Organizations: College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics · MIIT Key Laboratory of Pattern Analysis and Machine Intelligence · Graduate School of Information Science and Technology, The University of Osaka
Offline reinforcement learning (RL) typically mitigates distribution shift by imposing divergence constraints on the action distributions of the learned and behavior policies. However, this paradigm cannot ensure the underlying dynamic consistency structure: even minor action deviations can lead to drastically different transitions, inadvertently driving the agent away from the offline dataset. To address this, we explore policy constraints through their induced state-consequence distributions rather than relying on pure action-distribution matching. Nevertheless, directly enforcing such consequence-aware constraints is computationally intractable without access to the true underlying dynamics model. To bypass this issue, we propose Structural Behavior Regularization (StBR), which replaces the intractable objective with a closed-form latent divergence. Structuring this latent space to reflect transition dynamics renders the latent divergence a theoretically bounded surrogate for the true consequence-distribution divergence. By regularizing the learned policy with this latent divergence, StBR adaptively tightens the behavior constraint in dynamics-sensitive regions, effectively preventing deviations outside the offline dataset. Empirically, we demonstrate that StBR achieves superior performance across diverse offline RL benchmarks.
Figures & tables
Figure 1: Conceptual illustration of divergence-based behavior regularization. Purely action distribution matching (left) neglects dynamic consistency, whereas ideal consequence-aware constraints (right) are computationally intractable without access to the true dynamics. Our StBR (middle) employs a Gaussian latent space as a tractable, closed-form surrogate of consequence-aware constraints.
Figure 2: The architecture of the proposed StBR framework.The blue flow represents the learning of latent representations (Eq. ( 8 )) through the proposed State Belief Gaussian Fitting. The red flow highlights the application of the surrogate latent divergence for behavior regularization in Eq. ( 12 ).
Task Name
BC
CQL
TD3BC
IQL
PBRL
POR
SDC
SPOT
FQL
ENSP
StBR (Ours)
halfcheetah
medium
41.2±0.4
46.9±0.4
48.2±0.1
47.1±0.1
57.9±1.5
48.8±0.5
45.9±0.5
58.4 ±1.0
54.4±2.2
55.4±0.6
60.7 ±0.7
medium-replay
32.9±3.4
45.3±0.3
44.6±0.1
44.3±0.3
45.1±8.0
43.5±0.9
45.1±0.5
52.2±1.2
53.2 ±0.6
43.4±1.5
54.4 ±1.0
medium-expert
50.4±4.0
95.0±1.4
91.7±1.9
89.2±1.2
92.3±1.1
94.7±2.2
76.3±5.2
86.9±4.3
95.3 ±1.3
88.1±4.9
97.8 ±0.2
hopper
medium
46.1±1.8
61.9±6.4
59.0±0.7
63.6±2.9
75.3±31.2
78.6±7.2
64.7±3.5
86.0 ±8.7
77.1±10.3
80.4±14.7
100.9 ±1.0
medium-replay
22.4±5.9
86.3±7.3
65.4±14.0
95.4±4.9
100.6 ±1.0
98.9±2.1
94.8±6.5
100.2±1.0
79.5±4.5
91.0±12.9
100.8 ±1.9
medium-expert
62.4±13.9
96.9±15.1
101.6±2.0
101.6±7.4
110.8 ±0.8
90.0±12.1
99.9±8.5
99.3±7.1
103.5±6.7
65.5±12.5
111.6 ±0.9
Table 1: The mean and standard deviation of normalized scores after 1M steps of offline RL training, averaged over 5 seeds and the final 10 evaluations (the final 4 for AntMaze). The highest score in each task is bolded, and the second-best is underlined.
Figure 3: Hyperparameter sensitivity analysis. (a-b) When evaluating the performance at varying levels of constraint strength ( λ ) on two representative tasks, StBR takes shape of the "upper envelope" of all methods, showing that StBR is highly robust to parameter choices, making it significantly easier to achieve superior performance during practical deployment. (c-d) Sensitivity analysis of SBGF-related hyperparameters regarding β and latent space dimension.
Figure 4: Theoretical validation experiments. (a-b) Demonstrating that a larger β should be chosen in high-dimensional tasks and highly stochastic environments to maintain superior performance. (c) Correlation analysis between dynamic sensitivity and different metrics: the proposed consequence-aware divergence and the action-distribution measure. Results validate that latent divergence (left, Spearman r=0.54 ) exhibits a significantly stronger correlation with dynamics sensitivity than the VAE-based density measure (right, r=0.16 ).
Figure 5: Percent performance difference of StBR variants compared to the original algorithm.
