<p>Over the years, homeless service providers have offered services to assist homeless individuals. Administrative data recorded by service providers have been previously used to infer the underlying network of homeless services that individuals navigate with the goal of securing stable housing. Methods have been developed to recommend service assignments based on this network so that the dynamics of the existing system can be replicated. In contrast to prior art, which neglects the real-life impact of service assignments to individuals, we propose a method that, given the history of individuals in the homeless system, recommends the next service assignment that is expected to best improve the exit and reentry outcomes for each individual. To the best of our knowledge, this is the first time that exit and non-reentry outcomes are considered in algorithmic recommendation of homeless service assignments. Extensive experimental evaluation shows that the proposed method significantly outperforms the state of the art.</p>