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The Markov decision process (MDP) formulation used to model many real-world sequential decision making problems does not efficiently capture the setting where the set of available decisions (actions) at each time step is stochastic. Recently, the stochastic action set Markov decision process (SAS-MDP) formulation has been proposed, which better captures the concept of a stochastic action set. In this paper we argue that existing RL algorithms for SAS-MDPs can suffer from potential divergence issues, and present new policy gradient algorithms for SAS-MDPs that incorporate variance reduction techniques unique to this setting, and provide conditions for their convergence. We conclude with experiments that demonstrate the practicality of our approaches on tasks inspired by real-life use cases wherein the action set is stochastic.

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