Heavy-Tailed Linear Bandits: Huber Regression with One-Pass Update
Authors: Jing Wang, Yu-Jie Zhang, Peng Zhao, Zhi-Hua Zhou
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we evaluate the empirical performance and time efficiency of our proposed Hvt-UCB algorithm. We present two experiments under heavy-tailed noise (Student s t) and light-tailed noise (Gaussian). |
| Researcher Affiliation | Academia | 1National Key Laboratory for Novel Software Technology, Nanjing University, China 2School of Artificial Intelligence, Nanjing University, China 3Center for Advanced Intelligence Project, RIKEN, Japan. |
| Pseudocode | Yes | Algorithm 1 Hvt-UCB |
| Open Source Code | No | The paper does not provide any explicit statement or link indicating that the source code for the methodology described in this paper is publicly available. |
| Open Datasets | No | We consider the linear model rt = X t θ + ηt... We conduct two synthetic experiments with different distributions for noise ηt: (a) Student s t-distribution with degree of freedom df = 2.1 to represent heavy-tailed noise; and (b) Gaussian noise sampled from N(0, 1) to represent light-tailed noise. |
| Dataset Splits | No | The paper uses synthetic data and thus does not involve traditional training/test/validation dataset splits. It specifies the number of rounds T = 18000 and the number of independent trials (10 or 5) for evaluation. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | We implement all three distributions using Python s scipy.stats. (No version numbers are provided for Python or scipy.) |
| Experiment Setup | Yes | Settings. We consider the linear model rt = X t θ + ηt, where the dimension d = 2, the number of rounds T = 18000, and the number of arms n = 50. Each dimension of the feature vectors for the arms is uniformly sampled from [ 1, 1] and subsequently rescaled to satisfy L = 1. Similarly, θ is sampled in the same way and rescaled to satisfy S = 1. We conduct two synthetic experiments with different distributions for noise ηt: (a) Student s t-distribution with degree of freedom df = 2.1 to represent heavy-tailed noise; and (b) Gaussian noise sampled from N(0, 1) to represent light-tailed noise. For the heavy-tailed experiment, we set ε = 0.99 and ν = 1.31, while for the light-tailed experiment, we set ε = 1. (From Section 5) Additionally, from Theorem 1: By setting σt, τt, τ0, α as in Lemma 1, and let λ = d, σmin = 1 T , δ = 1 8T |