[Paper Review] Efficient Learning for Clustering and Optimizing Context-Dependent Designs

Haidong Li, Henry Lam+1 more|arXiv (Cornell University)|Dec 10, 2020

Bayesian Methods and Mixture Models40 references4 citations

TL;DR

This paper proposes DSCO, a dynamic sampling policy that leverages Gaussian mixture models to jointly learn global performance clusters and local design-context performance in context-dependent simulation optimization. Under a Bayesian framework, DSCO adaptively allocates simulation replications to maximize the worst-case probability of correct selection (PCS_W), achieving consistency and asymptotically optimal sampling ratios, with numerical results showing significant efficiency gains over baseline methods.

ABSTRACT

We consider a simulation optimization problem for a context-dependent decision-making. A Gaussian mixture model is proposed to capture the performance clustering phenomena of context-dependent designs. Under a Bayesian framework, we develop a dynamic sampling policy to efficiently learn both the global information of each cluster and local information of each design for selecting the best designs in all contexts. The proposed sampling policy is proved to be consistent and achieve the asymptotically optimal sampling ratio. Numerical experiments show that the proposed sampling policy significantly improves the efficiency in context-dependent simulation optimization.

Motivation & Objective

• To address the challenge of efficiently selecting the best design across multiple contexts in simulation optimization, where performance is context-dependent and simulation is costly.
• To exploit performance clustering in design-context pairs to reduce the complexity of the optimization problem and improve sampling efficiency.
• To develop a dynamic sampling policy that simultaneously learns global cluster-level information and local design-specific performance.
• To ensure high worst-case probability of correct selection (PCS_W) across all contexts, even under limited simulation budgets.
• To provide a theoretically grounded, consistent, and asymptotically optimal sampling policy for context-dependent ranking and selection.

Proposed method

• A Gaussian mixture model (GMM) is used as a prior to capture performance clustering in design-context pairs, modeling both global cluster structure and local performance variation.
• Under a Bayesian framework, posterior distributions for performance and cluster assignments are sequentially updated using sampled data from simulation replications.
• The sampling policy, DSCO, dynamically allocates simulation replications based on posterior estimates of cluster means and variances, prioritizing high-impact design-context pairs.
• DSCO uses a stochastic dynamic programming formulation to balance exploration of cluster structure and exploitation of high-performing designs.
• The policy is designed to achieve the asymptotically optimal sampling ratio and is proven to be consistent, ensuring convergence to the correct selection in all contexts.
• Model hyperparameters, including cluster membership probabilities and GMM parameters, are estimated iteratively from observed simulation outcomes.

Experimental results

Research questions

• RQ1 How can performance clustering in design-context pairs be effectively modeled and exploited to improve simulation efficiency in context-dependent optimization?
• RQ2 What dynamic sampling policy can simultaneously learn global cluster-level performance and local design-specific performance under a Bayesian framework?
• RQ3 Can the proposed policy achieve consistency and asymptotically optimal sampling ratios in context-dependent simulation optimization?
• RQ4 How does the worst-case probability of correct selection (PCS_W) of the proposed method compare to existing sampling policies across diverse contexts?
• RQ5 To what extent does incorporating performance clustering reduce the required simulation budget for reliable selection of the best design in each context?

Key findings

• DSCO successfully identifies 4 design clusters and 6 context clusters in a real-world cancer prevention treatment simulation, with clusters corresponding to distinct drug types and patient age/blood pressure profiles.
• The method achieves a higher worst-case probability of correct selection (PCS_W) than EA, IZ, SUCB, and C-OCBA, with Figure 11 showing consistent superiority across all tested configurations.
• DSCO allocates more simulation replications to high-performing combinations—such as high-dose aspirin in hypertensive patients—aligning with clinical expectations and biological plausibility.
• The algorithm demonstrates consistency, with posterior estimates converging to true performance values as simulation budget increases.
• DSCO achieves the asymptotically optimal sampling ratio, meaning it allocates replications in the theoretically most efficient distribution across design-context pairs.
• Numerical experiments confirm that DSCO significantly improves efficiency in context-dependent simulation optimization by leveraging performance clustering, reducing the number of required simulations for reliable selection.