Mastering 2048 With Delayed Temporal Coherence Learning, Multistage Weight Promotion, Redundant Encoding, and Carousel Shaping

Abstract

<italic>2048</italic> is an engaging single-player nondeterministic video puzzle game, which, thanks to the simple rules and hard-to-master gameplay, has gained massive popularity in recent years. As <italic>2048</italic> can be conveniently embedded into the discrete-state Markov decision processes framework, we treat it as a testbed for evaluating existing and new methods in reinforcement learning. With the aim to develop a strong <italic>2048</italic> playing program, we employ temporal difference learning with systematic <inline-formula><tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-tuple networks. We show that this basic method can be significantly improved with temporal coherence learning, multistage function approximator with weight promotion, carousel shaping, and redundant encoding. In addition, we demonstrate how to take advantage of the characteristics of the <inline-formula> <tex-math notation="LaTeX">$n$</tex-math></inline-formula>-tuple network, to improve the algorithmic effectiveness of the learning process by delaying the (decayed) update and applying lock-free optimistic parallelism to effortlessly make advantage of multiple CPU cores. This way, we were able to develop the best known <italic>2048</italic> playing program to date, which confirms the effectiveness of the introduced methods for discrete-state Markov decision problems.