arXiv subjects

Luke Marshall

Publications and source records attributed to Luke Marshall.

3 recordsLinked to original sources

arXiv2026

Accelerating Column Generation in Highly Degenerate Integer Programming Problems with Template Pricing

We propose a new pricing strategy for column generation (CG), referred to as Template pricing. This method is motivated by the desire to coordinate solutions of different pricing subproblems in order to accelerate the convergence of the CG process and simultaneously obtain good quality integer feasible solutions. Instead of finding a column with the optimal reduced cost, Template pricing tries to maximize the similarity of columns with a given template vector, while restricting the search to columns with suitable reduced cost. We present an exact and heuristic method (based on Lagrangian relaxation) to efficiently solve the Template pricing problem. We conduct extensive computational experiments on benchmark instances of the Generalized Assignment Problem (GAP). Our results demonstrate that Template pricing can significantly accelerate the CG algorithm, especially in the presence of significant degeneracy, where several benchmark GAP instances solved over 1000x faster than Dantzig pricing, and over 100x with adaptive dual-smoothing. Template pricing allows us to achieve CG optimal bounds on all 1735 ISA instances, finding stronger bounds in 43% and improved integer solutions in 9% of these instances than previously released.

math.OC↗

arXiv2023

Rethinking Machine Learning Collective Communication as a Multi-Commodity Flow Problem

We show communication schedulers' recent work proposed for ML collectives does not scale to the increasing problem sizes that arise from training larger models. These works also often produce suboptimal schedules. We make a connection with similar problems in traffic engineering and propose a new method, TECCL, that finds better quality schedules (e.g., finishes collectives faster and/or while sending fewer bytes) and does so more quickly on larger topologies. We present results on many different GPU topologies that show substantial improvement over the state-of-the-art.

cs.NI↗

arXiv2022

Hindsight Learning for MDPs with Exogenous Inputs

Many resource management problems require sequential decision-making under uncertainty, where the only uncertainty affecting the decision outcomes are exogenous variables outside the control of the decision-maker. We model these problems as Exo-MDPs (Markov Decision Processes with Exogenous Inputs) and design a class of data-efficient algorithms for them termed Hindsight Learning (HL). Our HL algorithms achieve data efficiency by leveraging a key insight: having samples of the exogenous variables, past decisions can be revisited in hindsight to infer counterfactual consequences that can accelerate policy improvements. We compare HL against classic baselines in the multi-secretary and airline revenue management problems. We also scale our algorithms to a business-critical cloud resource management problem -- allocating Virtual Machines (VMs) to physical machines, and simulate their performance with real datasets from a large public cloud provider. We find that HL algorithms outperform domain-specific heuristics, as well as state-of-the-art reinforcement learning methods.

cs.LG↗