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In this paper, we prove that optimally solving an $n \times n \times n$ Rubik's Cube is NP-complete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous result that optimally solving an $n \times…

Computational Complexity · Computer Science 2018-04-30 Erik D. Demaine , Sarah Eisenstat , Mikhail Rudoy

We investigate reinforcement learning in the Game Of Hidden Rules (GOHR) environment, a complex puzzle in which an agent must infer and execute hidden rules to clear a 6$\times$6 board by placing game pieces into buckets. We explore two…

Machine Learning · Computer Science 2025-10-24 Christo Mathew , Wentian Wang , Jacob Feldman , Lazaros K. Gallos , Paul B. Kantor , Vladimir Menkov , Hao Wang

We present a new general board game (GBG) playing and learning framework. GBG defines the common interfaces for board games, game states and their AI agents. It allows one to run competitions of different agents on different games. It…

Artificial Intelligence · Computer Science 2019-07-16 Wolfgang Konen

Text-based games are long puzzles or quests, characterized by a sequence of sparse and potentially deceptive rewards. They provide an ideal platform to develop agents that perceive and act upon the world using a combinatorially sized…

Artificial Intelligence · Computer Science 2020-06-16 Prithviraj Ammanabrolu , Ethan Tien , Matthew Hausknecht , Mark O. Riedl

Tic Tac Toe is amongst the most well-known games. It has already been shown that it is a biased game, giving more chances to win for the first player leaving only a draw or a loss as possibilities for the opponent, assuming both the players…

Artificial Intelligence · Computer Science 2023-03-15 Bhavuk Kalra

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by…

Machine Learning · Computer Science 2023-06-23 Yining Li , Peizhong Ju , Ness Shroff

After the recent groundbreaking results of AlphaGo, we have seen a strong interest in reinforcement learning in game playing. General Game Playing (GGP) provides a good testbed for reinforcement learning. In GGP, a specification of games…

Artificial Intelligence · Computer Science 2018-05-22 Hui Wang , Michael Emmerich , Aske Plaat

Can agents be trained to answer difficult mathematical questions by playing a game? We consider the integer feasibility problem, a challenge of deciding whether a system of linear equations and inequalities has a solution with integer…

Machine Learning · Computer Science 2022-08-26 Yue Wu , Jesús A. De Loera

The diameter of the Cayley graph of the Rubik's Cube group is the fewest number of turns needed to solve the Cube from the hardest initial configuration. For the 2$\times$2$\times$2 Cube, the diameter is 11 in the half-turn metric, 14 in…

Discrete Mathematics · Computer Science 2024-10-02 So Hirata

Real-time control for robotics is a popular research area in the reinforcement learning community. Through the use of techniques such as reward shaping, researchers have managed to train online agents across a multitude of domains. Despite…

Robotics · Computer Science 2023-04-21 Mihai Anca , Jonathan D. Thomas , Dabal Pedamonti , Matthew Studley , Mark Hansen

In recent years, Reinforcement Learning (RL) has seen increasing popularity in research and popular culture. However, skepticism still surrounds the practicality of RL in modern video game development. In this paper, we demonstrate by…

Machine Learning · Computer Science 2020-12-14 Nancy Iskander , Aurelien Simoni , Eloi Alonso , Maxim Peter

Motivated by the challenge of achieving rapid learning in physical environments, this paper presents the development and training of a robotic system designed to navigate and solve a labyrinth game using model-based reinforcement learning…

Robotics · Computer Science 2023-12-18 Thomas Bi , Raffaello D'Andrea

Humans quickly solve tasks in novel systems with complex dynamics, without requiring much interaction. While deep reinforcement learning algorithms have achieved tremendous success in many complex tasks, these algorithms need a large number…

Artificial Neural Networks excel at identifying individual components in an image. However, out-of-the-box, they do not manage to correctly integrate and interpret these components as a whole. One way to alleviate this weakness is to expand…

Computer Vision and Pattern Recognition · Computer Science 2024-11-28 Simon Vandevelde , Laurent Mertens , Sverre Lauwers , Joost Vennekens

We propose a hybrid reinforcement and self-supervised learning framework for accelerating generalized Benders decomposition (GBD). In this framework, a graph based reinforcement learning agent operates on a bipartite representation of the…

Systems and Control · Electrical Eng. & Systems 2026-04-27 Bernard T. Agyeman , Zhe Li , Ilias Mitrai , Prodromos Daoutidis

Machine learning with artificial neural networks is revolutionizing science. The most advanced challenges require discovering answers autonomously. This is the domain of reinforcement learning, where control strategies are improved…

Quantum Physics · Physics 2018-10-03 Thomas Fösel , Petru Tighineanu , Talitha Weiss , Florian Marquardt

Rubik's Cube (RC) is a well-known and computationally challenging puzzle that has motivated AI researchers to explore efficient alternative representations and problem-solving methods. The ideal situation for planning here is that a problem…

Artificial Intelligence · Computer Science 2023-08-22 Bharath Muppasani , Vishal Pallagani , Biplav Srivastava , Forest Agostinelli

We study the problem of training a principal in a multi-agent general-sum game using reinforcement learning (RL). Learning a robust principal policy requires anticipating the worst possible strategic responses of other agents, which is…

Machine Learning · Computer Science 2022-12-21 Eric Zhao , Alexander R. Trott , Caiming Xiong , Stephan Zheng

Benders decomposition (BD), along with its generalized version (GBD), is a widely used algorithm for solving large-scale mixed-integer optimization problems that arise in the operation of process systems. However, the off-the-shelf…

Optimization and Control · Mathematics 2025-08-12 Zhe Li , Bernard T. Agyeman , Ilias Mitrai , Prodromos Daoutidis

Excavation of irregular rigid objects in clutter, such as fragmented rocks and wood blocks, is very challenging due to their complex interaction dynamics and highly variable geometries. In this paper, we adopt reinforcement learning (RL) to…

Robotics · Computer Science 2022-01-28 Qingkai Lu , Yifan Zhu , Liangjun Zhang