Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for performing a joint simulation for satisfying multiple different coexisting commitments to allocate digital resources. In one aspect, a method includes accessing logged data for prior allocations of digital resources, where the logged data includes at least one property associated with respective allocations of the digital resources. Different allocations of the digital resources included in the logged data are assigned to different ones of the multiple different commitments. For each commitment to allocate digital resources, an expected required resource amount that results in the commitment being allocated at least a specified minimum resource based on the allocations of digital resources of the logged data that were assigned to the multiple different commitments is determined.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for performing a joint simulation for satisfying multiple different coexisting commitments to allocate digital resources. In one aspect, a method includes accessing logged data for prior allocations of digital resources, where the logged data includes at least one property associated with respective allocations of the digital resources. Different allocations of the digital resources included in the logged data are assigned to different ones of the multiple different commitments. For each commitment to allocate digital resources, an expected required resource amount that results in the commitment being allocated at least a specified minimum resource based on the allocations of digital resources of the logged data that were assigned to the multiple different commitments is determined.