Learning to Rank under Multinomial Logit Choice
Authors: James A. Grant, David S. Leslie
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We propose upper confidence bound (UCB) algorithms to minimise regret in two settings where the position dependent parameters are known, and unknown. We present theoretical analysis leading to an Ω(JT) lower bound for the problem, an O(JT) upper bound on regret of the UCB algorithm in the known-parameter setting, and an O(K2JT) upper bound on regret, the first, in the more challenging unknown-position-parameter setting. Our analyses are based on tight new concentration results for Geometric random variables, and novel functional inequalities for maximum likelihood estimators computed on discrete data. (...) We now conduct empirical comparisons on three instances of MNL-LTR: (a) There are K = 4 slots with position biases λ = (1, 0.3, 0.2, 0.1). There are J = 6 items with attractiveness parameters α = (0.3, 0.28, 0.26, 0.24, 0.22, 0.2). (b) There are K = 3 slots with position biases λ = (1, 0.2, 0.9). There are J = 4 items with attractiveness parameters α = (0.05, 0.1, 0.15, 0.2). (c) There are K = 6 slots with position biases λ = (1, 0.9, 0.7, 0.3, 0.5, 0.7) and J = 30 items, four having attractiveness parameter 1, two having attractiveness parameter 0.8, and the remaining twenty-four having attractiveness parameter 0.1. |
| Researcher Affiliation | Academia | James A. Grant EMAIL Department of Mathematics and Statistics, Lancaster University, Lancaster, UK. David S. Leslie EMAIL Department of Mathematics and Statistics, Lancaster University, Lancaster, UK. |
| Pseudocode | Yes | Algorithm 1 EM Algorithm for MNL-LTR with Unknown Position Biases (...) Algorithm 2 Epoch-UCB algorithm for known position biases (...) Algorithm 3 Epoch-UCB algorithm for unknown position biases |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or links to code repositories for the methodology described. The license information provided is for the paper content itself, not for associated code. |
| Open Datasets | No | The paper describes three instances of MNL-LTR problems (a), (b), and (c) by specifying their parameters (number of slots K, position biases λ, number of items J, and attractiveness parameters α). These are simulated problem setups with defined parameters, not references to externally available public datasets with access information. |
| Dataset Splits | No | The paper describes problem instances with predefined parameters for simulation, such as 'K=4 slots' and 'J=6 items with attractiveness parameters'. It discusses 'decision-making rounds' and 'replications' for the simulations, but there are no traditional training/test/validation dataset splits mentioned as the problems are synthetic. |
| Hardware Specification | No | The paper describes running simulations for a certain number of decision-making rounds and replications but does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used for these experiments. |
| Software Dependencies | No | The paper discusses various algorithms (Epoch-UCB, Epoch-UCB UPB, Top Rank, PBUCB) and models, but it does not specify any programming languages, libraries, or software dependencies with version numbers that would be required to reproduce the experiments. |
| Experiment Setup | Yes | The paper specifies the parameters for the three problem instances (a, b, c) used in the experiments (e.g., 'K=4 slots with position biases λ = (1, 0.3, 0.2, 0.1). There are J = 6 items with attractiveness parameters α = (0.3, 0.28, 0.26, 0.24, 0.22, 0.2)'). It also describes a modification for one of its algorithms, 'Epoch-UCB* UPB, which is identical to Algorithm 3 except the UCB for item j [J] in epoch l [L] is calculated as αUCB j,l = αEM j,l + 0.5 q36β2 1,j,L log(Jl)'. Additionally, it states the number of 'decision-making rounds' (50000 or 8000) and 'replications' (40) for the simulations. |