  This is a short communication on a Lyapunov function argument for softmax in
bandit problems. There are a number of excellent papers coming out using
differential equations for policy gradient algorithms in reinforcement learning
\cite{agarwal2019optimality,bhandari2019global,mei2020global}. We give a short
argument that gives a regret bound for the soft-max ordinary differential
equation for bandit problems. We derive a similar result for a different policy
gradient algorithm, again for bandit problems. For this second algorithm, it is
possible to prove regret bounds in the stochastic case \cite{DW20}. At the end,
we summarize some ideas and issues on deriving stochastic regret bounds for
policy gradients.
