On the Power of Optimism in Constrained Online Convex Optimization

Authors: Haobo Zhang, Hengquan Guo, Xin Liu

IJCAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Experimental results further validate our theoretical findings, demonstrating the practical efficacy of the proposed algorithm. In this section, we present a series of synthetic experiments designed to evaluate the performance of the Optimistic COCO algorithm under both dynamic and slowly-changing environments.
Researcher Affiliation Academia Haobo Zhang , Hengqun Guo and Xin Liu Shanghai Tech University, Shanghai, China EMAIL
Pseudocode Yes Algorithm 1 Optimistic-COCO 1: Initialization: x0, x1 X0, Q0 = 0, L0(x) = L1(x) = 0, x X0, adaptive learning rates ηt = Θ( 1 Vt ) and ϕt = Θ( Vt). 2: for t = 1, , T do 3: Calculate the optimistic gradient: θt = 2 x Lt(xt, Qt) x Lt 1(xt 1, Qt 1). (5) 4: Take adaptive gradient decision: xt+1 = arg min x X0 θt, x + 1 2ηt x xt 2. (6) 5: Observe ft+1 and calculate: ϕt+1 and ηt+1. 6: Update virtual queue: Qt+1 = [Qt + g(xt+1)]+ . (7)
Open Source Code No The paper does not provide any statement or link indicating the availability of open-source code for the described methodology.
Open Datasets No Similar to the setups used in [Yu and Neely, 2020; Yi et al., 2021], we consider a scenario where the loss functions are linear, defined as ft(x) = ct, x , where ct is a time-varying coefficient. The constraint function is expressed as Ax b, with the decision variable x belonging to R2. The constraint matrix A R3 2 and vector b R2 are fixed and generated uniformly within the intervals [0.1, 0.5] for A and [0, 0.2] for b, respectively. We set the total number of rounds to T = 5000 and select the feasible set X0 = [ 1, 1]2.
Dataset Splits No The paper describes synthetic data generation for online convex optimization over T=5000 rounds and evaluation by averaging over 20 independent runs. It does not mention traditional dataset splits like training, validation, or test sets.
Hardware Specification No The paper does not provide specific hardware details such as GPU/CPU models, memory, or cloud instance types used for running the experiments.
Software Dependencies No The paper does not mention any specific software, libraries, or their version numbers used to implement and run the experiments.
Experiment Setup Yes In the dynamic setting, we define ct = c1(t) + c2(t) + c3(t), where c1(t) is uniformly drawn from [ t1/10, t1/10], c2(t) is uniformly drawn from [ 1, 0] for t [1, 1500] [2000, 3500] [4000, 5000] and from [0, 1] otherwise, and c3(t) = ( 1)µ(t), where µ(t) is a random permutation of the vector [1, T]. The loss functions remain fixed within each 100-round segment. At the start of each segment, the linear factor c is uniformly drawn from [0, 1], and ct = c remains constant for the following 100 rounds. We set the total number of rounds to T = 5000 and select the feasible set X0 = [ 1, 1]2. For each algorithm, we track and plot the cumulative loss and violation over time. Each value is plotted by averaging over 20 independent runs. Let the parameters be ϕt = max np Vt + Qt + 2F + R, ϕt 1 o 1 2ηt = max 4Gϕt Qt + 4M 2ϕt + 4F, 1 2ηt 1.