Online Frank-Wolfe with Arbitrary Delays
Authors: Yuanyu Wan, Wei-Wei Tu, Lijun Zhang
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we conduct simulation experiments to verify the performance of our delayed OFW for convex losses and strongly convex losses. All algorithms are implemented wtih Matlab R2017a and tested on a laptop with 2.4GHz CPU and 16GB memory. The code is available from https: //github.com/yuanyuwan/Neur IPS22. ... Fig. 1(a) shows the total loss of T rounds for each algorithm under different values of the maximum delay d. |
| Researcher Affiliation | Collaboration | Yuanyu Wan1,2, Wei-Wei Tu3,4, Lijun Zhang4, 1School of Software Technology, Zhejiang University, Ningbo, China 2Zhejiang University-China Southern Power Grid Joint Research Centre on AI, Hangzhou, China 34Paradigm Inc., Beijing, China 4National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China |
| Pseudocode | Yes | Algorithm 1 Delayed OFW for Convex Losses ... Algorithm 2 Delayed OFW for Strongly Convex Losses |
| Open Source Code | Yes | The code is available from https: //github.com/yuanyuwan/Neur IPS22. |
| Open Datasets | No | Specifically, we consider a delayed OCO problem with T = 10000 total rounds over the decision set K = x R1000 x 1 200 , which satisfies Assumption 2 with D = 400 due to x y 2 x 2 + y 2 x 1 + y 1 400 for any x, y K. Inspired by Li et al. [2019], in each round t [T], the adversary chooses the following loss function ft(x) = x 2 + bt, x where each element of bt R1000 is independently and uniformly sampled from [ 1, 1]. |
| Dataset Splits | No | The paper conducts experiments in an online convex optimization setting with a total of T=10000 rounds. It does not mention traditional train/validation/test dataset splits, as data is processed sequentially. |
| Hardware Specification | Yes | All algorithms are implemented wtih Matlab R2017a and tested on a laptop with 2.4GHz CPU and 16GB memory. |
| Software Dependencies | Yes | All algorithms are implemented wtih Matlab R2017a |
| Experiment Setup | Yes | The parameters of all algorithms are set as what their corresponding theories suggest. Specifically, according to our Theorems 1 and 2, we set η = D 2G(T +2)3/4 for our DOFW and set β = 2 for our DOFWsc. ...in BOLD-OFW, we set η = D 2G(T/d+2)3/4 for each instance of OFW for convex losses... In BOLD-OFWsc, we only need to set β = 2 for each instance of OFW for strongly convex losses. Moreover, for our delayed OFW and each instance of OFW, the initial decision is set to 1/50, where 1 denotes the all-ones vector. ... Specifically, we consider a delayed OCO problem with T = 10000 total rounds over the decision set K = x R1000 x 1 200 , which satisfies Assumption 2 with D = 400 ... satisfies Assumption 1 with G = 400 + 1000. We also notice that this loss function satisfies the definition of β-strongly convex function (i.e., Definition 1) with β = 2. Moreover, different values of the maximum delay d in the set {1, 51, 101, . . . , 501} are tried in our experiments. For each specific d, to simulate arbitrary delays, dt is independently and uniformly sampled from the set { 0.1d , 0.1d + 1, 0.1d + 2, . . . , d}. |