Papers › Parameter-free Stochastic Optimization of Variationally Coherent Functions
Parameter-free Stochastic Optimization of Variationally Coherent Functions
Francesco Orabona, Dávid Pál
We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on ℝᵈ. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The iterates of our algorithm on variationally coherent functions converge almost surely to the global minimizer x^*. Additionally, the very same algorithm with the same hyperparameters, after T iterations guarantees on convex functions that the expected suboptimality gap is bounded by O(x^* - x₀ T^(-1/2+ϵ)) for any ϵ>0. It is the first algorithm to achieve both these properties at the same time. Also, the rate for convex functions essentially matches the performance of parameter-free algorithms. Our algorithm is an instance of the Follow The Regularized Leader algorithm with the added twist of using \emph{rescaled gradients} and time-varying linearithmic regularizers.
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