Functional Critics Are Essential in Off-Policy Actor-Critic: Provable Convergence and Efficient Exploration

Off-policy reinforcement learning (RL) with function approximation offers an effective way to improve sample efficiency by reusing past experience. Within this setting, the actor-critic (AC) framework has achieved strong empirical success but suffers from the "moving target" problem, where the policy being evaluated changes continually. Functional critics, or policy-conditioned value functions, have been proposed to address this issue by including a representation of the policy as input. While the concept of generalizing value functions across policy space is appealing, previous efforts have struggled to remain competitive against state-of-the-art AC algorithms that do not utilize functional critics. In this work, we revisit functional critics within the off-policy AC framework and identify two aspects that render them a necessity rather than a luxury. First, in off-policy AC, critic learning contends with both the "deadly triad" instability and the "moving target" issue, while actor learning faces the challenge of estimating the exact off-policy policy gradient. This complex interplay makes theoretical convergence extremely difficult for practical algorithms. We demonstrate that a functional critic is essential for addressing this challenge and establish the first convergence proof for an off-policy target-based AC algorithm under linear function approximation. Second, we identify a crucial link between functional critic modeling and efficient exploration. Specifically, we show that approximating posterior sampling for exploration in model-free settings is infeasible without functional critics. Practically, we propose a tailored neural network architecture and a minimal AC algorithm that relies solely on these insights. In experiments on the DeepMind Control Suite, this implementation achieves performance competitive with state-of-the-art methods.