Hugging Face Trending Papers
Aug 19

On the Slow Convergence to Trivial Solutions of Algorithms for Hard Optimization Problems

The paper investigates how algorithms for hard combinatorial optimization problems converge to trivial solutions, focusing on finite-size behavior rather than asymptotic limits. By analyzing large-graph asymptotics and running numerical experiments on problems like maximum independent set and maximum K‑SAT, the authors show that convergence to theoretically predicted bounds is surprisingly slow. In the intermediate regime of high constraint density, local algorithms actually outperform their asymptotic predictions, highlighting a gap between finite-regime performance and asymptotic theory.

arXiv AI
Sep 25

Canopy: Exploiting Piecewise Smooth Tree Priors for Multi-Fidelity Bandits

CANOPY is a multi‑fidelity tree bandit algorithm that learns where a piecewise‑smooth prior holds instead of assuming global smoothness. It uses cheap random‑path probes to certify local aggregation bias and then focuses expensive leaf evaluations on cells where smoothness is violated. The method achieves provable fixed‑budget and regret guarantees that scale with the number of discontinuities, matching smooth‑tree rates when no violations exist and approaching structure‑blind search when violations are dense.

By Michael Jerge, Suman Jana
arXiv Machine Learning
Aug 20

On the Slow Convergence to Trivial Solutions of Algorithms for Hard Optimization Problems

The paper investigates how optimization algorithms for hard combinatorial problems converge to trivial solutions. By combining rigorous large‑graph asymptotics with numerical experiments on maximum independent set and maximum K‑SAT, the authors show that convergence to the theoretically predicted bounds is extremely slow, especially in the intermediate regime of high constraint density. This reveals a significant gap between finite‑size performance and asymptotic expectations, indicating that practical algorithm design remains essential even when theory predicts inevitable failure.

By Ali Hussaini Umar, Jean Barbier, Matthieu Jonckheere, Manuel S\'aenz