Cross-entropy optimization with prioritized constraints

2026-10-01

AI Summary

This study addresses the failure of constraint prioritization in constrained optimization caused by improper weight assignment. To overcome this, we propose TierCEM, an algorithm that directly incorporates strict constraint priorities into the elite selection mechanism. By enhancing cross-entropy optimization with recursive sequential filtering, TierCEM progressively filters candidate solutions layer by layer according to their priority levels. This approach ensures the rigorous satisfaction of high-priority constraints without requiring explicit weight tuning. Experimental evaluations on navigation and contact-rich manipulation tasks demonstrate that the proposed method accurately adheres to the prescribed constraint priority ordering while intelligently relaxing lower-priority constraints when necessary. Ultimately, TierCEM achieves efficient and robust hierarchical constraint handling, offering a principled alternative to conventional weighted-sum formulations in complex optimization problems.

Abstract

When constraints conflict, an optimizer must determine which requirements to preserve and which to relax. On the one hand, a priority ordering specifies which requirements take precedence. On the other hand, penalty-based formulations encode their relative importance through numerical weights. Depending on these weights, a solution can improve its weighted score while violating intended priorities. We introduce TierCEM, a variant of the cross-entropy method that incorporates strict constraint priorities directly into elite selection without requiring per-constraint importance weights. TierCEM works by sequentially filtering sampled candidates, from highest- to lowest-priority constraint. If and when a constraint eliminates all remaining candidates, TierCEM returns to the last nonempty set and selects elites with the smallest violations of that blocking constraint, recursively preserving satisfaction of all higher-priority constraints. We evaluate TierCEM on 2D navigation and contact-rich pushing tasks in proprioceptive and learned world-model settings. Experiments show that reversing the constraint ordering changes which constraints are violated under conflict. Prioritizing progress toward the task objective also enables TierCEM to relax lower-priority constraints when they would otherwise prevent further progress.

Problem

• constraint optimization
• prioritized constraints
• cross-entropy method
• conflict resolution

Innovation

• Cross-entropy method
• Prioritized constraints
• Elite selection
• Constraint satisfaction
• Model predictive control