Achievability of Asymptotic Minimax Regret by Horizon-Dependent and Horizon-Independent Strategies
Authors: Kazuho Watanabe, Teemu Roos
JMLR 2015 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our numerical experiments for the Bernoulli model demonstrate improved finite-sample performance by a number of novel horizon-dependent and horizon-independent algorithms. |
| Researcher Affiliation | Academia | Kazuho Watanabe EMAIL Department of Computer Science and Engineering Toyohashi University of Technology 1-1, Hibarigaoka, Tempaku-cho, Toyohashi, 441-8580, Japan Teemu Roos EMAIL Helsinki Institute for Information Technology HIIT Department of Computer Science, University of Helsinki PO Box 68, FI-00014, Finland |
| Pseudocode | No | The paper describes algorithms and derivations mathematically but does not present any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link regarding the availability of open-source code for the described methodology. |
| Open Datasets | No | Our numerical experiments for the Bernoulli model demonstrate improved finite-sample performance by a number of novel horizon-dependent and horizon-independent algorithms. The paper discusses theoretical models (multinomial, Bernoulli) and performs numerical experiments based on these models, rather than using specific pre-existing datasets. No concrete access information for a public dataset is provided. |
| Dataset Splits | No | The paper describes numerical experiments conducted within the Bernoulli model, which implies simulated data rather than the use of pre-existing datasets with explicit train/test/validation splits. |
| Hardware Specification | No | The paper does not provide any 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 provide specific software dependency details with version numbers for replication. |
| Experiment Setup | Yes | We calculated the maximum regrets of the Bayes mixtures in (5) with the hyperparameter optimized by the golden section search and with its asymptotic approximation in (19). We also investigated the maximum regrets of Xie and Barron s modified Jeffreys prior which is proved to be asymptotic minimax (Xie and Barron, 2000). The modified Jeffreys prior is q(n) MJ(θ) = ϵnδ + (1 ϵn)b1/2(θ), where δ is the Dirac s delta function and b1/2(θ) is the density function of the beta distribution with hyperparameters 1/2, Beta(1/2, 1/2), which is the Jeffreys prior for the Bernoulli model. We set ϵn = n 1/8 as proposed by Xie and Barron (2000) and also optimized ϵn by the golden section search so that the maximum regret max xn ln p(xn|ˆθ(xn)) R p(xn|θ)q(n) MJ(θ)dθ is minimized. The proposed procedure assigns probability (k + αn)/(n + mαn) to any outcome that has appeared k times in a sequence of length n, where m is the alphabet size and αn = 1/2 ln 2/(2 ln n) is a prior mass assigned to each outcome. |