  The advancement of artificial intelligence has cast a new light on the
development of optimization algorithm. This paper proposes to learn a two-phase
(including a minimization phase and an escaping phase) global optimization
algorithm for smooth non-convex functions. For the minimization phase, a
model-driven deep learning method is developed to learn the update rule of
descent direction, which is formalized as a nonlinear combination of historical
information, for convex functions. We prove that the resultant algorithm with
the proposed adaptive direction guarantees convergence for convex functions.
Empirical study shows that the learned algorithm significantly outperforms some
well-known classical optimization algorithms, such as gradient descent,
conjugate descent and BFGS, and performs well on ill-posed functions. The
escaping phase from local optimum is modeled as a Markov decision process with
a fixed escaping policy. We further propose to learn an optimal escaping policy
by reinforcement learning. The effectiveness of the escaping policies is
verified by optimizing synthesized functions and training a deep neural network
for CIFAR image classification. The learned two-phase global optimization
algorithm demonstrates a promising global search capability on some benchmark
functions and machine learning tasks.
