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Many problems in Reinforcement Learning (RL) seek an optimal policy withlarge discrete multidimensional yet unordered action spaces; these includeproblems in randomized allocation of resources such as placements of multiplesecurity resources and emergency response units, etc. A challenge in thissetting is that the underlying action space is categorical (discrete andunordered) 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 closedmathematical form. The allocation nature of the problem also prefers stochasticoptimal policies, if one exists. In this work, we address these challenges by(1) applying a (state) conditional normalizing flow to compactly represent thestochastic policy -- the compactness arises due to the network only producingone sampled action and the corresponding log probability of the action, whichis then used by an actor-critic method; and (2) employing an invalid actionrejection method (via a valid action oracle) to update the base policy. Theaction rejection is enabled by a modified policy gradient that we derive.Finally, we conduct extensive experiments to show the scalability of ourapproach compared to prior methods and the ability to enforce arbitrarystate-conditional constraints on the support of the distribution of actions inany state.

Generative Modelling of Stochastic Actions with Arbitrary Constraints in Reinforcement Learning