Offline reinforcement learning (RL) can fit strong value functions from fixed datasets, yet reliable deployment still hinges on the action selection interface used to query them. When the dataset induces a branched or multimodal action landscape, unimodal policy extraction can blur competing hypotheses and yield "in-between" actions that are weakly supported by data, making decisions brittle even with a strong critic. We introduce GEM (Guided Expectation-Maximization), an analytical framework that makes action selection both multimodal and explicitly controllable. GEM trains a Gaussian Mixture Model (GMM) actor via critic-guided, advantage-weighted EM-style updates that preserve distinct components while shifting probability mass toward high-value regions, and learns a tractable GMM behavior model to quantify support. During inference, GEM performs candidate-based selection: it generates a parallel candidate set and reranks actions using a conservative ensemble lower-confidence bound together with behavior-normalized support, where the behavior log-likelihood is standardized within each state's candidate set to yield stable, comparable control across states and candidate budgets. Empirically, GEM is competitive across D4RL benchmarks, and offers a simple inference-time budget knob (candidate count) that trades compute for decision quality without retraining.
Figures & tables
Figure 1: GEM mechanism (schematic at a fixed state in a 2-D action space). Training (top row): GEM learns three ingredients that will be combined only at test time: (i) a multimodal actor πθ(a∣s) (left; shown as logπθ(a∣s) ) that preserves multiple plausible action hypotheses, (ii) an independent behavior density μφ(a∣s) (middle; shown as logμφ(a∣s) ) used to quantify dataset support, and (iii) a conservative value statistic LCBλ(s,a) from a critic ensemble (right). Inference (bottom row): given a queried state s , GEM samples N candidates in parallel and adds a deterministic anchor (triangle), scores each candidate using Eq. 4 (conservative value plus behavior-normalized support), and executes the top-ranked action a⋆ (star). The green cluster highlights the small subset of candidates that remain competitive after scoring, illustrating how the interface filters many proposals down to a support-aligned, high-value choice under maximization.
Task
TD3+BC
AWAC
CQL
IQL
ReBRAC
SAC-N
EDAC
DT
IDQL
Diffusion-QL
FQL
SSAR
GEM(OURS)
Locomotion
HC-M
48.10
50.02
47.04
48.31
64.04
68.20
67.70
42.20
51.10
51.10
nan
60.00
54.42
HC-MR
44.84
45.13
45.04
44.46
51.18
60.70
62.06
38.91
45.90
47.80
nan
51.70
49.60
HC-ME
90.78
95.00
95.63
94.74
103.80
98.96
104.76
91.55
95.90
96.80
nan
98.50
100.95
H-M
60.30
63.02
59.08
67.53
102.29
40.82
101.70
65.10
65.40
90.50
nan
95.40
100.08
H-MR
64.42
98.88
95.11
97.43
94.98
100.33
99.66
81.77
92.10
101.30
nan
101.50
101.23
Table 1: Unified D4RL benchmark comparison (normalized score, higher is better). Suites: Locomotion (HalfCheetah/Hopper/Walker2d), AntMaze, and Maze2D.
Appendix figures & tables26 assets
Supplementary material from the paper’s appendix.
Appendix
Environment
Mean gap ± std
Maze2D-umaze
168.29 ± 7.71
Maze2D-medium
147.30 ± 6.85
Maze2D-large
142.64 ± 7.34
Antmaze-umaze-diverse
38.80 ± 3.46
Antmaze-umaze
31.53 ± 2.83
Antmaze-medium-diverse
23.73 ± 2.68
Appendix
Table 2: Per-environment NLL-gap statistics ( gap=NLLtop1−NLLgmm ; mean ± std). All entries are positive in the provided results, indicating consistent mixture benefits.
Figure 5: Locomotion suite: per-environment candidate-budget scaling for Score.
Figure 6: Locomotion suite: per-environment candidate-budget scaling for Violation .
Figure 7: Locomotion suite: per-environment candidate-budget scaling for CollapseDist .
Figure 8: AntMaze suite: per-environment candidate-budget scaling for Score.
Figure 9: AntMaze suite: per-environment candidate-budget scaling for Violation .
