Learning to optimize - the idea that we can learn from data algorithms that
optimize a numerical criterion - has recently been at the heart of a growing
number of research efforts. One of the most challenging issues within this
approach is to learn a policy that is able to optimize over classes of
functions that are fairly different from the ones that it was trained on. We
propose a novel way of framing learning to optimize as a problem of learning a
good navigation policy on a partially observable loss surface. To this end, we
develop Rover Descent, a solution that allows us to learn a fairly broad
optimization policy from training on a small set of prototypical
two-dimensional surfaces that encompasses the classically hard cases such as
valleys, plateaus, cliffs and saddles and by using strictly zero-order
information. We show that, without having access to gradient or curvature
information, we achieve state-of-the-art convergence speed on optimization
problems not presented at training time such as the Rosenbrock function and
other hard cases in two dimensions. We extend our framework to optimize over
high dimensional landscapes, while still handling only two-dimensional local
landscape information and show good preliminary results.

通过 Rover Descent 方法，我们提出了一种学习良好导航策略来优化局部表面的方法，它可以用最小的二维数据集训练学习，从而在高维空间中达到良好的优化状态，而且仅使用零阶信息和不需要梯度或曲率信息。

Rover 降落：通过在原型丢失平面上导航学习优化

Rover Descent: Learning to optimize by learning to navigate on  prototypical loss surfaces

We present an algorithm for minimizing a sum of functions that combines the
computational efficiency of stochastic gradient descent (SGD) with the second
order curvature information leveraged by quasi-Newton methods. We unify these
disparate approaches by maintaining an independent Hessian approximation for
each contributing function in the sum. We maintain computational tractability
and limit memory requirements even for high dimensional optimization problems
by storing and manipulating these quadratic approximations in a shared, time
evolving, low dimensional subspace. Each update step requires only a single
contributing function or minibatch evaluation (as in SGD), and each step is
scaled using an approximate inverse Hessian and little to no adjustment of
hyperparameters is required (as is typical for quasi-Newton methods). This
algorithm contrasts with earlier stochastic second order techniques that treat
the Hessian of each contributing function as a noisy approximation to the full
Hessian, rather than as a target for direct estimation. We experimentally
demonstrate improved convergence on seven diverse optimization problems. The
algorithm is released as open source Python and MATLAB packages.

该研究提出了一种算法，它结合了随机梯度下降的计算效率和拟牛顿法利用的二阶曲率信息，通过维护和操作每个贡献函数的独立 Hessian 近似值实现不同的方法的统一。该算法适用于高维度优化问题，通过将这些二次近似值存储和操作在一个共享的、时变的、低维度子空间中，保持了计算可行性和限制了内存需求，且需要很少或不需要调整超参数。该算法与早期的随机二阶技术相反，早期技术将每个贡献函数的 Hessian 视为完整 Hessian 的噪声近似，而不是直接估计的目标。在七个不同的优化问题上进行了实验性的改进收敛表现，算法已发布为开源 Python 和 MATLAB 软件包。