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cs.DS updates on arXiv.org

PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
When Location Shapes Choice: Placement Optimization of Su...
Omar El Housni, Rajan Udwani · 2023-10-13 · via cs.DS updates on arXiv.org

Strategic product placement can have a strong influence on customer purchase behavior in physical stores as well as online platforms. Motivated by this, we consider the problem of optimizing the placement of substitutable products in designated display locations to maximize the expected revenue of the seller. We model the customer behavior as a two-stage process: first, the customer visits a subset of display locations according to a browsing distribution; second, the customer chooses at most one product from the displayed products at those locations according to a choice model. Our goal is to design a general algorithm that can select and place the products optimally for any browsing distribution and choice model, and we call this the Placement problem. We give a randomized algorithm that utilizes an $α$-approximate algorithm for cardinality constrained assortment optimization and outputs a $\frac{Θ(α)}{\log m}$-approximate solution (in expectation) for Placement with $m$ display locations, i.e., our algorithm outputs a solution with value at least $\frac{Ω(α)}{\log m}$ factor of the optimal and this is tight in the worst case. We also give algorithms with stronger guarantees in some special cases. In particular, we give a deterministic $\frac{Ω(1)}{\log m}$-approximation algorithm for the Markov choice model, and a tight $(1-1/e)$-approximation algorithm for the problem when products have identical prices.