Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1]
Streaming kernel regression with provably adaptive mean, variance, and regularization
Authors: Audrey Durand, Odalric-Ambrym Maillard, Joelle Pineau
JMLR 2018 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we illustrate the results introduced in the previous Sections 2 and 3 on a few examples. The first one is the concentration result on the mean from Theorem 1, the second one is the variance estimate from Theorem 3, and the last one combines the formers by using the noise estimate to tune λt+1 = σ2 t /C2 in Theorem 2, which corresponds to Corollary 1. We finally show the performance of kernelized bandits techniques using the provided variance estimates and adaptative regularization schemes. We conduct the experiments using the function f shown by Figure 1, which has norm f K = θ 2 = 2.06 in the RKHS induced by a Gaussian kernel k(x, x ) = e (x x )2 with length scale ρ = 0.3. |
| Researcher Affiliation | Collaboration | Audrey Durand EMAIL Universit e Laval, Qu ebec, Canada; Odalric-Ambrym Maillard EMAIL INRIA, Lille, France; Joelle Pineau EMAIL Mc Gill University & Facebook AI Research, Montreal, Canada |
| Pseudocode | Yes | Algorithm 1 Kernel TS with adaptive variance estimation and regularization tuning. Input: discrete space X. Parameters: regularization sequence λ, variance inflation factor v2 t for each t. 1: for all t 1 do 2: compute the posterior mean bft 1 = (fλt,t 1(x))x X 3: compute the posterior covariance bΣt 1 = σ2 +,t 1 λt kλt,t 1(x, x ) x,x X 4: sample ft = N(bft 1, v2 t bΣt 1) 5: play xt = argmaxx X ft(x) 6: observe outcome yt = f (xt) + ξt 7: end for |
| Open Source Code | No | The paper does not provide an explicit statement or link to open-source code for the methodology described. |
| Open Datasets | No | The paper describes generating synthetic data for experiments: 'We conduct the experiments using the function f shown by Figure 1, which has norm f K = θ 2 = 2.06 in the RKHS induced by a Gaussian kernel k(x, x ) = e (x x )2 with length scale ρ = 0.3. This function results from the linear product between features ϕ(x), explicited using a Taylor expansion2, and a randomly generated parameter vector θ . We consider the space X = [0, 1] and zero-centered Gaussian noise with σ = 0.1.' No concrete access information for a public dataset is provided. |
| Dataset Splits | No | The paper describes a synthetic experimental setup where data is generated or sampled interactively by the algorithms: 'We consider the space X = [0, 1] and zero-centered Gaussian noise with σ = 0.1.' and 'We consider X as the linearly discretized space X = [0, 1] into 100 arms.' Observations are then 'uniformly sampled from X' or 'sampled from X using the bandits algorithms.' There are no traditional training/test/validation dataset splits specified, as the data generation is part of the experimental process. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU, GPU models, or memory specifications) used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers (e.g., library names like PyTorch or TensorFlow with their respective versions) required to replicate the experiments. |
| Experiment Setup | Yes | We conduct the experiments using the function f shown by Figure 1, which has norm f K = θ 2 = 2.06 in the RKHS induced by a Gaussian kernel k(x, x ) = e (x x )2 with length scale ρ = 0.3. [...] We consider the space X = [0, 1] and zero-centered Gaussian noise with σ = 0.1. All further experiments use the upper-bound C = 5 on f K and the lower-bound σ = 0.01 on σ. [...] In both cases, we use a fixed confidence level δ = 0.1. [...] We consider X as the linearly discretized space X = [0, 1] into 100 arms. [...] Kernel UCB uses δ = 0.1/4 and Kernel TS uses δ = 0.1/12 such that their regret bounds respectively hold with probability 0.9. [...] Configurations b) and c) use σ+ = 1, while the oracle a) uses σ+ = σ. |