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
Value
StBR
Optimizer
Adam
Activation function
ReLU
Critic learning rate
3×10−4
Actor learning rate
3×10−4
Batch size
256
Discount factor
0.99
Appendix
Table 2: Hyperparameters in StBR
Task Name
λ
β
λENSP
halfcheetah
medium
0.03
0.001
0.05
medium-replay
0.03
0.001
0.05
medium-expert
0.05
0.001
0.2
hopper
medium
0.03
0.001
0.1
medium-replay
0.05
0.001
0.05
medium-expert
0.05
0.001
0.2
Appendix
Table 3: Detailed configurations of λ and β across different tasks.
Figure 6: The results of StBR and StBR+BC on the MuJoCo task. The shaded area indicates the minimum and maximum score across 5 seeds, with the solid line depicting their mean.
Figure 7: The results of StBR and StBR+BC on the AntMaze and Adroit task. The shaded area indicates the minimum and maximum score across 5 seeds, with the solid line depicting their mean.
Figure 8: The figure tracks the latent divergence across gradient steps for OOD actions and learned policy’s actions. Notably, the latent divergence of the constrained policy is significantly lower than that of the OOD actions, demonstrating that our latent divergence effectively separates in-distribution (ID) from OOD actions.
Limited Valuable Dataset
CQL
SDC
FQL
StBR
Walker2d-r0.5-e0.5
88.3±4.9
88.8±3.9
108.9±4.5
113.9 ±3.1
Walker2d-r0.6-e0.4
81.5±6.3
65.9±5.0
91.7±6.6
106.1 ±2.4
Walker2d-r0.7-e0.3
48.3±5.8
85.5±4.7
88.7±9.1
99.9 ±8.1
Walker2d-r0.8-e0.2
50.5±7.2
49.8±5.6
70.4±11.5
87.7 ±5.5
Walker2d-r0.9-e0.1
17.6±3.0
26.8±2.1
66.7±23.6
73.4 ±22.9
Appendix
Table 4: Normalized scores on mixed walker2d datasets with varying proportions of random (r) and expert (e) transitions. Results are averaged over four seeds. StBR demonstrates significant robustness against limited valuable data dilution.
Dataset-size(%)
100
50
25
10
5
1
StBR(Ours)
100.9±1.0
100.4±1.2
99.5±1.5
97.2±4.1
78.2±2.7
65.6±14.5
SPOT
86.0±8.7
83.2±14.0
83.6±6.2
72.9±4.5
44.1±15.0
38.8±19.0
Appendix
Table 5: Normalized scores with varying dataset-size. Results are averaged over 5 seeds.
Task Name
σoos=0
σoos=0.001
σoos=0.01
σoos=0.1
AntMaze-medium-play
94.2±1.9
97.1 ±2.4
92.6±3.1
44.4±7.4
AntMaze-medium-diverse
90.6±3.6
95.1 ±1.8
91.0±4.5
47.4±4.8
AntMaze-large-play
84.2±2.7
88.5 ±2.7
84.5±2.2
19.6±6.2
AntMaze-large-diverse
85.8±5.1
86.2 ±3.3
83.1±6.1
12.8±7.4
Total
354.8
354.8 → 366.9
354.8 → 351.2
354.8 → 124.2
Appendix
Table 6: The mean and standard deviation of averaged normalized scores after 1M steps of OOS state recovery training, averaged over 5 seeds and the final 4 evaluations. The highest scores in each task are bolded.
Task Name
MOPO
RAMBO
StBR+MB
StBR(ours)
halfcheetah
medium
42.3±1.6
71.0 ±2.9
41.4±2.8
60.7 ±0.7
medium-replay
53.1±2.0
67.0 ±1.5
55.8 ±3.1
54.4±1.0
medium-expert
63.3±38.0
79.3±2.9
90.6 ±5.9
97.8 ±0.2
hopper
medium
28.0±12.4
91.2 ±16.3
80.3±7.3
100.9 ±1.0
medium-replay
67.5±24.7
97.6 ±3.4
90.6±2.6
100.8 ±1.9
medium-expert
23.7±6.0
89.5 ±11.1
77.8±6.5
111.6 ±0.9
Appendix
Table 7: The mean and standard deviation of averaged normalized scores after 3M steps of model-based offline RL training, averaged over 5 seeds and the final 10 evaluations. The top-2 highest scores in each task are bolded.
BC
CQL
TD3BC
IQL
PBRL
POR
SDC
SPOT
FQL
StBR(ours)
Runtime (ms/step)
2.0
24.2
4.7
6.5
26.7
8.8
25.0
6.7
6.6
6.8
Wall time (minutes)
33
403
78
108
444
147
417
111
110
114
Inference time (ms)
-
-
476
-
-
909
-
-
492
476
Appendix
Table 8: The runtime of StBR on hopper-medium-v2 task using a GeForce RTX 2080Ti GPU and Intel Xeon Gold 5218 CPU.
