In this paper we derive convergence rates for Q-learning. We show an interesting relationship between the convergence rate and the learning rate used in Q-learning. For a polynomial learning rate, one which is 1/t at time t where ω ∈ (1/2, 1), we show that the convergence rate is polynomial in 1/(1− γ), where γ is the discount factor. In contrast we show that for a linear learning rate, one whi...

In this paper, the mathematical model of HIV infection for CD8+ T-cells is illustrated. The homotopy analysis method and the Laplace transformations are combined for solving this model. Also, the convergence theorem is proved to demonstrate the abilities of presented method for solving non-linear mathematical models. The numerical results for $N=5, 10$ are presented. Several $hbar$-c...

T his paper is to study the convergence of per capita income. Convergence clubs hypothesis is one of the forms of convergence hypotheses, implying that countries with the same initial level of economic development, technology, and government policies, tend to be similar in per capita income and thus have a tendency to cluster around a small number of poles. In order to test the hypot...

T he purpose of this study is to analyze the effect of foreign direct investment and portfolio investment on the convergence occurrence of economic growth of countries in the ASEAN + 3 region and to determine the time or speed required to achieve convergence. The type of data used in this research is secondary data panel which is combination between time series data and cross-section...

Here we will present some deeper results in renewal theory such as a central limit theorem for counting processes, stationary versions of renewal processes, renewal equations, the key renewal theorem, weak convergence. 1 Central limit theorem for counting processes Consider a renewal process {t n : n ≥ 1} with iid interarrival times X n = t n − t n−1 , n ≥ 0, such that 0 < E(X) = 1/λ < ∞ and 0 ...

For an invertible diagonal matrix D , the convergence of the power scaled matrix sequence N N D A  is investigated. As a special case, necessary and sufficient conditions are given for the convergence of N N D T  , where T is triangular. These conditions involve both the spectrum as well as the diagraph of the matrix T . The results are then used to privide a new proof for the convergence of ...

T he purpose of this paper is the evaluation of suitability ofspatial error STAR model for modeling convergence of social welfare of Iran's provinces between 2000 and 2013. In this paper the LM tests show that the non-linear method is appropriate for convergence evaluation. In addition, the results indicate that 2 groups of provinces are separable: group 1 in which the social welfare...

We extend the classic convergence rate theory for subgradient methods to apply to non-Lipschitz functions. For the deterministic projected subgradient method, we present a global O(1/ √ T ) convergence rate for any convex function which is locally Lipschitz around its minimizers. This approach is based on Shor’s classic subgradient analysis and implies generalizations of the standard convergenc...

Keywords: Baskakov-Szász operators Modulus of continuity Asymptotic formula Simultaneous approximation Statistical convergence Bounded variation a b s t r a c t In the present paper, we introduce generalized Baskakov-Szász type operators and study some approximation properties of these operators e.g., rate of convergence in ordinary and simultaneous approximation, statistical convergence and th...

In this article we study various convergence results for a class of nonlinear fractional heat equations of the form ⎧ ⎨ ⎩ ut(t, x)− I[u(t, ·)](x) = f(t, x), (t, x) ∈ (0, T )× Rn, u(0, x) = u0(x), x ∈ Rn, where I is a nonlocal nonlinear operator of Isaacs type. Our aim is to study the convergence of solutions when the order of the operator changes in various ways. In particular, we consider zero...