Stochastic Direct Search Methods for Blind Resource Allocation
Authors: Juliette Achddou, Olivier Cappé, Aurélien Garivier
TMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In our experiments, we focus on the case in which there are seven resources (d = 6), and the loss functions are of the same form as in Section 2.2, and wi(x) = τi log(1+γx)log(1+γ) with γ = 2, τ1 = 1, τ2 = τ3 = τ4 = 0.75, τ5 = 0.89, and τ6 = τ7 = 0.95. On Figure 2, we compare FDS-Seq and FDS-Plan to UCB on a discretization of the space, and gradient descent with an homothetic perturbation. Both methods are explained in Section 2.2. The comparison with HOO is made impossible by the numerical complexity of HOO. We set the horizon to T = 500,000 and use a Gaussian noise with standard deviation σ = 0.1. The set of directions used in FDS-Seq and FDS-Plan are chosen with the method of Griffin et al. (2008). The step parameter of the grid of UCB is set as T 1/(d+2) = T 1/8. The regrets of the algorithms strongly depend on the chosen function. In the case of UCB, the position of the maximizer with respect to the grid that it relies on is important. To alleviate this issue, we plot the mean regret of all the algorithms, when randomly shifting the loss function by a random vector whose coordinates are in [0.05, 0.05]. We use 1200 Monte Carlo repetitions. The shaded area represents the region between the first and third quartile. |
| Researcher Affiliation | Academia | Juliette Achddou EMAIL Department of Computer Science Università degli Studi di Milano Olivier Cappé EMAIL Department of Computer Science ENS Paris Aurélien Garivier EMAIL Department of Mathematics ENS Lyon |
| Pseudocode | Yes | Algorithm 1: Direct Search with sufficient decrease, Algorithm 2: FDS-Plan, Algorithm 3: FDS-Seq |
| Open Source Code | No | The paper describes new algorithms and their analysis, but there is no explicit statement about releasing source code or a link to a code repository provided in the document. |
| Open Datasets | No | In our experiments, we focus on the case in which there are seven resources (d = 6), and the loss functions are of the same form as in Section 2.2, and wi(x) = τi log(1+γx)log(1+γ) with γ = 2, τ1 = 1, τ2 = τ3 = τ4 = 0.75, τ5 = 0.89, and τ6 = τ7 = 0.95. The paper describes using a simulated environment with defined loss functions, not an external dataset. |
| Dataset Splits | No | The paper uses a simulated environment based on defined loss functions and noise parameters. There are no external datasets requiring explicit train/test/validation splits described. |
| Hardware Specification | No | The paper mentions running experiments and simulations, but it does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used for these experiments. |
| Software Dependencies | No | The paper describes algorithms and experiments, but it does not specify any software dependencies or version numbers for libraries, frameworks, or programming languages used. |
| Experiment Setup | Yes | In our experiments, we focus on the case in which there are seven resources (d = 6), and the loss functions are of the same form as in Section 2.2, and wi(x) = τi log(1+γx)log(1+γ) with γ = 2, τ1 = 1, τ2 = τ3 = τ4 = 0.75, τ5 = 0.89, and τ6 = τ7 = 0.95. We set the horizon to T = 500,000 and use a Gaussian noise with standard deviation σ = 0.1. The parameters of both versions of feasible direct search are α0 = 0.2, c = 5 and θ = 0.7, and the initial point corresponds to the allocation x(0) = (1/3, 1/3, 1/3). The set of directions used in FDS-Seq and FDS-Plan are chosen with the method of Griffin et al. (2008). The step parameter of the grid of UCB is set as T 1/(d+2) = T 1/8. We use 1200 Monte Carlo repetitions. |