Title: ACQL: An Adaptive Conservative Q-Learning Framework for Offline Reinforcement Learning. Abstract: Offline Reinforcement Learning (RL), which relies only on static datasets without additional interactions with the environment, provides an appealing alternative to learning a safe and promising control policy. Most existing offline RL methods did not consider relative data quality and only crudely constrained the distribution gap between the learned policy and the behavior policy in general. Moreover, these algorithms cannot adaptively control the conservative level in more fine-grained ways, like for each state-action pair, leading to a performance drop, especially over highly diversified datasets. In this paper, we propose an Adaptive Conservative Q-Learning (ACQL) framework that enables more flexible control over the conservative level of Q-function for offline RL. Specifically, we present two adaptive weight functions to shape the Q-values for collected and out-of-distribution data. Then we discuss different conditions under which the conservative level of the learned Q-function changes and define the monotonicity with respect to data quality and similarity. Motivated by the theoretical analysis, we propose a novel algorithm with the ACQL framework, using neural networks as the adaptive weight functions. To learn proper adaptive weight functions, we design surrogate losses incorporating the conditions for adjusting conservative levels and a contrastive loss to maintain the monotonicity of adaptive weight functions. We evaluate ACQL on the commonly-used D4RL benchmark and conduct extensive ablation studies to illustrate the effectiveness and state-of-the-art performance compared to existing offline DRL baselines.