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:2607. 15440v1 Announce Type: new Abstract: We introduce Stochastic Reset Pathfinding (SRP), an episodic learning problem on a known directed graph with unknown stationary edge success probabilities.
By Guni Sharon, Wei Zhang
Consistent submodular maximization studies the tradeoff between solution quality and stability when elements arrive over time. For a monotone submodular objective, which models diminishing returns, an...
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
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
arXiv:2606. 07047v1 Announce Type: new Abstract: Heuristics play a central role in the performance of bidirectional search algorithms, which commonly rely on two main classes.
By Alvin Zou, Muhammad Suhail Saleem, Maxim Likhachev
arXiv:2607. 23679v1 Announce Type: new Abstract: Recent years have witnessed increasing interests in tackling heteroscedastic noise in bandits and reinforcement learning.
By Heyang Zhao, Tianyuan Jin, Weixin Wang, Vincent Y. F. Tan, Pan Xu, Quanquan Gu
arXiv:2606. 29203v1 Announce Type: new Abstract: We study the Bayesian fixed-budget best-arm identification problem in which a learner can abstain from making a terminal recommendation.
By Yuqi Huang, Yunlong Hou, Vincent Y. F. Tan
arXiv:2609.06489v1 Announce Type: cross
Abstract: Monte Carlo Tree Search (MCTS) has demonstrated success in online planning for deterministic environments, yet significant challenges remain in adapt...
By Tuan Dam
arXiv:2606. 18807v1 Announce Type: cross Abstract: The field of learning-augmented algorithms has demonstrated that machine-learned predictions can bypass worst-case lower bounds across a wide range of problems.
By Tatiana Belova, Yuriy Dementiev, Danil Sagunov
The paper presents the first PAC learning framework for general-sum concurrent stochastic games with uncertain transitions, addressing the challenge of Nash equilibrium existence. It introduces data‑driven L¹ confidence sets over transition kernels and a robust CSG solver that computes a social‑welfare optimal ε‑NE, or provides a certificate that no exact NE exists. The algorithm achieves polynomial sample complexity under a minimum reachability condition and is validated on benchmark CSGs with near‑optimal performance.
By Angel Y. He, David Parker
arXiv:2606. 04860v1 Announce Type: cross Abstract: Finding optimal solution paths for combinatorial puzzles like the Rubik's Cube, sliding tile puzzles, and Lights Out remains a classical challenge in artificial intelligence.
By Siddharth Sahay