In this paper, we develop a systematic framework for the time-sequential compression of dynamic probabilistic occupancy grids. Our approach leverages ideas from signal compression theory to formulate an optimization problem that searches for a multi-resolution hierarchical encoder that balances the quality of the compressed map (distortion) with its description size, the latter of which relates to the bandwidth required to reliably transmit the map to other agents or to store map estimates in on-board memory. The resulting optimization problem allows for multi-resolution map compressions to be obtained that satisfy available communication or memory resources, and does not require knowledge of the occupancy map dynamics. We develop an algorithm to solve our problem, and demonstrate the utility of the proposed framework in simulation on both static (i.e., non-time varying) and dynamic (time-varying) occupancy maps.