Beyond State-Wise Mirror Descent: Offline Policy Optimization with Parametric Policies

Offline RL methods commonly jointly train the actor and critic, where the critic is used to guide the actor toward higher-value actions. This coupled learning process is well motivated in online RL, where an improved actor collects new data that can further update the actor and the critic. However, training data remains fixed in offline RL, making actor-side policy improvement unable to generate new data to validate or correct the critic. Moreover, retaining this coupled paradigm leads to two related challenges. Firstly, actor updates can drift toward high-valued but potentially out-of-distribution (OOD) actions and amplify critic overestimation. Secondly, conservative value estimation or behavior-cloning regularization creates a difficult trade-off between suppressing OOD actions and selecting high-value actions within the data-supported region. Motivated by this observation, we revisit the conventional offline RL paradigm and propose decoupling policy improvement from actor training. Specifically, we train the actor solely to model the behavior distribution and perform policy improvement at inference time by reranking multiple actor-generated proposals with a separately learned critic. We refer to this paradigm as the decoupled policy extraction paradigm. Under such paradigm, the actor provides behavior-supported action candidates, while the critic performs value-based selection within this candidate set. Extensive experiments show that the decoupled policy extraction paradigm outperforms both behavior cloning and jointly learned offline RL methods, while remaining effective even with a naive Q-learning critic.

Offline reinforcement learning (RL) has received increasing attention for learning policies from previously collected data without interaction with the real environment, which is particularly important in high-stakes applications. While a growing body of work has developed offline RL algorithms, these methods often rely on restrictive assumptions about data coverage and suffer from distribution shift. In this paper, we propose a residuals-based offline RL framework for general state and action spaces. Specifically, we define a residuals-based Bellman optimality operator that explicitly incorporates estimation error in learning transition dynamics into policy optimization by leveraging empirical residuals. We show that this Bellman operator is a contraction mapping and identify conditions under which its fixed point is asymptotically optimal and possesses finite-sample guarantees. We further develop a residuals-based offline deep Q-learning (DQN) algorithm. Using a stochastic CartPole environment, we demonstrate the effectiveness of our residuals-based offline DQN algorithm.

Behavior regularization in offline reinforcement learning limits the exploitation of critic errors, but strong anchoring can also restrict policy improvement. We study how policy improvement is composed through multi-step proximal policy improvement (MPI), which re-centers each proximal objective on the preceding policy. We parameterize the procedure by a nominal total horizon $T$ and $K$ stages with local horizon $T/K$, distinguishing subdivision at a fixed total horizon from additional refinement at a common local horizon. Our analysis shows that sequential re-centering can reach endpoints unavailable to any single proximal step and characterizes how subdivision reduces the leading local discretization error of ideal updates under a fixed critic. We consider TD3+BC and IQL-based policy extraction to examine how improvement composition interacts with actor objectives and policy geometry. TD3+BC experiments on D4RL locomotion suggest that subdivision can broaden the range of useful total horizons, while adding refinement stages at a fixed small local horizon can improve return. The results identify improvement composition as a design choice alongside regularization strength, with distinct effects from horizon subdivision and additional policy extraction.