Multi-Stage Temporal Difference Learning for 2048-like Games

TL;DR

This paper introduces multi-stage TD learning, a hierarchical reinforcement learning approach that significantly enhances the ability of AI programs to reach large tiles in 2048-like games, outperforming traditional TD methods.

Contribution

The paper proposes a novel multi-stage TD learning method that improves large tile reaching rates in 2048-like games, demonstrating its effectiveness and adaptability to similar games.

Findings

MS-TD learning increased large tile reach rates to 31.75% in 2048.

The method enabled reaching a 65536-tile for the first time.

MS-TD improved performance in Threes, reaching 6144-tiles at 7.83% rate.

Abstract

Szubert and Jaskowski successfully used temporal difference (TD) learning together with n-tuple networks for playing the game 2048. However, we observed a phenomenon that the programs based on TD learning still hardly reach large tiles. In this paper, we propose multi-stage TD (MS-TD) learning, a kind of hierarchical reinforcement learning method, to effectively improve the performance for the rates of reaching large tiles, which are good metrics to analyze the strength of 2048 programs. Our experiments showed significant improvements over the one without using MS-TD learning. Namely, using 3-ply expectimax search, the program with MS-TD learning reached 32768-tiles with a rate of 18.31%, while the one with TD learning did not reach any. After further tuned, our 2048 program reached 32768-tiles with a rate of 31.75% in 10,000 games, and one among these games even reached a 65536-tile, which is the first ever reaching a 65536-tile to our knowledge. In addition, MS-TD learning method can be easily applied to other 2048-like games, such as Threes. Based on MS-TD learning, our experiments for Threes also demonstrated similar performance improvement, where the program with MS-TD learning reached 6144-tiles with a rate of 7.83%, while the one with TD learning only reached 0.45%.