AntMaze
IQL
Cal-QL
StBR (Ours)
umaze
89.6 → 96.2
76.8 → 99.8
99.2 →99.6±0.4
umaze-diverse
65.6 → 87.2
32.0 → 98.5
95.6 →99.4±0.7
medium-play
76.4 → 94.0
71.8 → 98.8
93.6 →99.0±0.8
medium-diverse
72.8 → 92.0
62.0 → 98.3
89.8 →99.1±0.7
large-play
42.0 → 51.0
31.8 → 97.3
78.0 →96.9±1.1
large-diverse
46.0 → 58.4
44.0 → 91.5
77.8 →96.5±1.2
Appendix
Table 9: Online fine-tuning results on AntMaze tasks, showing initial performance after offline RL and performance after 1M steps of online RL. All results are averaged over 5 seeds.
Figure 9: Online fine-tuning training curves on AntMaze tasks, showing initial performance after offline RL and performance after 1M steps of online RL. (5 seeds)
Offline reinforcement learning (RL) aims to learn an effective policy from a static dataset, but its performance is fundamentally limited by dataset coverage. Action preference queries leverage expert feedback without additional environment interaction, enabling policy improvement during offline training. However, existing methods still face two key challenges: selecting informative preference queries and effectively exploiting the collected feedback. Current approaches typically rely only on the distance between policy actions and dataset actions for query selection, while enforcing fixed constraints that keep the policy close to queried preferences. Such strategies often lead to unstable policy updates and integrate poorly with value regularization. To address these limitations, we propose Conservative Query and Adaptive Regularization under Uncertainty Estimation, a lightweight framework that jointly improves preference querying and preference exploitation. Specifically, we employ a Morse network to estimate the uncertainty of policy actions with respect to the offline dataset. Based on this uncertainty, we introduce a conservative query strategy that selectively queries actions near the dataset to preserve Bellman-update stability, together with an uncertainty-aware adaptive regularization scheme that dynamically adjusts data-level constraints during policy optimization. We integrate our framework with CQL and evaluate it extensively on the D4RL benchmark. Experimental results demonstrate superior or competitive performance across a wide range of tasks.
Li-Rong Zhou, Qin-Wen Luo, Sheng-Jun Huang
Nanjing University of Aeronautics and Astronautics, Nanjing, China
Offline reinforcement learning (RL) allows robots to learn from offline datasets without risky exploration. Yet, offline RL's performance often hinges on a brittle trade-off between (1) return maximization, which can push policies outside the dataset support, and (2) behavioral constraints, which typically require sensitive hyperparameter tuning. Latent steering offers a structural way to stay within the dataset support during RL, but existing offline adaptations commonly approximate action values using latent-space critics learned via indirect distillation, which can lose information and hinder convergence. We propose Latent Policy Steering (LPS), which enables high-fidelity latent policy improvement by backpropagating original-action-space Q-gradients through a differentiable one-step MeanFlow policy to update a latent-action-space actor. By eliminating proxy latent critics, LPS allows an original-action-space critic to guide end-to-end latent-space optimization, while the one-step MeanFlow policy serves as a behavior-constrained generative prior. This decoupling yields a robust method that works out-of-the-box with minimal tuning. Across OGBench and real-world robotic tasks, LPS achieves state-of-the-art performance and consistently outperforms behavioral cloning and strong latent steering baselines.
Hokyun Im, Andrey Kolobov, Jianlong Fu +1
Department of Artificial Intelligence, Yonsei University · Microsoft Research
Offline reinforcement learning (RL) aims to optimize policies from pre-collected datasets. A bottleneck of this paradigm is managing epistemic uncertainty, which arises from limited data coverage (sample-level) and the ambiguity in identifying transition dynamics from finite data (model-level). To provide a unified quantification of these uncertainties, Bayesian RL has been proposed by treating the dynamics model as a random variable and maintaining a corresponding belief. Despite its theoretical appeal, policy optimization in Bayesian RL remains computationally challenging as it requires solving composite objectives with expectations. Prior methods either employ search-based techniques with poor computational scalability or impose restrictive posterior assumptions that sacrifice the adaptability of Bayesian RL. To address these limitations, we propose Posterior Hybrid Bayesian Belief (PhyB), which reformulates the expectation as a convex combination over a subset of dynamics models. Theoretical analysis demonstrates that the objective discrepancy induced by this approximation remains bounded. Based on PhyB, we develop an iterative regularized policy optimization algorithm that provides metric-agnostic guarantees for monotonic improvement until convergence. Empirical results demonstrate that PhyB achieves state-of-the-art performance on various benchmarks.