The Hedge Algorithm on a Continuum
Authors: Walid Krichene, Maximilian Balandat, Claire Tomlin, Alexandre Bayen
ICML 2015 | Conference 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 WALID@EECS.BERKELEY.EDU University of California, 652 Sutardja Dai Hall, Berkeley, CA 94720 USA Maximilian Balandat BALANDAT@EECS.BERKELEY.EDU University of California, 736 Sutardja Dai Hall, Berkeley, CA 94720 USA Claire Tomlin TOMLIN@EECS.BERKELEY.EDU University of California, 721 Sutardja Dai Hall, Berkeley, CA 94720 USA Alexandre Bayen BAYEN@BERKELEY.EDU 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. |