US Patent 12106352 Systems and methods for bi-level optimization of stochastic recommendations

An optimized substitution system can include a computing device that is configured to receive a notification indicating an order and a first item identifier and, based on the first item identifier, identify a set of substitute item identifiers. Each substitute item identifier of the set of substitute item identifiers includes a probability value using an optimization computation based on a similarity and a value of the corresponding set of substitute item identifiers and the first item identifier. The similarity and the value are stored in a database. The compute device is also configured to, based on the probability values corresponding to the set of substitute item identifiers, select a first substitute item identifier of the set of substitute item identifiers and update the order to include the first substitute item identifier and exclude the first item identifier.