Figure 10: AntMaze suite: per-environment candidate-budget scaling for CollapseDist .
Figure 11: Maze2D suite: per-environment candidate-budget scaling for Score.
Figure 12: Maze2D suite: per-environment candidate-budget scaling for Violation .
Figure 13: Maze2D suite: per-environment candidate-budget scaling for CollapseDist .
Figure 14: Robustness (aggregated) under mass-scaling perturbations on the Locomotion suite.
Figure 15: Robustness (aggregated) under mass-scaling perturbations on Maze2D.
Figure 16: Robustness (aggregated) under mass-scaling perturbations on AntMaze. Near-zero scores across MassScale indicate widespread failure under this dynamics shift under our evaluation protocol.
Figure 18: Effect of support normalization at N=1024 (Mode= zscore minus Mode= raw ). Top: Δ Score (positive is better). Middle: Δ Violation . Bottom: Δ CollapseDist . This comparison isolates scale sensitivity: raw logμφ(a∣s) can vary substantially across states, so its additive influence can make a single global wp behave inconsistently across the state space.
Method
Setting
Latency (ms)
Peak alloc (MB)
Peak reserved (MB)
Params (M)
Decision Transformer
N1
0.88 ± 0.05
20.71 ± 0.00
25.00 ± 0.00
5.27
Decision Transformer
N64
0.88 ± 0.05
20.71 ± 0.00
25.00 ± 0.00
5.27
Decision Transformer
N1024
0.88 ± 0.05
20.71 ± 0.00
25.00 ± 0.00
5.27
Decision Transformer
N2048
0.88 ± 0.05
20.71 ± 0.00
25.00 ± 0.00
5.27
Decision Transformer
T10
0.88 ± 0.05
20.71 ± 0.00
25.00 ± 0.00
5.27
Decision Transformer
T20
0.88 ± 0.05
20.71 ± 0.00
25.00 ± 0.00
5.27
Appendix
Table 3: Full deployment compute measurements (mean ± std). Latency is in milliseconds; memory is peak allocated/reserved MB; Params is model parameter count (millions).
TestEnv
GEM
n
SupportZ
Viol
Collapse
SPS
antmaze-large-diverse-v2
1.00 ± 1.41
3
1.99
0.0019
0.308
2742
antmaze-large-play-v2
5.00 ± 1.41
3
2.02
0.0024
0.318
2760
antmaze-medium-diverse-v2
11.76 ± 10.54
3
1.86
0.0031
0.357
2913
antmaze-medium-play-v2
76.36 ± 33.43
3
1.05
0.0356
0.748
2962
antmaze-umaze-diverse-v2
57.37 ± 5.55
3
2.03
0.0002
0.278
3173
antmaze-umaze-v2
75.71 ± 20.55
3
0.81
0.0189
0.309
3195
Appendix
Table 4: GEM primary performance (Mode=zscore, N=1024 ) aggregated by D4RL task. Columns report normalized score (mean ± std across training seeds), average support z-score, support violation rate, collapse distance, and evaluation throughput.
Variant
Mean
Delta
SupportZ
Viol
Collapse
SPS
n
GEM
76.88
0.00 ± 0.00
1.25
0.0069
0.273
3064
47
anchor_bary
76.29
-0.60 ± 3.87
1.24
0.0070
0.271
3043
47
behavior_only_cands
79.92
3.03 ± 20.58
0.93
0.0144
0.240
3077
47
no_anchor
77.04
0.15 ± 2.32
1.24
0.0069
0.273
3109
47
no_lcb
74.84
-2.04 ± 16.02
1.27
0.0085
0.270
3093
47
no_pw
65.31
-11.57 ± 37.56
-0.90
0.2169
0.647
3082
47
Appendix
Table 5: Mechanism ablations at N=1024 (Mode=zscore), aggregated over all tasks and training seeds. Δ is the per-task score difference relative to GEM (mean ± std across tasks).
