A Surrogate Objective Framework for Prediction+Optimization with Soft Constraints
This work addresses a bottleneck in real-world optimization tasks where soft constraints are common, offering an incremental improvement over existing decision-focused approaches.
The paper tackled the inconsistency between prediction model training and downstream optimization goals in prediction+optimization problems with soft constraints, proposing a novel differentiable surrogate objective framework that outperforms traditional and other decision-focused methods in applications like portfolio optimization and resource provisioning.
Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal of the downstream optimization problem. Recently, decision-focused prediction approaches, such as SPO+ and direct optimization, have been proposed to fill this gap. However, they cannot directly handle the soft constraints with the $max$ operator required in many real-world objectives. This paper proposes a novel analytically differentiable surrogate objective framework for real-world linear and semi-definite negative quadratic programming problems with soft linear and non-negative hard constraints. This framework gives the theoretical bounds on constraints' multipliers, and derives the closed-form solution with respect to predictive parameters and thus gradients for any variable in the problem. We evaluate our method in three applications extended with soft constraints: synthetic linear programming, portfolio optimization, and resource provisioning, demonstrating that our method outperforms traditional two-staged methods and other decision-focused approaches.