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]
Contaminated Online Convex Optimization
Authors: Tomoya Kamijima, Shinji Ito
TMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In online convex optimization, some efficient algorithms have been designed for each of the individual classes of objective functions, e.g., convex, strongly convex, and exp-concave. ... This paper introduces a novel approach to address such cases, proposing a new regime we term as contaminated online convex optimization. For the contaminated case, we demonstrate that the regret is lower bounded by Ω(log T + k). ... We also demonstrate that the regret is bounded by O(log T + k log T) when universal algorithms are used. When our proposed algorithms with additional information are employed, the regret is bounded by O(log T + k), which matches the lower bound. ... In this section, we explain experimental results. We compare the performances of 5 OCO algorithms; OGD with stepsizes ηt = D/(G t), ONS, Meta Grad, Algorithm 1 with S1 = (Con-ONS), and Algorithm 1 with S2 = (Con-OGD). |
| Researcher Affiliation | Collaboration | Tomoya Kamijima EMAIL Department of Mathematical Informatics The University of Tokyo Shinji Ito EMAIL Department of Mathematical Informatics The University of Tokyo NEC Corporation (affiliation upon submission) RIKEN AIP |
| Pseudocode | Yes | Algorithm 1 Algorithm using additional information Input: convex set X Rd, x1 X, T, D, G, α, λ Algorithm 2 Online Gradient Descent (Zinkevich, 2003) Algorithm 3 Online Newton step (Hazan et al., 2006) Algorithm 4 Meta Grad Master (Van Erven & Koolen, 2016) Algorithm 5 Meta Grad Slave (Van Erven & Koolen, 2016) Algorithm 6 Maler Meta (Wang et al., 2020) Algorithm 7 Maler Convex Expert (Wang et al., 2020) Algorithm 8 Maler Exp-concave Expert (Wang et al., 2020) Algorithm 9 Maler Strongly Convex Expert (Wang et al., 2020) Algorithm 10 Universal Strategy for Online Convex Optimization (USC) (Zhang et al., 2022) |
| Open Source Code | No | The paper does not explicitly state that source code for the methodology is openly available, nor does it provide any links to a code repository. It mentions "All the experiments are implemented in Python 3.9.2" but this is not a statement of code release. |
| Open Datasets | No | Example 3.7. (Online least mean square regressions) Consider the situation where a batch of input-output data (at,i, bt,i) Rd R (i {1, 2, . . . , n}) is given in each round t... In this experiment, each component of the vector at,i is taken from a uniform distribution on [1, 2] independently. We set X = [0, 1]d and assume there exists an optimal solution x which is taken from a uniform distribution on X, i.e., we take bt,i = at,i, x . The paper describes synthetic data generation and does not use or provide access to any publicly available datasets. |
| Dataset Splits | No | The paper describes experiments using synthetically generated data but does not specify any training/test/validation splits, as the experiments are online learning scenarios where data is revealed sequentially. There are no traditional dataset splits mentioned. |
| Hardware Specification | Yes | All the experiments are implemented in Python 3.9.2 on a Mac Book Air whose processor is 1.8 GHz dual-core Intel Core i5 and memory is 8GB. |
| Software Dependencies | Yes | All the experiments are implemented in Python 3.9.2 on a Mac Book Air whose processor is 1.8 GHz dual-core Intel Core i5 and memory is 8GB. |
| Experiment Setup | Yes | Table 2: Parameter setting in Experiment 1. x1 x T k D G α 0 0.02 1000 250 1 100 1 Table 3: Parameter setting in Experiment 2. x1 x T k D G λ 0 2/3 1000 250 1 1 1 Table 4: Parameter setting in Experiment 3. x1 n d T k D 0 10 5 1000 250 The parameters of ONS are set as γ = 0.005 and ε = 1/(γ2D2) = 40000. We repeat this numerical experiment in 100 different random seeds and calculate their mean and standard deviation. |