1. A method comprising: generating buyer decision information by presenting a sequence of sale offer menus to a sequence of buyers and conducting actual sale transactions based on sale offers accepted by buyers; and at a selected time in the generating, updating a buyer valuation distribution belief and the current sale offer menu of the sequence of sale offer menus to optimize a buyer's utility comprising a buyer's utility function constrained by a robust learning constraint that is computed based on a local differential of an earlier buyer's utility function with respect to the earlier buyer's valuation.