In the last years, proportional fairness has attracted attention in the literature on multi-rate IEEE 802.11 WLANs. One way to improve the performance of wireless networks is contention window tuning based on proportional fairness. In this thesis, we investigate how to apply a bandit convex optimization algorithm - a powerful framework for wireless network optimization - to proportional fair resource allocation in wireless networks. We propose an algorithm which is able to learn the optimal slot transmission probability only by monitoring the throughput of the network. We have evaluated the Online Gradient Descent with Sequential Multi-Point Gradient Estimates algorithm both by using the true value of the function to optimize, as well as adding estimation errors by using a network simulator. By means of the proposed algorithm, we provide extensive experimental results which illustrate the sensitivity of the algorithm to different exploration schedules, exploration parameters and gradient descent step size. We also show the sensitivity of the algorithm to noisy gradient estimates. We believe this research can be considered as a practical solution in order to improve the performance of wireless networks, in particular, in commercial WiFi cards.