Notice: This website is continuously updated as new conference proceedings and journal volumes are published. Consequently, the figures presented here may differ from those reported in our publications.
A brief overview of our methodology is provided on the Methods page, along with references to publications documenting our approach and links to the code and data used in each study.
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.
Efficiently avoiding saddle points with zero order methods: No gradients required
Authors: Emmanouil-Vasileios Vlatakis-Gkaragkounis, Lampros Flokas, Georgios Piliouras
NeurIPS 2019 | Venue PDF | LLM Run Details | Input Tokens: 17,396 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 5,258 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section we use simulations to verify our theoretical findings. Specifically we are interested in verifying if zero order methods can avoid saddle points as efficiently as first order methods. To do this we use the two dimensional Rastrigin function, a popular benchmark in the non-convex optimization literature. |
| Researcher Affiliation | Academia | Lampros Flokas Department of Computer Science Columbia University New York, NY 10025 EMAIL Emmanouil V. Vlatakis-Gkaragkounis Department of Computer Science Columbia University New York, NY 10025 EMAIL Georgios Piliouras Engineering Systems and Design Singapore University of Technology and Design Singapore EMAIL |
| Pseudocode | Yes | Algorithm 1 PAGD(x0) and Algorithm 2 Escape Saddle (ˆx) |
| Open Source Code | No | The paper does not provide an explicit statement about the release of open-source code for the described methodology or a link to a code repository. |
| Open Datasets | No | The experiments use the two-dimensional Rastrigin function and the octopus function, which are mathematical functions rather than datasets that require specific access information. |
| Dataset Splits | No | The paper evaluates performance on mathematical functions (Rastrigin and Octopus functions) and does not describe any specific training, validation, or test dataset splits. |
| Hardware Specification | No | The paper describes simulations but does not provide any specific details about the hardware (CPU, GPU, memory, etc.) used to run these experiments. |
| Software Dependencies | No | The paper does not provide specific details on software dependencies, such as programming languages, libraries, or solvers with their version numbers, used for the experiments. |
| Experiment Setup | Yes | For both gradient descent and approximate gradient descent we used η = 1/(4ℓ). Then for approximate gradient descent we used symmetric differences to approximate the gradients and β = 0.95 as well as h0 = 0.15. Zero order methods use symmetric differencing with h = 0.01 |