That undoubtedly worked in the team’s favor here. They do not generally benefit from a proof that they can be solved in a small number of moves, as the Rubik’s Cube problem does. Whether these problems will be as amenable to this approach is not clear.
Indeed, McAleer and co have other goals in their sights: “We are working on extending this method to find approximate solutions to other combinatorial optimization problems such as prediction of protein tertiary structure.” That’s interesting because it has implications for a variety of other tasks that deep learning has struggled with, including puzzles like Sokoban, games like Montezuma’s Revenge, and problems like prime number factorization. “Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves-less than or equal to solvers that employ human domain knowledge,” say McAleer and co. The result is an algorithm that performs remarkably well. Having been trained, the network then uses a standard search tree to hunt for suggested moves for each configuration. This process is not perfect, but deep learning helps the system figure out which moves are generally better than others. To do this, it must be able to evaluate the move.Īutodidactic iteration does this by starting with the finished cube and working backwards to find a configuration that is similar to the proposed move. Given an unsolved cube, the machine must decide whether a specific move is an improvement on the existing configuration. The trick that McAleer and co have mastered is to find a way for the machine to create its own system of rewards. These guys have pioneered a new kind of deep-learning technique, called “autodidactic iteration,” that can teach itself to solve a Rubik’s Cube with no human assistance. That just isn’t the case for the Rubik’s Cube.Įnter Stephen McAleer and colleagues from the University of California, Irvine. In chess, by contrast, there is a relatively large search space but each move can be evaluated and rewarded accordingly. And a sequence of random turns can go on for a long time without reaching a solution, so the end-state reward can only be offered rarely. In other words, it helps the machine learn.īut this doesn’t work in many real-world situations, because rewards are often rare or hard to determine.įor example, random turns of a Rubik’s Cube cannot easily be rewarded, since it is hard to judge whether the new configuration is any closer to a solution. This reward process is hugely important because it helps the machine to distinguish good play from bad play. Crucially, it is rewarded at each step according to how it performs. In these scenarios, a deep-learning machine is given the rules of the game and then plays against itself. One idea is to use the same kind of approach that has been so successful with games like chess and Go. More recently, computer scientists have tried to find ways for machines to solve the problem themselves. Rubik himself, within a month of inventing the toy, came up with an algorithm that could do this.īut attempts to automated the process have all relied on algorithms that have been hand-crafted by humans. The answer, proved in 2014, turns out to be 26.Īnother common challenge is to design algorithms that can solve the cube from any position.
One question that has intrigued them is the smallest number of moves needed to solve it from any position. The puzzle has also attracted considerable interest from computer scientists and mathematicians. It became an international best-selling toy and sold over 350 million units. The Rubik’s Cube is a three-dimensional puzzle developed in 1974 by the Hungarian inventor Erno Rubik, the object being to align all squares of the same color on the same face of the cube.
The milestone is significant because the new approach tackles an important problem in computer science-how to solve complex problems when help is minimal.įirst some background. A new kind of deep-learning machine has taught itself to solve a Rubik’s Cube without any human assistance. Yet another bastion of human skill and intelligence has fallen to the onslaught of the machines.