We cast policy gradient methods as the repeated application of two operators: a policy improvement operator $\\mathcal{I}$, which maps any policy $\\pi$ to a better one $\\mathcal{I}\\pi$, and a projection operator $\\mathcal{P}$, which finds the best approximation of $\\mathcal{I}\\pi$ in the set of realizable policies. We use this framework to introduce operator-based versions of traditional policy gradient methods such as REINFORCE and PPO, which leads to a better understanding of their original counterparts. We also use the understanding we develop of the role of $\\mathcal{I}$ and $\\mathcal{P}$ to propose a new global lower bound of the expected return. This new perspective allows us to further bridge the gap between policy-based and value-based methods, showing how REINFORCE and the Bellman optimality operator, for example, can be seen as two sides of the same coin.<\/p>\n","protected":false},"excerpt":{"rendered":"
We cast policy gradient methods as the repeated application of two operators: a policy improvement operator $\\mathcal{I}$, which maps any policy $\\pi$ to a better one $\\mathcal{I}\\pi$, and a projection operator $\\mathcal{P}$, which finds the best approximation of $\\mathcal{I}\\pi$ in the set of realizable policies. We use this framework to introduce operator-based versions of traditional 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