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Szubert and Jaskowski successfully used temporal difference (TD) learningtogether with n-tuple networks for playing the game 2048. However, we observeda phenomenon that the programs based on TD learning still hardly reach largetiles. In this paper, we propose multi-stage TD (MS-TD) learning, a kind ofhierarchical reinforcement learning method, to effectively improve theperformance for the rates of reaching large tiles, which are good metrics toanalyze the strength of 2048 programs. Our experiments showed significantimprovements over the one without using MS-TD learning. Namely, using 3-plyexpectimax search, the program with MS-TD learning reached 32768-tiles with arate of 18.31%, while the one with TD learning did not reach any. After furthertuned, our 2048 program reached 32768-tiles with a rate of 31.75% in 10,000games, and one among these games even reached a 65536-tile, which is the firstever reaching a 65536-tile to our knowledge. In addition, MS-TD learning methodcan be easily applied to other 2048-like games, such as Threes. Based on MS-TDlearning, our experiments for Threes also demonstrated similar performanceimprovement, where the program with MS-TD learning reached 6144-tiles with arate of 7.83%, while the one with TD learning only reached 0.45%.

Multi-Stage Temporal Difference Learning for 2048-like Games