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 and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Volumetric Spanners: An Efficient Exploration Basis for Learning
Authors: Elad Hazan, Zohar Karnin
JMLR 2016 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper we consider a generic approach to exploration, and quantify what efficient exploration with low variance requires in general. Given a set in Euclidean space, a low-variance exploration basis is a subset with the following property: given noisy estimates of a linear function over the basis, one can construct an estimate for the linear function over the entire set without increasing the variance of the estimates. [...] Henceforth we define a novel construction for a low variance exploration basis called volumetric spanners and give efficient algorithms to construct them. We further investigate the convex geometry implications of our construction, and define the notion of a minimal volumetric ellipsoid of a convex body. We give structural theorems on the existence and properties of these ellipsoids, as well as constructive algorithms to compute them in several cases. We complement our findings with two applications to machine learning. The first application is to the problem of experiment design, in which we give an efficient algorithm for hard-margin active linear regression with optimal bounds. Next, we advance a well-studied open problem that has exploration as its core difficulty: an efficient and near-optimal regret algorithm for bandit linear optimization (BLO). |
| Researcher Affiliation | Collaboration | Elad Hazan EMAIL Princeton University, Department of Computer Science Princeton, NJ 08540, USA. Zohar Karnin EMAIL Yahoo Haifa Labs Matam, Haifa 31905, Israel. |
| Pseudocode | Yes | Algorithm 1 Fast Volumetric Spanner construction Algorithm 2 Sample(K) Algorithm 3 Primal-Dual Algorithm for ALR Algorithm 4 Verification Algorithm 5 Geometric Hedge with Volumetric Spanners Exploration |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or provide links to a code repository. |
| Open Datasets | No | The paper does not explicitly state the use of any publicly available or open datasets. It refers to a generic 'pool of data points K = {x1, ..., xn} Rd'. |
| Dataset Splits | No | The paper does not mention any specific dataset splits such as training, validation, or test sets, as it primarily focuses on theoretical contributions rather than empirical evaluation on specific datasets. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running experiments, such as CPU or GPU models. This is consistent with a theoretical paper that does not report empirical results. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers. It mentions general mathematical and algorithmic methods like 'ellipsoid method or path-following interior point methods' and 'linear programming', but not as specific software tools used for its implementation. |
| Experiment Setup | No | The paper does not provide details about an experimental setup, including hyperparameters or system-level training settings. It is a theoretical paper describing algorithms and their properties, not reporting empirical experimental results. |