  We study the budget allocation problem in online marketing campaigns that
utilize previously collected offline data. We first discuss the long-term
effect of optimizing marketing budget allocation decisions in the offline
setting. To overcome the challenge, we propose a novel game-theoretic offline
value-based reinforcement learning method using mixed policies. The proposed
method reduces the need to store infinitely many policies in previous methods
to only constantly many policies, which achieves nearly optimal policy
efficiency, making it practical and favorable for industrial usage. We further
show that this method is guaranteed to converge to the optimal policy, which
cannot be achieved by previous value-based reinforcement learning methods for
marketing budget allocation. Our experiments on a large-scale marketing
campaign with tens-of-millions users and more than one billion budget verify
the theoretical results and show that the proposed method outperforms various
baseline methods. The proposed method has been successfully deployed to serve
all the traffic of this marketing campaign.
