Linear Hamilton Jacobi Bellman Equations in High Dimensions

The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems with more than moderate state space size due to the curse of dimensionality. This work combines recent results in the structure of the HJB, and its reduction to a linear Partial Differential Equation (PDE), with methods based on low rank tensor representations, known as a separated representations, to address the curse of dimensionality. The result is an algorithm to solve optimal control problems which scales linearly with the number of states in a system, and is applicable to systems that are nonlinear with stochastic forcing in finite-horizon, average cost, and first-exit settings. The method is demonstrated on inverted pendulum, VTOL aircraft, and quadcopter models, with system dimension two, six, and twelve respectively.Comment: 8 pages. Accepted to CDC 201

Towards Informed Exploration for Deep Reinforcement Learning

In this thesis, we discuss various techniques for improving exploration for deep reinforcement learning. We begin with a brief review of reinforcement learning (RL) and the fundamental v.s. exploitation trade-off. Then we review how deep RL has improved upon classical and summarize six categories of the latest exploration methods for deep RL, in the order increasing usage of prior information. We then explore representative works in three categories discuss their strengths and weaknesses. The first category, represented by Soft Q-learning, uses regularization to encourage exploration. The second category, represented by count-based via hashing, maps states to hash codes for counting and assigns higher exploration to less-encountered states. The third category utilizes hierarchy and is represented by modular architecture for RL agents to play StarCraft II. Finally, we conclude that exploration by prior knowledge is a promising research direction and suggest topics of potentially impact