Za dodatne pojedinosti čitatelja upućujemo na diplomski rad [10]

AlphaZero: strojno učenje podrškom bez domenskog znanja

U ovom članku ćemo opisati AlphaZero, algoritam tvrtke DeepMind koji tabula rasa (to jest, bez unaprijed implementirane ikakve strategije igranja osim samih pravila) može postići nadljudski učinak u raznovrsnim izazovnim domenama, poput šaha, shogija (japanskog šaha) i igre Go. Predstavljen u [14], ovaj algoritam je uvjerljivo pobijedio ponajbolje svjetske igrače u navedenim trima igrama, a njegovu su izuzetnost šahovski velemajstori usporedili s igrom kakvu bi prezentirala superiorna vanzemaljska vrsta. Stvaranje algoritma koji tabula rasa stječe nadljudsku vještinu u zahtjevnim domenama bio je dugogodišnji cilj umjetne inteligencije te upravo AlphaZero, svojom sposobnošću prilagođavanja raznolikim pravilima igre, predstavlja njegovo ispunjenje i značajan korak naprijed prema ostvarenju općeg sustava za igranje igara. U članku ćemo izložiti osnovne koncepte algoritma AlphaZero, te demonstrirati rezultate dobivene njegovom implementacijom za igru Connect Four (Četiri u nizu) pomoću programskog jezika Python i njegovih dodatnih biblioteka. Za dodatne pojedinosti čitatelja upućujemo na diplomski rad [10]