  Many problems in Reinforcement Learning (RL) seek an optimal policy with
large discrete multidimensional yet unordered action spaces; these include
problems in randomized allocation of resources such as placements of multiple
security resources and emergency response units, etc. A challenge in this
setting is that the underlying action space is categorical (discrete and
unordered) and large, for which existing RL methods do not perform well.
Moreover, these problems require validity of the realized action (allocation);
this validity constraint is often difficult to express compactly in a closed
mathematical form. The allocation nature of the problem also prefers stochastic
optimal policies, if one exists. In this work, we address these challenges by
(1) applying a (state) conditional normalizing flow to compactly represent the
stochastic policy -- the compactness arises due to the network only producing
one sampled action and the corresponding log probability of the action, which
is then used by an actor-critic method; and (2) employing an invalid action
rejection method (via a valid action oracle) to update the base policy. The
action rejection is enabled by a modified policy gradient that we derive.
Finally, we conduct extensive experiments to show the scalability of our
approach compared to prior methods and the ability to enforce arbitrary
state-conditional constraints on the support of the distribution of actions in
any state.
