Two linesearch-based generalized conditional gradient methods, including a parameter-free variant from Ito et al., are proven to converge to stationary points without any Lipschitz or Hölder gradient assumption.
A H\"olderian backtracking method for min-max and min-min problems
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abstract
We present a new algorithm to solve min-max or min-min problems out of the convex world. We use rigidity assumptions, ubiquitous in learning, making our method applicable to many optimization problems. Our approach takes advantage of hidden regularity properties and allows us to devise a simple algorithm of ridge type. An original feature of our method is to come with automatic step size adaptation which departs from the usual overly cautious backtracking methods. In a general framework, we provide convergence theoretical guarantees and rates. We apply our findings on simple GAN problems obtaining promising numerical results.
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Convergence of linesearch-based generalized conditional gradient methods without smoothness assumptions
Two linesearch-based generalized conditional gradient methods, including a parameter-free variant from Ito et al., are proven to converge to stationary points without any Lipschitz or Hölder gradient assumption.