  The combination of deep learning and Monte Carlo Tree Search (MCTS) has shown
to be effective in various domains, such as board and video games. AlphaGo
represented a significant step forward in our ability to learn complex board
games, and it was rapidly followed by significant advances, such as AlphaGo
Zero and AlphaZero. Recently, MuZero demonstrated that it is possible to master
both Atari games and board games by directly learning a model of the
environment, which is then used with MCTS to decide what move to play in each
position. During tree search, the algorithm simulates games by exploring
several possible moves and then picks the action that corresponds to the most
promising trajectory. When training, limited use is made of these simulated
games since none of their trajectories are directly used as training examples.
Even if we consider that not all trajectories from simulated games are useful,
there are thousands of potentially useful trajectories that are discarded.
Using information from these trajectories would provide more training data,
more quickly, leading to faster convergence and higher sample efficiency.
Recent work introduced an off-policy value target for AlphaZero that uses data
from simulated games. In this work, we propose a way to obtain off-policy
targets using data from simulated games in MuZero. We combine these off-policy
targets with the on-policy targets already used in MuZero in several ways, and
study the impact of these targets and their combinations in three environments
with distinct characteristics. When used in the right combinations, our results
show that these targets can speed up the training process and lead to faster
convergence and higher rewards than the ones obtained by MuZero.
