Annealing by Increasing Resampling (AIR) is a stochastic hill-climbing optimization by resampling with increasing size for evaluating an objective function. In this paper, we introduce a unified view of the conventional Simulated Annealing (SA) and AIR. In this view, we generalize both SA and AIR to a stochastic hill-climbing for objective functions with stochastic fluctuations, i.e., logit and probit, respectively. Since the logit function is approximated by the probit function, we show that AIR is regarded as an approximation of SA. The experimental results on sparse pivot selection and annealing-based clustering also support that AIR is an approximation of SA. Moreover, when an objective function requires a large number of samples, AIR is much faster than SA without sacrificing the quality of the results.