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In fact, a new program Alpha Go Zero has outperformed the previous version of Alpha Go known as Master after 40 days of self-training by playing millions of games against itself in quick succession and with no input from human players 8, indicating the current best policy can still be improved.

For some complicated games like Go, despite the great empirical success of Alpha Go based on deep reinforcement learning 7, the optimal strategy remains unknown. To do so, a player needs to take a sequence of actions as his/her strategy to increase the winning rate and/or decrease the cost (such as time or the number of steps). The most common object of a games is to beat the opponents, whether they are computers or other human players.

As a powerful approach in decision and control theory, RL has attracted extensive focus, with wide applications in the fields of robotics 1, quantitative finance 2, computer vision 3, healthcare 4, career planning 5, gaming 6 etc. Reinforcement learning (RL) serves as an important branch of machine learning.

Least common multiple game with dice