Implicitly Regularized RL with Implicit Q-Values
This addresses a bottleneck in reinforcement learning for continuous action spaces, though it appears incremental as it builds on existing actor-critic architectures.
The paper tackled the limitation of computing softmax policies in continuous action spaces by proposing an implicit Q-function parametrization as the sum of a log-policy and a value function, resulting in a deep RL algorithm that competes with state-of-the-art methods on classic control tasks.
The $Q$-function is a central quantity in many Reinforcement Learning (RL) algorithms for which RL agents behave following a (soft)-greedy policy w.r.t. to $Q$. It is a powerful tool that allows action selection without a model of the environment and even without explicitly modeling the policy. Yet, this scheme can only be used in discrete action tasks, with small numbers of actions, as the softmax cannot be computed exactly otherwise. Especially the usage of function approximation, to deal with continuous action spaces in modern actor-critic architectures, intrinsically prevents the exact computation of a softmax. We propose to alleviate this issue by parametrizing the $Q$-function implicitly, as the sum of a log-policy and of a value function. We use the resulting parametrization to derive a practical off-policy deep RL algorithm, suitable for large action spaces, and that enforces the softmax relation between the policy and the $Q$-value. We provide a theoretical analysis of our algorithm: from an Approximate Dynamic Programming perspective, we show its equivalence to a regularized version of value iteration, accounting for both entropy and Kullback-Leibler regularization, and that enjoys beneficial error propagation results. We then evaluate our algorithm on classic control tasks, where its results compete with state-of-the-art methods.