Abstract: Dynamic treatment regimens (DTRs) are sequential decisions over one or more stages that tailor treatments to individual characteristics and their intermediate outcomes. For many chronic diseases such as type 2 diabetes (T2D), benefit-risk tradeoff is usually an important concern for decision making in the sense that treatments with a higher benefit may lead to an increased risk of adverse outcomes (e.g., more intensive insulin treatment may lead to more hypoglycemia events). It is thus desirable to learn the optimal DTRs while constraining the risk to be within a tolerable range. In this talk, we propose a learning framework for this purpose. The framework allows the risk constraint to be imposed either at each stage for an acute risk outcome, or cumulatively over all the stages for a long-term risk outcome. Using surrogate loss functions in empirical risk minimization, the optimal DTRs are obtained by solving a sequence of weighted support vector machine problems in a backward fashion. Theoretically, we show that the estimated DTRs are Fisher consistent and we further provide the convergence rates for the value and risk functions associated with the estimated DTRs. Lastly, the proposed method is demonstrated via simulation studies and an application to a two-stage clinical trial for treating T2D.