  For Internet applications like sponsored search, cautions need to be taken
when using machine learning to optimize their mechanisms (e.g., auction) since
self-interested agents in these applications may change their behaviors (and
thus the data distribution) in response to the mechanisms. To tackle this
problem, a framework called game-theoretic machine learning (GTML) was recently
proposed, which first learns a Markov behavior model to characterize agents'
behaviors, and then learns the optimal mechanism by simulating agents' behavior
changes in response to the mechanism. While GTML has demonstrated practical
success, its generalization analysis is challenging because the behavior data
are non-i.i.d. and dependent on the mechanism. To address this challenge,
first, we decompose the generalization error for GTML into the behavior
learning error and the mechanism learning error; second, for the behavior
learning error, we obtain novel non-asymptotic error bounds for both parametric
and non-parametric behavior learning methods; third, for the mechanism learning
error, we derive a uniform convergence bound based on a new concept called
nested covering number of the mechanism space and the generalization analysis
techniques developed for mixing sequences. To the best of our knowledge, this
is the first work on the generalization analysis of GTML, and we believe it has
general implications to the theoretical analysis of other complicated machine
learning problems.
