Simon Du (IAS/Princeton) - Foundations of Learning Systems with (Deep) Function Approximators

Foundations of Learning Systems with (Deep) Function Approximators

Function approximators, such as deep neural networks, play a crucial role in building learning systems that make predictions and decisions. In this talk, I will discuss my work on understanding, designing, and applying function approximators.

First, I will focus on understanding deep neural networks. The main result is that the over-parameterized neural network is equivalent to a new kernel, Neural Tangent Kernel. This equivalence implies two surprising phenomena: 1) the simple algorithm gradient descent provably finds the global optimum of the highly non-convex empirical risk, and 2) the learned neural network generalizes well despite being highly over-parameterized.  Furthermore, this equivalence helps us design a new class of function approximators: we transform (fully-connected and graph) neural networks to (fully-connected and graph) Neural Tangent Kernels, which achieve superior performance on standard benchmarks. 

In the second part of the talk, I will focus on applying function approximators to decision-making, aka reinforcement learning, problems. In sharp contrast to the (simpler) supervised prediction problems, solving reinforcement learning problems requires an exponential number of samples, even if one applies function approximators.  I will then discuss what additional structures that permit statistically efficient algorithms.

Host: Michael Maire