The Lazy Online Subgradient Algorithm is Universal on Strongly Convex Domains

Authors: Daron Anderson, Douglas Leith

NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Here we present numerical simulations for Online Lazy Gradient Descent, using a range of strongly convex domains and i.i.d opponents.
Researcher Affiliation Academia Daron Anderson School of Computer Science and Statistics Trinity College Dublin Douglas Leith School of Computer Science and Statistics Trinity College Dublin
Pseudocode Yes Algorithm 1: Online Lazy Gradient Descent Data: Cost vectors a1, a2, . . . Rd. Parameter η > 0. Domain X Rd. 1 for n = 0, 1, . . . do 2 xn+1 =ΠX η n Pn i=1 ai 3 Receive an+1 and pay cost an+1 xn+1
Open Source Code No The paper does not provide any statement about releasing source code or a link to a code repository.
Open Datasets No The paper generates synthetic cost vectors for simulations ('cost vectors an = a + µn') but does not refer to a publicly available dataset or provide access information for one.
Dataset Splits No The paper does not mention using a validation set or describe any data splitting for training, validation, or testing.
Hardware Specification No The paper mentions 'The higher dimensional simulations ran on the order of minutes, due to use of an all-purpose Python package to compute minimisers.' but does not specify any hardware details like GPU/CPU models or memory.
Software Dependencies No The paper mentions 'an all-purpose Python package to compute minimisers' but does not specify any software names with version numbers.
Experiment Setup Yes For simplicity we use stepsize η = 1. When searching for worst-case performance it is enough, by symmetry of the domain, to only consider E[an] = a with nonnegative nondecreasing components. We consider a = b/ b for b(i) = (i/d)r and a range of parameters r 0. For example three degenerate cases are a = 1 d(1, . . . , 1) for r = 0; a = q 2 d(d+1)(1, 2, . . . , d) for r = 1 and a = (0, . . . , 0, 1) for r . We use cost vectors an = a + µn for two types of noise: (1) µn(j) = 1 d(Bn 1 , . . . , Bn d ) (2) µn(j) = (0, . . . , 0, Bn d ).