Decision-Focused Learning (DFL) focuses on a setting where a system gets as input some features and needs to predict coefficients to a downstream optimization problem. Classically, one would apply a two-stage solution, which trains the predictor as a regression task and only uses the optimizer during evaluation. However, the two-stage solution fails to optimize the downstream optimization problem. As such, one might use DFL techniques to train the predictor. Nonetheless, these fail to take the entire solution space into account and only optimize toward the optimal true solution, and as such, they might fail to optimize the total downstream value. Furthermore, these techniques are computationally expensive.

We tackle these two problems using Decision Diagrams (DDs) for DFL. DDs for DFL have three main benefits. First, the DD can be cached between runs, speeding up the training loop. Second, we present four novel loss functions that use DDs to reason efficiently over entire solution spaces. Furthermore, we introduce a novel method to relax the DDs to reduce solve-time during training.

We experimentally show that the DDs speed up the training loop substantially. We further show that the DFL losses perform on par with other state-of-the-art DFL losses. Finally, we experimentally show when and which losses work with relaxed DDs.

The superoptimizer STOKE has previously been shown to be effective at optimizing programs containing floating-point numbers. The STOKE optimizer obtains these results by running a stochastic search over the set of all programs and selecting the best-optimized one. This study aims to find more clearly what floating-point programs STOKE optimizes particularly well and for which ones it fails to find significant rewrites. To answer the research question, STOKE and GCC optimized multiple small programs, and I compared these on execution speed. The results showed numerous cases where STOKE failed to obtain a better optimization than GCC. The results suggest that for specific floating-point functions, there exist limitations in both the test case generator and the STOKE search algorithm that prevent it from finding good optimizations. The findings of this paper suggest further research on the STOKEs test case generator to improve its performance.