Learning From Scenarios for Stochastic Repairable Scheduling

TL;DR

This work addresses stochastic scheduling with uncertain processing times where constraints induce potential infeasibilities and repairs are necessary. It introduces decision-focused learning (DFL) with stochastic smoothing to minimize post-hoc regret, adapting the score-function gradient to a scenario-based scheduling context. Through extensive experiments on RCPSP variants, the study shows that stochastic programming can dominate for small, highly penalized instances, while DFL scales better and often matches or exceeds performance on larger problems, highlighting a complementary relationship between approaches. The results suggest that incorporating constraint uncertainty through DFL offers practical benefits and motivates future work on feature-rich inputs and alternative gradient estimators for repairable scheduling.

Abstract

When optimizing problems with uncertain parameter values in a linear objective, decision-focused learning enables end-to-end learning of these values. We are interested in a stochastic scheduling problem, in which processing times are uncertain, which brings uncertain values in the constraints, and thus repair of an initial schedule may be needed. Historical realizations of the stochastic processing times are available. We show how existing decision-focused learning techniques based on stochastic smoothing can be adapted to this scheduling problem. We include an extensive experimental evaluation to investigate in which situations decision-focused learning outperforms the state of the art for such situations: scenario-based stochastic optimization.

Figures (5)

• Figure 1: Deterministic opt. schedule
• Figure 2: Repair action when $y_2=6$
• Figure 3: Smoothing
• Figure 4: Training curves
• Figure 5: Normalized post-hoc regret per instance set - penalty setting (smaller regret is better). The box spans from the 25th to the 75th percentile, visualizing the median and interquartile range.