Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm
Authors: Adil Salim, Peter Richtarik
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In the first part of this paper, we establish a strong duality result for this minimization problem. In the second part of this paper, we use the duality gap arising from the first part to study the complexity of the Proximal Stochastic Gradient Langevin Algorithm (PSGLA), which can be seen as a generalization of the Projected Langevin Algorithm. Our approach relies on viewing PSGLA as a primal dual algorithm and covers many cases where the target distribution is not fully supported. In particular, we show that if the potential is strongly convex, the complexity of PSGLA is O(1/ε2) in terms of the 2-Wasserstein distance. Finally, we conduct some numerical experiments for sampling from a distribution supported by a set of matrices (see appendix). |
| Researcher Affiliation | Academia | Adil Salim Peter Richtárik King Abdullah University of Science and Technology, Thuwal, Saudi Arabia |
| Pseudocode | No | The paper provides algorithmic steps for PSGLA as mathematical equations (e.g., equation 3, 24, 25) but does not present them in a clearly labeled or formatted pseudocode or algorithm block. |
| Open Source Code | No | The paper does not provide concrete access to source code (e.g., a specific repository link or an explicit code release statement) for the methodology described. |
| Open Datasets | No | The paper refers to sampling from a "log concave probability distribution" and conducting "numerical experiments for sampling from a distribution supported by a set of matrices". It does not specify the use of a named, publicly available dataset with concrete access information such as a link, DOI, or formal citation. |
| Dataset Splits | No | The paper does not provide specific dataset split information (e.g., exact percentages, sample counts, or methodology) needed to reproduce data partitioning for training, validation, or testing. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library names with version numbers, needed to replicate the experiment. |
| Experiment Setup | No | The paper refers to conducting "numerical experiments" but does not provide specific experimental setup details such as concrete hyperparameter values, training configurations, or system-level settings in the main text. It mentions "γ > 0" as a parameter for PSGLA but no concrete values. |