In this paper, we present a generic framework that allows accelerating almost
arbitrary non-accelerated deterministic and randomized algorithms for smooth
convex optimization problems. The main approach of our envelope is the same as
in Catalyst (Lin et al., 2015): an accelerated proximal outer gradient method,
which is used as an envelope for a non-accelerated inner method for the
$\ell_2$ regularized auxiliary problem. Our algorithm has two key differences:
1) easily verifiable stopping criteria for inner algorithm; 2) the
regularization parameter can be tunned along the way. As a result, the main
contribution of our work is a new framework that applies to adaptive inner
algorithms: Steepest Descent, Adaptive Coordinate Descent, Alternating
Minimization. Moreover, in the non-adaptive case, our approach allows obtaining
Catalyst without a logarithmic factor, which appears in the standard Catalyst
(Lin et al., 2015, 2018).

本文提出了一个通用框架，允许加速几乎任意非加速确定性和随机算法用于光滑凸优化问题，其中通过使用加速的近端外梯度方法作为非加速内方法的包络来实现。该算法有两个关键不同之处：容易验证的内部算法停止标准和学习率的可调节性，使得此工作的主要贡献是适用于自适应内部算法 Steepset Descent、Adaptive Coordinate Descent 和 Alternating Minimization 的新框架。此外，在非自适应情况下，我们的方法允许获得没有对数因子的 Catalyst，这与标准 Catalyst 不同。