Almost-Zero Duality Gaps in Model-Free Resource Allocation for Wireless Systems

We investigate optimal resource management in wireless systems, directly in the model-free setting. Starting with a generic resource allocation task formulated as a variational program with nonconvex stochastic constraints, we leverage classical results on Gaussian smoothing to formulate a finite dimensional, smoothed problem surrogate, effectively solvable in a model-free fashion, without the need of a baseline system model. Further assuming a near-universal policy parameterization, we present explicit upper and lower bounds on the gap between the optimal value of the original variational problem, and the dual optimal value of the smoothed surrogate. In fact, we show that this duality gap depends linearly on smoothing and near-universality parameters, and therefore, it can be made arbitrarily small at will. Our results effectively quantify the effects of both policy parameterization and smoothing on approximating both the value and optimal solution of the original variational program via surrogate dualization, and provide explicit near-optimality guarantees in the model-free regime. We also provide empirical illustration via indicative numerical simulations.