The Hedge Algorithm on a Continuum
Authors: Walid Krichene, Maximilian Balandat, Claire Tomlin, Alexandre Bayen
ICML 2015 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We test our algorithm on a numerical example in R2 with convex quadratic loss functions of the form ℓ(t)(s) = 1 2(s µt) Qt(s µt) + ct restricted to the domain S R2 shown in Figure 2. ... For a simulation horizon of T = 104, we randomly generated the parameters µt, Qt and ct of the loss functions subject to the uniform bounds M = 10 and L = 5. We simulated the algorithm 2500 times for each of the different choices of the learning rates. Figure 3 shows means (solid lines), regret bounds (dashed lines) and regions between the 10% and 90% quantiles (shaded) of the per-round cumulative regret over these simulations. |
| Researcher Affiliation | Academia | Walid Krichene EMAIL University of California, 652 Sutardja Dai Hall, Berkeley, CA 94720 USA Maximilian Balandat EMAIL University of California, 736 Sutardja Dai Hall, Berkeley, CA 94720 USA Claire Tomlin EMAIL University of California, 721 Sutardja Dai Hall, Berkeley, CA 94720 USA Alexandre Bayen EMAIL University of California, 642 Sutardja Dai Hall, Berkeley, CA 94720 USA |
| Pseudocode | Yes | Algorithm 1 Hedge algorithm with initial density x(0) and learning rates (ηt). ... Algorithm 2 Dual averaging method with input sequence (ℓ(t)) and learning rates (ηt) |
| Open Source Code | No | The paper does not provide any explicit links or statements regarding the availability of open-source code. |
| Open Datasets | No | The paper uses randomly generated parameters and simulation for its numerical example, not a publicly available dataset. There is no mention of accessing a public dataset for training. |
| Dataset Splits | No | The paper describes a simulation-based numerical example with randomly generated parameters and a simulation horizon. It does not mention train/validation/test dataset splits. |
| Hardware Specification | No | The paper describes numerical simulations but does not specify any hardware (CPU, GPU, etc.) used to run these simulations. |
| Software Dependencies | No | The paper describes the algorithms and their theoretical properties and presents numerical simulation results, but it does not list any specific software dependencies with version numbers. |
| Experiment Setup | Yes | For a simulation horizon of T = 104, we randomly generated the parameters µt, Qt and ct of the loss functions subject to the uniform bounds M = 10 and L = 5. We simulated the algorithm 2500 times for each of the different choices of the learning rates. |