In the supplementary, we first discuss the experimental details and hyperparameters in Section A. Section B, and further present the visualization in RLBench in Section C. Finally, we discuss how to MLP with 512 hidden units and Mish activations. The probability ϵ of random actions is set to 0. 03 in Stochastic Environments. So the sampled trajectories still lead to the collision. Figure 1 illustrates a problematic sampled trajectory after execution. We further evaluate the performance with different replanning steps in Table 1.

We assume that the lower-level objective functiong is convex but notstrongly convex,sothelower-levelproblem mayhavemultiple optimal solutions.

Graph learning from signals is a core task in graph signal processing (GSP). A significant subclass of graph signals called the stationary graph signals that broadens the concept of stationarity of data defined on regular domains to signals on graphs is gaining increasing popularity in the GSP community. The most commonly used model to learn graphs from these stationary signals is SpecT, which forms the foundation for nearly all the subsequent, more advanced models. Despite its strengths, the practical formulation of the model, known as rSpecT, has been identified to be susceptible to the choice of hyperparameters. More critically, it may suffer from infeasibility as an optimization problem.

When some parameters of a constrained optimization problem (COP) are uncertain, this gives rise to a predict-then-optimize (PtO) problem, comprising two stages: the prediction of the unknown parameters from contextual information and the subsequent optimization using those predicted parameters. Decision-focused learning (DFL) implements the first stage by training a machine learning (ML) model to optimize the quality of the decisions made using the predicted parameters. When the predicted parameters occur in the constraints, they can lead to infeasible solutions. Therefore, it is important to simultaneously manage both feasibility and decision quality. We develop a DFL framework for predicting constraint parameters in a generic COP. While prior works typically assume that the underlying optimization problem is a linear program (LP) or integer LP (ILP), our approach makes no such assumption. We derive two novel loss functions based on maximum likelihood estimation (MLE): the first one penalizes infeasibility (by penalizing predicted parameters that lead to infeasible solutions), while the second one penalizes suboptimal decisions (by penalizing predicted parameters that make the true optimal solution infeasible). We introduce a single tunable parameter to form a weighted average of the two losses, allowing decision-makers to balance suboptimality and feasibility. We experimentally demonstrate that adjusting this parameter provides decision-makers control over this trade-off. Moreover, across several COP instances, we show that adjusting the tunable parameter allows a decision-maker to prioritize either suboptimality or feasibility, outperforming the performance of existing baselines in either objective.

This class of problems is referred to as the "simple bilevel problem" [

Re "...how decomposing the polytope now allows it to be mapped?" If you meant "how does the decomposition help map the problem of computing an optimal correlated Re "I wasn't sure what I was supposed to take away from the experiments" As We'll take all of them into account. Re "broader impact" Thanks for the feedback, we agree with all your points. As you correctly recognized, we use the term "social welfare" to mean the sum of utilities of the players as is typical in the game The maximum payoff is 15. Gurobi is freely available for academic use, but we'll also mention the open-source We are definitely the first to compute optimal EFCE in it. We strongly disagree that " this paper just tells us that the work in Farina et al. [12] is Extending the construction by Farina et al. to handle the more general We strongly disagree with that.

In the supplementary, we first discuss the experimental details and hyperparameters in Section A. Section B, and further present the visualization in RLBench in Section C. Finally, we discuss how to MLP with 512 hidden units and Mish activations. The probability ϵ of random actions is set to 0. 03 in Stochastic Environments. So the sampled trajectories still lead to the collision. Figure 1 illustrates a problematic sampled trajectory after execution. We further evaluate the performance with different replanning steps in Table 1.