Demand-Side Management (DSM) systems represent an efficient method to improve the performance of Smart Grid infrastructures by controlling users’ power loads. In this paper, we focus our analysis on fully distributed DSM systems especially designed to reduce the peak demand of groups of residential users. In our proposed scheme, each appliance decides autonomously its scheduling using only limited information on the energy price fixed by the retailer, thus greatly reducing the system complexity as well as the need of information exchanges. We develop two schedule-selection policies based on the Proportional Imitation Rule, where at each iteration all appliances switch to a new schedule with a probability proportional to the cost difference between the actual and cheapest schedules of the previous iteration. We analyze the proposed learning methods based on realistic instances in several use-case scenarios, and show their effectiveness in terms of cost reductions (both local and system-wide) as well as convergence speed to stable and efficient system equilibria.