Model-Free Unsupervised Learning for Optimization Problems with Constraints

--In many optimization problems in wireless communications, the expressions of objective function or constraints are hard or even impossible to derive, which makes the solutions difficult to find. In this paper, we propose a model-free learning framework to solve constrained optimization problems without the supervision of the optimal solution. Neural networks are used respectively for parameterizing the function to be optimized, parameterizing the Lagrange multiplier associated with instantaneous constraints, and approximating the unknown objective function or constraints. We provide learning algorithms to train all the neural networks simultaneously, and reveal the connections of the proposed framework with reinforcement learning. Numerical and simulation results validate the proposed framework and demonstrate the efficiency of model-free learning by taking power control problem as an example. I NTRODUCTION V arious resource allocation and transceivers in wireless networks, such as power allocation, beamforming, and caching policy, can be designed by solving optimization problems with constraints, say imposed by the maximal transmit power, cache size, and the minimal data rate requirement [1, 2]. Depending on the applications, the objective function, constraints and the policy to be optimized may vary in different timescales.