Submodular Order Functions and Assortment Optimization

Authors: Rajan Udwani

ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. We give fast algorithms with strong approximation guarantees for maximizing submodular order functions under a variety of constraints. We also show an intriguing connection to the maximization of monotone submodular functions in the streaming model, where we recover best known approximation guarantees as a corollary of our results.
Researcher Affiliation Academia 1Department of IEOR, University of California, Berkeley, USA. Correspondence to: Rajan Udwani <rudwani@berkeley.edu>.
Pseudocode Yes ALGORITHM 1: 1/2 for Cardinality; ALGORITHM 2: Threshold Add(k, τ); ALGORITHM 3: 1/4 for Matroid Constraint; ALGORITHM 4: 1/3 for Budget; ALGORITHM 5: B-Threshold Add(B, τ); ALGORITHM 6: 0.5 for Budget Constraint; ALGORITHM 7: Final Add; ALGORITHM 8: Constrained Assortment Optimization for Compatible Choice Models
Open Source Code No The paper does not provide any explicit statements about releasing source code or links to a code repository.
Open Datasets No This paper is theoretical in nature, presenting algorithms and proofs without empirical evaluation on datasets, thus no training data information is provided.
Dataset Splits No This paper is theoretical in nature and does not involve empirical evaluation on datasets, therefore no validation split information is provided.
Hardware Specification No The paper is theoretical and focuses on algorithm design and approximation guarantees, thus it does not describe any specific hardware used for experiments.
Software Dependencies No The paper is theoretical and does not specify any software dependencies with version numbers, as it does not report on empirical experiments.
Experiment Setup No The paper is theoretical and does not include details such as hyperparameters or system-level training settings as part of an experimental setup.