Parallel dynamic programming through rank convergence

The techniques and/or systems described herein implement parallel processing of a dynamic programming problem across stages and/or clusters by breaking dependencies between stages and/or clusters. For instance, the techniques and/or systems may identify dependencies between sub-problems of the dynamic programming problem and group the sub-problems into stages. The techniques and/or systems may also group the stages into clusters (e.g., at least two clusters to be parallel processed). Then, the techniques and/or systems generate one or more solutions to use instead of actual solutions so that the dynamic programming problem can be parallel processed across stages and/or clusters.