TestEnv
GEM
no-pw
no-lcb
unimodal-actor
behavior-only
antmaze-large-diverse-v2
0.00
+1.00
+0.00
+8.00
+0.00
antmaze-large-play-v2
4.00
+0.00
-1.00
-2.00
-4.00
antmaze-medium-diverse-v2
6.00
+68.14
+0.00
-4.00
+2.00
antmaze-medium-play-v2
76.47
-56.47
-37.05
+23.53
-19.80
antmaze-umaze-diverse-v2
52.42
-31.42
-9.06
-11.93
-16.23
antmaze-umaze-v2
71.58
-68.58
-5.00
+0.00
-6.00
Appendix
Table 6: Per-task ablation deltas at N=1024 (Mode=zscore). Columns report mean normalized score of GEM and mean score change ( Δ ) of each variant relative to GEM (positive is better).
N
Score
Std
SupportZ
Viol
Collapse
Steps/s
n
0
64.24
30.99
0.00
0.0000
0.265
5625
846
1
65.77
30.53
0.92
0.0000
0.271
5254
846
64
72.32
34.25
1.26
0.0027
0.257
5383
846
1024
72.79
34.46
1.33
0.0048
0.237
3105
846
2048
73.41
35.00
1.34
0.0055
0.233
1958
846
Appendix
Table 7: Test-time scaling with candidate budget N for GEM (Mode=zscore), aggregated over all sweep runs. Larger N improves average score while reducing throughput.
TestEnv
Delta
n
antmaze-large-diverse-v2
0.00 ± 0.00
2
antmaze-large-play-v2
5.00 ± 1.41
2
antmaze-medium-diverse-v2
9.76
1
antmaze-medium-play-v2
19.89 ± 25.51
2
antmaze-umaze-diverse-v2
3.81 ± 19.59
2
antmaze-umaze-v2
-1.12 ± 6.91
2
Appendix
Table 8: Effect of support normalization: baseline GEM difference between Mode=zscore and Mode=raw (reported as Scorez−Scoreraw ) aggregated by task.
Environment
Gap
Seeds
antmaze-large-diverse-v2
42.71 ± 7.04
3
antmaze-large-play-v2
43.22 ± 15.75
3
antmaze-medium-diverse-v2
57.16 ± 9.94
3
antmaze-medium-play-v2
48.45 ± 13.97
3
antmaze-umaze-diverse-v2
48.42 ± 7.08
3
antmaze-umaze-v2
48.86 ± 7.26
3
Appendix
Table 9: Multimodality diagnostic (dataset NLL gap). Larger gap indicates higher cost of a unimodal projection, motivating multimodal proposals.
Method
T10
T100
T20
T50
DT
0.934 ± 0.122
0.866 ± 0.008
0.874 ± 0.013
0.866 ± 0.010
FQL
1.479 ± 0.014
1.487 ± 0.018
1.480 ± 0.012
1.474 ± 0.024
GEM
1.296 ± 0.016
1.301 ± 0.043
1.270 ± 0.006
1.292 ± 0.052
IDQL
2.042 ± 0.017
20.367 ± 0.163
4.112 ± 0.014
10.096 ± 0.050
IFQL
1.831 ± 0.017
1.827 ± 0.010
1.821 ± 0.019
1.804 ± 0.026
Appendix
Table 10: Inference latency (ms) under diffusion-step sweep T (mean ± std).
Method
N1
N1024
N2048
N64
DT
0.886 ± 0.006
0.884 ± 0.007
0.878 ± 0.006
0.865 ± 0.008
FQL
1.483 ± 0.015
1.506 ± 0.014
1.465 ± 0.038
1.482 ± 0.010
GEM
1.307 ± 0.007
1.276 ± 0.016
1.254 ± 0.002
1.279 ± 0.010
IDQL
10.168 ± 0.046
10.175 ± 0.051
10.115 ± 0.108
10.107 ± 0.072
IFQL
1.796 ± 0.008
1.837 ± 0.035
1.865 ± 0.076
1.830 ± 0.012
Appendix
Table 11: Inference latency (ms) under candidate-budget sweep N (mean ± std).
