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. |