Occupancy-based Policy Gradient: Estimation, Convergence, and Optimality

Occupancy functions play an instrumental role in reinforcement learning (RL) for guiding exploration, handling distribution shift, and optimizing general objectives beyond the expected return. Y et, computationally efficient policy optimization methods that use (only) occupancy functions are virtually non-existent. In this paper, we establish the theoretical foundations of model-free policy gradient (PG) methods that compute the gradient through the occupancy for both online and offline RL, without modeling value functions. Our algorithms reduce gradient estimation to squared-loss regression and are computationally oracle-efficient. We characterize the sample complexities of both local and global convergence, accounting for both finite-sample estimation error and the roles of exploration (online) and data coverage (offline). Occupancy-based PG naturally handles arbitrary offline data distributions, and, with one-line algorithmic changes, can be adapted to optimize any differentiable objective functional.