Improving Variable Orderings of Approximate Decision Diagrams Using Reinforcement Learning
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Bibliographic record
Abstract
Prescriptive analytics provides organizations with scalable solutions for large-scale, automated decision making. At the core of prescriptive analytics methodology is optimization, a field devoted to the study of algorithms that solve complex decision-making problems. Optimization algorithms rely heavily on generic methods for identifying tight bounds, which provide both solutions to problems and optimality guarantees. In the last decade, decision diagrams (DDs) have demonstrated significant advantages in obtaining bounds compared with the standard linear relaxation commonly used by commercial solvers. However, the quality of the bounds computed by DDs depends heavily on the variable ordering chosen for the construction. Besides, the problem of finding an ordering that optimizes a given metric is generally NP-hard. This paper studies how machine learning, specifically deep reinforcement learning (DRL), can be used to improve bounds provided by DDs, in particular through learning a good variable ordering. The introduced DRL models improve primal and dual bounds, even over standard linear programming relaxations, and are integrated in a full-fledged branch-and-bound algorithm. This paper, therefore, provides a novel mechanism for utilizing machine learning to tighten bounds, adding to recent research on using machine learning to obtain high-quality heuristic solutions and, for the first time, using machine learning to improve relaxation bounds through a generic bounding method. We apply the methods on a classic optimization problem, the maximum independent set, and demonstrate through computational testing that optimization bounds can be significantly improved through DRL. We provide the code to replicate the results obtained on the maximum independent set. Summary of Contribution: This paper studies the use of reinforcement learning to compute a variable ordering of decision diagram-based approximations for discrete optimization problems. This is among the first works to propose the use of machine learning to improve upon generic bounding methods for discrete optimization problems, thereby establishing a critical bridge between optimization and learning.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it