Modern intelligent systems highly depends on their capabilities to learn from experience and takecontrol actions in uncertain environments. In this paper, we propose a random walk approach for ana-lyzing the performance of learning and control of intelligent systems. We show that in many situations,the learning and control problem can be formulated as a random walk in a hyperspace with stoppingboundary deˉned by parameters of learning and control policies. We show that the performance ofthe intelligent systems can be measured by a function of the stopping time and associated values ofstochastic processes. Under some mild regularity conditions, we demonstrate that the performancemeasure follows stochastic functional laws of the iterated logarithm as the parameters of learning andcontrol policies tend to certain values.
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