Human-AI complementarity is important when neither the algorithm nor the human yields dominant performance across all instances in a given context. Recent work that explored human-AI collaboration has considered decisions that correspond to classification tasks. However, in many important contexts where humans can benefit from AI complementarity, humans undertake course of action. In this paper, we propose a framework for a novel human-AI collaboration for selecting advantageous course of action, which we refer to as Learning Complementary Policy for Human-AI teams (\textsc{lcp-hai}). Our solution aims to exploit the human-AI complementarity to maximize decision rewards by learning both an algorithmic policy that aims to complement humans by a routing model that defers decisions to either a human or the AI to leverage the resulting complementarity. We then extend our approach to leverage opportunities and mitigate risks that arise in important contexts in practice: 1) when a team is composed of multiple humans with differential and potentially complementary abilities, 2) when the observational data includes consistent deterministic actions, and 3) when the covariate distribution of future decisions differ from that in the historical data. We demonstrate the effectiveness of our proposed methods using data on real human responses and semi-synthetic, and find that our methods offer reliable and advantageous performance across setting, and that it is superior to when either the algorithm or the AI make decisions on their own. We also find that the extensions we propose effectively improve the robustness of the human-AI collaboration performance in the presence of different challenging settings.