Applying Metric Regularity to Compute a Condition Measure of a Smoothing Algorithm for Matrix Games
This work provides a theoretical foundation for analyzing algorithm conditioning in zero-sum matrix games, but is incremental as it applies known concepts to a specific algorithm.
The authors develop a variational analysis approach to compute a condition measure for a smoothing algorithm in matrix games, establishing its relationship with metric regularity of an associated set-valued mapping.
We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed by Gilpin et al. [Proceedings of the 23rd AAAI Conference (2008) pp. 75-82] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.