Title: Generalization bounds and algorithms for estimating the effect of multiple treatments and dosage. Abstract: Estimating conditional treatment effects has been a longstanding challenge for fields of study such as epidemiology or economics that require a treatment-dosage pair to make decisions, but may not be able to run randomized trials to precisely quantify their effect. In the context of representation learning, there is an extensive literature relating model architectures with regularization techniques to solve this problem using observational data. However, theoretically motivated loss functions and bounds on generalization errors only exist in select circumstances, such as in the presence of binary treatments. In this paper, we introduce new bounds on the counterfactual generalization error in the context of multiple treatments and continuous dosage parameters, which subsume existing results. This result, in a principled manner, guides the definition of new learning objectives that can be used to train representation learning algorithms. We show empirically new state-of-the-art performance results across several benchmark datasets for this problem, including in comparison to doubly-robust estimation methods.