Clustering is a powerful tool for decision-making under uncertainty!

Work w/ my students Irina Wang (lead) and Cole Becker, in collab. w/
Bart Van Parys

🧵 (7/7)

We have several examples in the paper. Here is a sparse portfolio optimization one. Clustering barely affects the solution objective. Speedups are more than 3 orders of magnitude. 🧵 (6/7)

By varying the number of clusters K, our method bridges Robust and Distributionally Robust optimization! We also derive theoretical bounds on 1) how to adjust the Wasserstein ball radius to compensate for clustering, and 2) how to exactly quantify the effect of clustering 🧵 (5/7)

In Mean Robust Optimization, we define an uncertainty set around the cluster centroids with weights defined by the amount of samples in each cluster. 🧵 (4/7)

Our procedure: we first cluster N data points into K clusters. Then, we solve the Mean Robust Optimization problem. 🧵 (3/7)

Robust optimization is tractable but, often, very conservative. Wasserstein Distributionally Robust Optimization is less conservative but, often, computationally expensive. How can we bridge the two? 🧵 (2/7)

Cool! Thanks for creating this. Could you please add me? :)

👋👋👋

Congratulations @atlaswang.bsky.social :)

Thanks @tmaehara.bsky.social It looks great! I will let you know if I find anything wrong but from a brief look at the first post it looks exactly what one would expect. Thanks again!

By the way, do you consider linear optimization a technology? (if use the 1-norm Mosek gives the correct answer)