Method
T10
T100
T20
T50
DT
21.1 ± 0.0
21.1 ± 0.0
21.1 ± 0.0
21.1 ± 0.0
FQL
20.7 ± 0.0
20.7 ± 0.0
20.7 ± 0.0
20.7 ± 0.0
GEM
50.8 ± 0.0
50.8 ± 0.0
50.8 ± 0.0
50.8 ± 0.0
IDQL
20.7 ± 0.0
20.7 ± 0.0
20.7 ± 0.0
20.7 ± 0.0
IFQL
20.8 ± 0.0
20.8 ± 0.0
20.8 ± 0.0
20.8 ± 0.0
Appendix
Table 12: Peak GPU allocated memory (MB) under diffusion-step sweep T (mean ± std).
Method
N1
N1024
N2048
N64
DT
21.1 ± 0.0
21.1 ± 0.0
21.1 ± 0.0
21.1 ± 0.0
FQL
20.7 ± 0.0
20.7 ± 0.0
20.7 ± 0.0
20.7 ± 0.0
GEM
50.8 ± 0.0
50.8 ± 0.0
50.8 ± 0.0
50.8 ± 0.0
IDQL
20.7 ± 0.0
20.7 ± 0.0
20.7 ± 0.0
20.7 ± 0.0
IFQL
20.8 ± 0.0
20.8 ± 0.0
20.8 ± 0.0
20.8 ± 0.0
Appendix
Table 13: Peak GPU allocated memory (MB) under candidate-budget sweep N (mean ± std).
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.
Xuyao Lin, Yixiang Shan, Jinru Duan +7
Simplexity Robotics, Rensselaer Polytechnic Institute · Simplexity Robotics · Simplexity Robotics, Northeastern University
One-step offline RL actors are attractive because they avoid backpropagating through long iterative samplers and keep inference cheap, but they still have to improve under a critic without drifting away from actions that the dataset can support. In recent one-step extraction pipelines, a strong iterative teacher provides one target action for each latent draw, and the same student output is asked to do both jobs: move toward higher Q and stay near that paired endpoint. If those two directions disagree, the loss resolves them as a compromise on that same sample, even when a nearby better action remains locally supported by the data. We propose DROL, a latent-conditioned one-step actor trained with top-1 dynamic routing. For each state, the actor samples K candidate actions from a bounded latent prior, assigns each dataset action to its nearest candidate, and updates only that winner with Behavior Cloning and critic guidance. Because the routing is recomputed from the current candidate geometry, ownership of a supported region can shift across candidates over the course of learning. This gives a one-step actor room to make local improvements that pointwise extraction struggles to capture, while retaining single-pass inference at test time. On OGBench and D4RL, DROL is competitive with the one-step FQL baseline, improving many OGBench task groups while remaining strong on both AntMaze and Adroit. Project page: https://muzhancun.github.io/preprints/DROL.
Zhancun Mu, Guangyu Zhao, Yiwu Zhong +1
School of Intelligence Science and Technology, Peking University
Recent offline reinforcement learning methods increasingly rely on expressive generative policies and specialized value-guidance mechanisms. We ask whether comparable progress can instead come from systematically modernizing a conventional behavior-regularized actor-critic while preserving its algorithmic simplicity. We introduce ReBRAC-v2, which directly trains an exact-likelihood normalizing flow as the RL actor, combines likelihood, MSE, and MAE behavior regularization, and integrates a classification-based residual critic, staged optimization, and multi-sample test-time action selection. Rather than tuning this recipe separately for every task, we develop a single shared configuration via roughly 600 Bayesian proposals on six challenging OGBench tasks, freeze all structural and optimization choices, and adapt only two behavior-regularization coefficients over a 16-point grid. Across ten common state-based OGBench categories, ReBRAC-v2 averages 74.8 compared to 52.3 for the next-best aggregate result and ranks first in eight categories. The same recipe, without structural changes, obtains the strongest averages in our comparisons on D4RL AntMaze (90.2) and Adroit (33.6). Fixed-recipe ablations show the largest sensitivity to the selected mixed cloning objective, staged training, sufficient flow capacity, and multi-sample inference, while showing that several smaller choices depend on the values of other hyperparameters. These results show that disciplined, transferable engineering can achieve state-of-the-art aggregate performance without abandoning a minimalist offline RL foundation.