We consider unconstrained stochastic optimization problems with no available gradient information. Such arise in settings from derivative-free simulation to reinforcement learning. propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of function evaluations within a common random number framework. develop modified versions norm test and inner...

It has been known that the Schwarzschild-de Sitter (Sch-dS) black hole may not be in thermal equilibrium and also found to thermodynamically unstable standard thermodynamics. In present work, we investigate possibility realize thermodynamical stability of Sch-dS as an effective system by using R\'{e}nyi statistics, which includes non-extensive nature holes. Our results indicate non-extensivity ...

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation the gradient potential function. In several real-world scenarios, obtaining evaluations might either be computationally expensive, or simply impossible. this work, we propose analyze stochastic zeroth-order algorithms discretizing overdamped unde...

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method pos...

We analyze the phase diagram of the zeroth Landau level of bilayer graphene, taking into account the realistic effects of screening of the Coulomb interaction and strong mixing between two degenerate sublevels. We identify robust quantum Hall states at filling factors ν=-1, -4/3, -5/3, -8/5, -1/2 and discuss the nature of their ground states, collective excitations, and relation to the more fam...