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We study the problem of load balancing the traffic from a set of unicast and multicast sessions. The problem is formulated as an optimization problem. However, we assume that the gradient of the network cost function is not available and needs to be estimated. Multiple paths are provided between a source and a destination using application-layer overlay. We propose a novel algorithm that is based on what is known as simultaneous perturbation stochastic approximation and utilizes only noisy measurements collected and reported to the sources, using an overlay architecture. We consider three network models that reflect different sets of assumptions regarding multicast capabilities of the network. Using an analytical model we first prove the almost sure convergence of the algorithm to a corresponding optimal solution under each network model considered in this paper with decreasing step sizes. Then, we establish the weak convergence (or convergence in distribution) with a fixed step size. In addition, we investigate the benefits acquired from implementing additional multicast capabilities by studying the relative performance of our algorithm under the three network models.