We propose a nonparametric data-driven algorithm called DDM for the management of stochastic periodicreview multi-product inventory systems with a warehouse-capacity constraint. The demand distribution is not known a priori and the firm only has access to past sales data (often referred to as censored demand data). We measure performance of DDM through regret, the difference between the total expected cost of DDM and that of an oracle with access to the true demand distribution acting optimally. We characterize the rate of convergence guarantee of DDM. More specifically, we show that the average expected T -period cost incurred under DDM converges to the optimal cost at the rate of O(1/ √ T ). Our asymptotic analysis significantly generalizes approaches used in Huh and Rusmevichientong (2009) for the uncapacitated single-product inventory systems. We also discuss several extensions and conduct numerical experiments to demonstrate the effectiveness of our proposed algorithm.