32 research outputs found
On Testing the Simulation Theory
Can the theory that reality is a simulation be tested? We investigate this question
based on the assumption that if the system performing the simulation is nite
(i.e. has limited resources), then to achieve low computational complexity, such a
system would, as in a video game, render content (reality) only at the moment that
information becomes available for observation by a player and not at the moment of
detection by a machine (that would be part of the simulation and whose detection
would also be part of the internal computation performed by the Virtual Reality
server before rendering content to the player). Guided by this principle we describe
conceptual wave/particle duality experiments aimed at testing the simulation theory
Primal-dual accelerated gradient methods with small-dimensional relaxation oracle
In this paper, a new variant of accelerated gradient descent is proposed. The
pro-posed method does not require any information about the objective function,
usesexact line search for the practical accelerations of convergence, converges
accordingto the well-known lower bounds for both convex and non-convex
objective functions,possesses primal-dual properties and can be applied in the
non-euclidian set-up. Asfar as we know this is the rst such method possessing
all of the above properties atthe same time. We also present a universal
version of the method which is applicableto non-smooth problems. We demonstrate
how in practice one can efficiently use thecombination of line-search and
primal-duality by considering a convex optimizationproblem with a simple
structure (for example, linearly constrained)
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
New Version of Mirror Prox for Variational Inequalities with Adaptation to Inexactness
18 pages, 5 figures, X International Conference Optimization and Applications (OPTIMA-2019) dedicated to the 80th anniversary of Academician Yury G. EvtushenkoPetrovac, Montenegro, September 30 - October 4, 2019Some adaptive analogue of the Mirror Prox method for variational inequalities is proposed. In this work we consider the adaptation not only to the value of the Lipschitz constant, but also to the magnitude of the oracle error. This approach, in particular, allows us to prove a complexity near for variational inequalities for a special class of monotone bounded operators. This estimate is optimal for variational inequalities with monotone Lipschitz-continuous operators. However, there exists some error, which may be insignificant. The results of experiments on the comparison of the proposed approach with some known analogues are presented. Also, we discuss the results of the experiments for matrix games in the case of using non-Euclidean proximal setup