We investigate the greedy version of the -optimal vector quantization problem for an -valued random vector . We show the existence of a sequence such that minimizes
(-mean quantization error at level induced by ). We show that this sequence produces -rate optimal -tuples (i.e. the -mean quantization error at level induced by goes to at rate . Greedy optimal sequences also satisfy, under natural additional assumptions, the distortion mismatch property: the -tuples remain rate-optimal with respect to the -norms, . Finally, we propose optimization methods to compute greedy sequences, adapted from usual Lloyd’s I and Competitive Learning Vector Quantization procedures, either in their deterministic (implementable when ) or stochastic versions.