Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy $\gamma_t = 2/(t+2)$, obtaining a $\mathcal{O}(1/t)$ convergence rate for this class of functions in terms of primal gap and Frank-Wolfe gap, where $t$ is the iteration count. This avoids the use of second-order information or the need to estimate local smoothness parameters of previous work. We also show improved convergence rates for various common cases, e.g., when the feasible region under consideration is uniformly convex or polyhedral.

翻译：通用自协调是许多重要学习问题客观功能中的一个关键属性。 我们确立了简单的Frank-Wolfe变体的趋同率,该变体使用开放环级规模战略$\gamma_t=2/(t+2)美元,获得美元=mathcal{O}(1/t)美元=这一类功能的趋同率,即初偏差和弗兰克-Wolfe差,即转差值为美元。这避免了使用二阶信息,或需要估计以往工作的地方平稳度参数。我们还显示了各种常见案例的趋同率有所改善,例如,所考虑的可行区域是统一的 convex 或 多元区域。