# A Convergent Online Single Time Scale Actor Critic Algorithm

## TL;DR

This paper introduces a novel online actor-critic reinforcement learning algorithm where both actor and critic operate on the same time scale, simplifying convergence analysis and potentially enhancing biological plausibility.

## Contribution

It presents a convergent single time scale actor-critic algorithm using temporal difference learning, unlike previous methods requiring different time scales for convergence.

## Key findings

- Converges to a neighborhood of a local maximum of average reward.
- Uses the same temporal difference signal for both actor and critic.
- Operates with both components on a similar time scale.

## Abstract

Actor-Critic based approaches were among the first to address reinforcement learning in a general setting. Recently, these algorithms have gained renewed interest due to their generality, good convergence properties, and possible biological relevance. In this paper, we introduce an online temporal difference based actor-critic algorithm which is proved to converge to a neighborhood of a local maximum of the average reward. Linear function approximation is used by the critic in order estimate the value function, and the temporal difference signal, which is passed from the critic to the actor. The main distinguishing feature of the present convergence proof is that both the actor and the critic operate on a similar time scale, while in most current convergence proofs they are required to have very different time scales in order to converge. Moreover, the same temporal difference signal is used to update the parameters of both the actor and the critic. A limitation of the proposed approach, compared to results available for two time scale convergence, is that convergence is guaranteed only to a neighborhood of an optimal value, rather to an optimal value itself. The single time scale and identical temporal difference signal used by the actor and the critic, may provide a step towards constructing more biologically realistic models of reinforcement learning in the brain.