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A novel framework for the online learning of expected cost-to-go functions characterizing wireless networks performance is proposed. The framework is based on the observation that wireless protocols induce structured and correlated behavior of the Finite State Machine (FSM) modeling the operations of the network. As a result, a significant dimension reduction can be achieved by projecting the cost-to-go function on a graph wavelet basis set capturing typical sub-structures in the graph associated with the FSM. Sparse approximation with random projection is then used to identify a concise set of coefficients representing the cost-to-go function in the wavelet domain. This Compressed Sensing (CS) approach enables a considerable reduction in the number of observations needed to achieve an accurate estimate of the cost-to-go function.
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