Generalization Analysis for Game-Theoretic Machine Learning
Authors: Haifang Li, Fei Tian, Wei Chen, Tao Qin, Zhi-Ming Ma, Tie-Yan Liu
AAAI 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we present a formal analysis on the generalization ability of GTML. Specifically, utilizing the stability property of the stationary distribution of Markov chain (Mitrophanov 2005), we decompose the generalization error for GTML into the behavior learning error and the mechanism learning error. The former relates to the process of learning a Markov behavior model from data, and the latter relates to the process of learning the optimal mechanism based on the learned behavior model. For the behavior learning error, we offer novel non-asymptotic error bounds for both parametric and non-parametric behavior learning methods: for parametric behavior learning method, we upper bound the behavior learning error by parameter learning error; for non-parametric behavior learning method, we derive a new upper bound for the gap between transition frequency and transition probability of a Markov chain. After that, we apply the Hoeffding inequality for Markov chains to both of the upper bounds, and obtain the error bound for both parametric and non-parametric behavior learning methods. For the mechanism learning error, we make use of a new concept called nested covering number of the mechanism space. Specifically, we first partition the mechanism space into subspaces (i.e., a cover) according to the similarity between the stationary distributions of the data induced by mechanisms. In each subspace, the data distribution is similar and therefore one can substitute the data sample associated with each mechanism by a common sample without affecting the expected risk by much. Second, for each mechanism subspace, we derive a uniform convergence bound based on its covering number (Anthony and Bartlett 2009) by using the generalization analysis techniques developed for mixing sequences. In the end of this paper, we apply our generalization analysis of GTML to sponsored search, and give theoretical guarantee to GTML in this scenario. To the best of our knowledge, this is the first work that performs formal generalization analysis on GTML, and we believe the methodologies we use have their general implications to the theoretical analysis of other complicated machine learning problems as well. |
| Researcher Affiliation | Collaboration | Haifang Li1, , Fei Tian2, , Wei Chen3, , Tao Qin3, Zhi-Ming Ma1, Tie-Yan Liu3 1Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R.China 2University of Science and Technology of China, Hefei, P.R.China 3Microsoft Research, Building 2, No. 5 Danling Street, Beijing, P.R.China |
| Pseudocode | No | The paper focuses on theoretical derivations and proofs, and does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link regarding the availability of source code for the described methodology. |
| Open Datasets | No | The paper is theoretical and does not conduct empirical experiments using specific datasets. It refers to 'training data' conceptually as input to the GTML framework, not as data used in their own research for evaluation. |
| Dataset Splits | No | The paper is theoretical and does not describe empirical experiments with specific dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe any empirical experiments, therefore no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe any empirical experiments, therefore no specific software dependencies with version numbers are mentioned. |
| Experiment Setup | No | The paper is theoretical and does not describe any empirical experiments or their setup, thus no hyperparameters or training configurations are provided. |