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].

Lower Bounds and Accelerated Algorithms for Bilevel Optimization

Authors: Kaiyi ji, Yingbin Liang

JMLR 2023 | Venue PDF | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Our theoretical results are validated by numerical experiments. Keywords: Bilevel optimization, lower bounds, accelerated algorithms, computational complexity, convergence rate, optimality.
Researcher Affiliation Academia Kaiyi Ji EMAIL Department of Computer Science and Engineering University at Buffalo Buffalo, NY 14260-2500, USA Yingbin Liang EMAIL Department of Electrical and Computer Engineering The Ohio State University Columbus, OH 98195-4322, USA
Pseudocode Yes Algorithm 1 Accelerated Bilevel Optimization (Acc Bi O) Algorithm; Algorithm 2 Accelerated Bilevel Optimization Method under Bounded Gradient Assumption (Acc Bi O-BG)
Open Source Code No The paper does not contain any explicit statement about releasing the source code for the described methodology, nor does it provide any links to a code repository.
Open Datasets No In this section, we conduct experiments to validate our theoretical results. We consider the following bilevel optimization problem, where the upper and lower functions are given by f(x, y) = 1 2x T U2x + 1 2x T V y and g(x, y) = 1 2y T (H2 + I)y 1 2x T V y + b T y, where U, H and V are random matrices with each entry sampled from [0, 1) uniformly at random.
Dataset Splits No The paper uses randomly generated matrices for its optimization problem, rather than a predefined dataset. Therefore, traditional dataset splits (training, validation, test) are not applicable or mentioned.
Hardware Specification No The paper does not explicitly mention any specific hardware (e.g., GPU/CPU models, memory specifications) used for running the numerical experiments. It only refers to 'running time /s'.
Software Dependencies No The paper mentions 'PyTorch or Tensor Flow' in a general context regarding automatic differentiation capabilities but does not specify which software, along with version numbers, was used for their specific implementation or experiments. Other software like CPLEX is mentioned as general examples, not as dependencies for this work.
Experiment Setup Yes Hyperparameter setting. For AID and ITD, we choose their best innerand outer-loop learning rates from {10i, i = 6, 5, 4, 3, 2, 1, 0, 1, 2, ..., 6}. For Acc Bi O, we choose the coefficients α and β in the inner-loop acceleration updates yt k = st 1 k α yg(xk, st 1 k ), st k = (1 + β)yt k βyt 1 k from {10i, i = 5, ..., 4, 5}. Similarly, we choose the coefficients in the outer-loop acceleration updates (i.e., line 8-9 in Algorithm 2) from {10i, i = 7, 6, ..., 6, 7}. For ITD, we choose the number N of inner-loop iterations from {5, 10, 15, 20}. For AID and our Acc Bi O method, we choose N from {5, 10, 15, 20} and the number M of the iterations for solving the linear system from {5, 10, 15}.