Contextual Decision-Making with Knapsacks Beyond the Worst Case
Authors: Zhaohua Chen, Rui Ai, Mingwei Yang, Yuqi Pan, Chang Wang, Xiaotie Deng
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 6 Numerical Validations In this section, we use numerical experiments to verify our analysis. We perform our simulation experiments with either full or partial information feedback under two cases. The first is with a degenerate optimal solution, and the second is with a unique and non-degenerate optimal solution. We delay more details, including the choice of the problem instances, to Appendix F. Figure 1 describes the relationship between the regret and the number of total rounds T = 2000 2k for integer 0 k 5. The figure displays both the sample mean (the line) and the 99%-confidence interval (the light color zone) calculated by the results of 50 estimations for the regret, where each estimation comprises 400 independent trials. |
| Researcher Affiliation | Academia | Zhaohua Chen School of Computer Science Peking University Haidian, Beijing, China chenzhaohua@pku.edu.cn Rui Ai IDSS & LIDS Massachusetts Institute of Technology Cambridge, MA 02139, USA ruiai@mit.edu Mingwei Yang Dept. of Management Science and Engineering Stanford University Stanford, CA 94305, USA mwyang@stanford.edu Yuqi Pan School of Engineering and Applied Sciences Harvard University Cambridge, MA 02138, USA yuqipan@g.harvard.edu Chang Wang Dept. of Computer Science Northwestern University Evanston, IL 60208, USA wc@u.northwestern.edu Xiaotie Deng School of Computer Science Institute for Artificial Intelligence Peking University Haidian, Beijing, China xiaotie@pku.edu.cn |
| Pseudocode | Yes | Algorithm 1 Re-Solving with Empirical Estimation. |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code for their methodology, nor does it provide a link to a code repository. |
| Open Datasets | No | We set the horizon T to be 2000 2k for integer 0 k 5. ... The unknown mass function of context and external factor are (u(θ1), u(θ2), u(θ3)) = (0.3, 0.3, 0.4) and (v(γ1), v(γ2)) = (0.5, 0.5), respectively. The resource consumption is represented by... The reward function is represented by... For a degenerate instance, we set ρ = (1, 1.15) with the optimal solution x = (1, 0.5, 1). For a non-degenerate problem instance, we set the average resources as ρ = (1, 1) and the unique optimal solution is x = (2/3, 2/3, 1). |
| Dataset Splits | No | The figure displays both the sample mean (the line) and the 99%-confidence interval (the light color zone) calculated by the results of 50 estimations for the regret, where each estimation comprises 400 independent trials. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory, or processing power) used for running the numerical simulations. |
| Software Dependencies | No | The paper does not provide specific software dependencies (e.g., library names with version numbers) needed to replicate the numerical experiments. |
| Experiment Setup | Yes | We set the horizon T to be 2000 2k for integer 0 k 5. ... The unknown mass function of context and external factor are (u(θ1), u(θ2), u(θ3)) = (0.3, 0.3, 0.4) and (v(γ1), v(γ2)) = (0.5, 0.5), respectively. The resource consumption is represented by... The reward function is represented by... For a degenerate instance, we set ρ = (1, 1.15) with the optimal solution x = (1, 0.5, 1). For a non-degenerate problem instance, we set the average resources as ρ = (1, 1) and the unique optimal solution is x = (2/3, 2/3, 1). |