Ronald E. Parr

Kavosh Asadi, Neev Parikh, Ronald E. Parr et al.

A core operation in reinforcement learning (RL) is finding an action that is optimal with respect to a learned value function. This operation is often challenging when the learned value function takes continuous actions as input. We introduce deep radial-basis value functions (RBVFs): value functions learned using a deep network with a radial-basis function (RBF) output layer. We show that the maximum action-value with respect to a deep RBVF can be approximated easily and accurately. Moreover, deep RBVFs can represent any true value function owing to their support for universal function approximation. We extend the standard DQN algorithm to continuous control by endowing the agent with a deep RBVF. We show that the resultant agent, called RBF-DQN, significantly outperforms value-function-only baselines, and is competitive with state-of-the-art actor-critic algorithms.

Zhao Song, Ronald E. Parr, Lawrence Carin

The impact of softmax on the value function itself in reinforcement learning (RL) is often viewed as problematic because it leads to sub-optimal value (or Q) functions and interferes with the contraction properties of the Bellman operator. Surprisingly, despite these concerns, and independent of its effect on exploration, the softmax Bellman operator when combined with Deep Q-learning, leads to Q-functions with superior policies in practice, even outperforming its double Q-learning counterpart. To better understand how and why this occurs, we revisit theoretical properties of the softmax Bellman operator, and prove that $(i)$ it converges to the standard Bellman operator exponentially fast in the inverse temperature parameter, and $(ii)$ the distance of its Q function from the optimal one can be bounded. These alone do not explain its superior performance, so we also show that the softmax operator can reduce the overestimation error, which may give some insight into why a sub-optimal operator leads to better performance in the presence of value function approximation. A comparison among different Bellman operators is then presented, showing the trade-offs when selecting them.