We consider a policy gradient algorithm applied to finite-arm bandit problem with Bernoulli rewards. allow learning rates depend on the current state of rather than using deterministic time-decreasing rate. The forms Markov chain probability simplex. apply Foster–Lyapunov techniques analyze stability this chain. prove that, if are well-chosen, then is transient chain, and converges optimal arm ...

Let X be a reflexive Banach space such that for any x 6= 0 the set {x∗ ∈ X∗ : ‖x∗‖ = 1 and x∗(x) = ‖x‖} is compact. We prove that any unrestricted product of of a finite number of (W ) contractions on X converges weakly. Recall a (bounded) linear operator on a Banach space X is said to be contraction if ‖Tx‖ ≤ ‖x‖ for all x ∈ X . T is said to satisfy condition (W ) if {xn} is bounded and ‖xn‖ −...

We prove that, in all finite generic extensive-form games of perfect information, a continuous-time best response dynamic always converges to a Nash equilibrium component. We show the robustness of convergence by an approximate best response dynamic: whatever the initial state and an allowed approximate best response dynamic, the state is close to the set of Nash equilibria most of the time. In...

We study some finite time transport properties of isotropic Brownian flows. Under a certain nondegeneracy condition on the potential spectral measure, we prove that uniform shrinking or expansion of balls under the flow over some bounded time interval can happen with positive probability. We also provide a control theorem for isotropic Brownian flows with drift. Finally, we apply the above resu...

We introduce and analyze a space-time least-squares method associated with the unsteady Navier–Stokes system. Weak solution in two dimensional case regular three are considered. From any initial guess, we construct minimizing sequence for functional which converges strongly to of After finite number iterations related value viscosity coefficient, convergence is quadratic. Numerical experiments ...

in this study, the performance of an irreversible regenerative brayton cycle is sought through power maximizations using finite-time thermodynamic concept in finite-size components. optimizations are performed using a genetic algorithm. in order to take into account the finite-time and finite-size concepts in the current problem, a dimensionless mass-flow rate parameter is used to deploy time v...

in this paper, an advanced formulation of the spectral finite element method (sfem) is presented and applied in order to carry out site response analysis of 2d topographic structures subjected to vertically propagating incident in-plane waves in time-domain. the accuracy, efficiency and applicability of the formulation are demonstrated by solving some wave scattering examples. a numerical param...

Abstract Let X and Y be two independent random walks on Z with zero mean and finite variances, and let Lt(X,Y ) be the local time of X −Y at the origin at time t. We show that almost surely with respect to Y , Lt(X,Y )/ log t conditioned on Y converges in distribution to an exponential random variable with the same mean as the distributional limit of Lt(X,Y )/ log t without conditioning. This q...

Consider a one dimensional stepping stone model with colonies of size M and per generation migration probability ν, or a voter model on Z in which interactions occur over a distance of order K. Sample one individual at the origin and one at L. We show that if Mν/L and L/K2 converge to positive finite limits, then the genealogy of the sample converges to a pair Brownian motions that coalesce aft...