PIQL: Projective Implicit Q-Learning with Support Constraint for Offline Reinforcement Learning

Offline Reinforcement Learning (RL) faces a fundamental challenge of extrapolation errors caused by out-of-distribution (OOD) actions. Implicit Q-Learning (IQL) employs expectile regression to achieve in-sample learning. Nevertheless, IQL relies on a fixed expectile hyperparameter and a density-based policy improvement method, both of which impede its adaptability and performance. In this paper, we propose Projective IQL (PIQL), a projective variant of IQL enhanced with a support constraint. In the policy evaluation stage, PIQL substitutes the fixed expectile hyperparameter with a projection-based parameter and extends the one-step value estimation to a multi-step formulation. In the policy improvement stage, PIQL adopts a support constraint instead of a density constraint, ensuring closer alignment with the policy evaluation. Theoretically, we demonstrate that PIQL maintains the expectile regression and in-sample learning framework, guarantees monotonic policy improvement, and introduces a progressively more rigorous criterion for advantageous actions. Experiments on D4RL and NeoRL2 benchmarks demonstrate robust gains across diverse domains, achieving state-of-the-art performance overall.