Related papers: On Reinforcement Learning for the Game of 2048

The game of 2048 is a highly addictive game. It is easy to learn the game, but hard to master as the created game revealed that only about 1% games out of hundreds million ever played have been won. In this paper, we would like to explore…

2048 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 2048 can be conveniently embedded into the…

Optimizing artificial intelligence (AI) for dynamic environments remains a fundamental challenge in machine learning research. In this paper, we examine evolutionary training methods for optimizing AI to solve the game 2048, a 2D sliding…

2048 is a stochastic single-player game involving 16 cells on a 4 by 4 grid, where a player chooses a direction among up, down, left, and right to obtain a score by merging two tiles with the same number located in neighboring cells along…

Delayed and sparse rewards present a fundamental obstacle for reinforcement-learning (RL) agents, which struggle to assign credit for actions whose benefits emerge many steps later. The sliding-tile game 2048 epitomizes this challenge:…

2048 is a single player video game, played by millions mostly on mobile devices. We prove rigorously for the first time that there is an algorithm with winning probability at least 0.99969, and that there is a strategy for achieving the 256…

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…

In recent years, reinforcement learning has seen interest because of deep Q-Learning, where the model is a convolutional neural network. Deep Q-Learning has shown promising results in games such as Atari and AlphaGo. Instead of learning the…

We theoretically analyze the popular mobile app game `2048' for the first time in $n$-dimensional space. We show that one can reach the maximum value $2^{n_1n_2+1}$ and $2^{\left({\prod_{i=1}^{d} n_i}\right)+1}$ for the two dimensional…

This paper investigates a class of multi-player discrete games where each player aims to maximize its own utility function. Each player does not know the other players' action sets, their deployed actions or the structures of its own or the…

Temporal difference (TD) learning and its variants, such as multistage TD (MS-TD) learning and temporal coherence (TC) learning, have been successfully applied to 2048. These methods rely on the stochasticity of the environment of 2048 for…

Going from research to production, especially for large and complex software systems, is fundamentally a hard problem. In large-scale game production, one of the main reasons is that the development environment can be very different from…

We examine online safe multi-agent reinforcement learning using constrained Markov games in which agents compete by maximizing their expected total rewards under a constraint on expected total utilities. Our focus is confined to an episodic…

The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by…

We propose a novel training algorithm for reinforcement learning which combines the strength of deep Q-learning with a constrained optimization approach to tighten optimality and encourage faster reward propagation. Our novel technique…

We present tournament results and several powerful strategies for the Iterated Prisoner's Dilemma created using reinforcement learning techniques (evolutionary and particle swarm algorithms). These strategies are trained to perform well…

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…

Playing two-player games using reinforcement learning and self-play can be challenging due to the complexity of two-player environments and the possible instability in the training process. We propose that a reinforcement learning algorithm…

Reinforcement learning methods have recently been very successful at performing complex sequential tasks like playing Atari games, Go and Poker. These algorithms have outperformed humans in several tasks by learning from scratch, using only…

Deep reinforcement learning (RL) has achieved outstanding results in recent years, which has led a dramatic increase in the number of methods and applications. Recent works are exploring learning beyond single-agent scenarios and…