On the Generic Structure and Stability of Stackelberg Equilibria

Bressan, Alberto; Jiang, Yilun

doi:10.1007/s10957-019-01574-z

Cited by 2 publications

(1 citation statement)

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“…Still, this remains an open question as the function giving 1's value for a strategy x given that 2 best responds to it according to her payoff function is discontinuous, and the computation of discontinuities is a harder problem than computing a Stackelberg Equilibrium. Showing that there only exists a finite number of discontinuities (which was proven for the one-dimensional case for a dense set of payoff functions [28]) should enable the use of an ϵ-greedy version of BiDOO asymptotically converging towards an ϵ-Stackelberg equilibrium for any α-Hölder game.…”

Section: Discussionmentioning

confidence: 99%

Global min-max Computation for α-Hölder Games

Delage,

Buffet,

Dibangoye

2023

2023 IEEE 35th International Conference on Tools With Artificial Intelligence (ICTAI)

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min-max optimization problems recently arose in various settings. From Generative Adversarial Networks (GANs) to aerodynamic optimization through Game Theory, the assumptions on the objective function vary. Motivated by the applications to deep learning and especially GANs, most recent works assume differentiability to design local search algorithms such as Gradient Descend Ascent (GDA). In contrast, this work will only require α-Hölder properties to tackle general gametheoretic problems with poor continuity assumptions. Focusing on the example of problems in which max and min optimization variables live in simplices, we provide a simple algorithm, based on Deterministic Optimistic Optimization (DOO), relying on an outer min-optimization using the solutions of an inner maxoptimization. The algorithm is shown to converge in finite time to an ϵ-global optimum. Experimental validations are given and the time complexity of our algorithm is studied.

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Section: Discussionmentioning

confidence: 99%