报告题目：Accelerate Convex Optimization in Machine Learning by Leveraging Functional Growth Conditions
报告校内联系人：肖现涛 教授 联系电话：84708351-8307
报告摘要: In recent years, unprecedented growths in scale and dimensionality of data raise big computational challenges for traditional optimization algorithms; thus it becomes very important to develop efficient and effective optimization algorithms for solving numerous machine learning problems. Many traditional algorithms (e.g., gradient descent method) are black-box algorithms, which are simple to implement but ignore the underlying geometrical property of the objective function. Recent trend in accelerating these traditional black-box algorithms is to leverage geometrical properties of the objective function such as strong convexity. However, most existing methods rely too much on the knowledge of strong convexity, which makes them not applicable to problems without strong convexity or without knowledge of strong convexity. To bridge the gap between traditional black-box algorithms without knowing the problem's geometrical property and accelerated algorithms under strong convexity, how can we develop adaptive algorithms that can be adaptive to the objective function's underlying geometrical property? To answer this question, in this talk we focus on convex optimization problems and propose to explore an error bound condition that characterizes the functional growth condition of the objective function around a global minimum. Under this error bound condition, we develop algorithms that (1) can adapt to the problem's geometrical property to enjoy faster convergence in stochastic optimization; (2) can leverage the problem's structural regularizer to further improve the convergence speed; (3) can address both deterministic and stochastic optimization problems with explicit max-structural loss.