论文标题
具有错误的近端梯度算法的尖锐界限
Sharper Bounds for Proximal Gradient Algorithms with Errors
论文作者
论文摘要
我们分析了在存在梯度和近端计算不存在的情况下，近端梯度算法的融合。我们得出了新的更严格的确定性和概率界限，用于验证模拟（MPC）和合成（LASSO）优化问题在还原的机器上解决，并结合使用不准确的近端操作员。我们还展示了概率界限如何更强大地用于算法验证，并且更准确地用于应用程序性能保证。根据一些统计假设，我们还证明了一些累积错误术语遵循Martingale属性。并符合观察，例如，在\ cite {schmidt2011 convergence}中，我们还展示了算法的加速度如何放大梯度和近端计算错误。
We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to verify a simulated (MPC) and a synthetic (LASSO) optimization problems solved on a reduced-precision machine in combination with an inaccurate proximal operator. We also show how the probabilistic bounds are more robust for algorithm verification and more accurate for application performance guarantees. Under some statistical assumptions, we also prove that some cumulative error terms follow a martingale property. And conforming to observations, e.g., in \cite{schmidt2011convergence}, we also show how the acceleration of the algorithm amplifies the gradient and proximal computational errors.
