In this work, the problem of multi-object tracking (MOT) is studied, particularly the challenges that arise from object occlusions. A solution based on a principled approximate dynamic programming approach called ADPTrack is presented. ADPTrack relies on existing MOT solutions and directly improves them. When matching tracks to objects at a particular frame, the proposed approach simulates executions of these existing solutions into future frames to obtain approximate track extensions, from which a comparison of past and future appearance feature information is leveraged to improve overall robustness to occlusion-based error. The proposed solution when applied to the renowned MOT17 dataset empirically demonstrates a 0.7% improvement in the association accuracy (IDF1 metric) over a state-of-the-art baseline that it builds upon while obtaining minor improvements with respect to all other metrics. Moreover, it is shown that this improvement is even more pronounced in scenarios where the camera maintains a fixed position. This implies that the proposed method is effective in addressing MOT issues pertaining to object occlusions.