Modern robotic agents are increasingly expected to support steerable control, where a single policy can adjust its behavioral style at runtime under changing user preferences. Preference-conditioned reinforcement learning provides this interface, but conditioning alone does not ensure that a requested behavior change is strong, does not leak into unrelated behaviors, and does not compromise task performance. Our evaluation combines Preference Reward Responsiveness (PRR) with coverage and utility metrics. We use these measures to compare reward-level, advantage-level, loss-level, and PCGrad-based aggregation across two humanoid-control frameworks. No aggregation level performs best across all environments and criteria. Experiments show that aggregating objectives early produces a wider range of behavioral responses but greater unintended changes in other objectives, while aggregating them later improves control precision at some cost to responsiveness.
Figures & tables
Responsiveness
Monotonicity
Selectivity
Task preservation
Failure behavior
Method
Hypervolume ↑
Exp. Utility ↑
Self-PRR ↑
Rank acc. ↑
Selectivity ↑
Cross-PRR ↓
Jtask↑
Fall rate ↓
Reward-level
0.316 ± .016
0.763 ± .007
0.454 ± .004
0.847 ± .018
1.61 ± .11
0.285 ± .019
0.761 ± .014
7.4 ± .1%
Advantage-level
0.109 ± .011
0.568 ± .014
0.232 ± .045
0.811 ± .001
2.16 ± .15
0.108 ± .013
0.409 ± .019
8.0 ± .3%
Loss-level
0.103 ± .007
0.572 ± .010
0.225 ± .004
0.792 ± .033
2.04 ± .06
0.112 ± .006
0.414 ± .017
7.9 ± .1%
PCGrad
0.104 ± .016
0.558 ± .029
0.233 ± .004
0.800 ± .047
2.07 ± .17
0.114 ± .008
0.393 ± .027
8.4 ± .1%
Table 1: Main comparison on ProtoMotions (G1 humanoid), mean ± std over 3 training seeds at 1.2B environment steps. Column groups correspond to the five evaluation axes in Section 1 : responsiveness, monotonicity, selectivity, task preservation, and failure behavior. Bold marks the best value per column; ↑ / ↓ indicate the preferred direction.
Figure 1: Per-dimension preference sweep. Each panel shows the normalized reward achieved for one style dimension as its preference weight increases, mean ± std shading over 3 training seeds.
Responsiveness
Monotonicity
Selectivity
Task preservation
Failure behavior
Method
Hypervolume ↑
Exp. Utility ↑
Self-PRR ↑
Rank acc. ↑
Selectivity ↑
Cross-PRR ↓
Jtask↑
Fall rate ↓
Reward-level
0.238 ± .029
0.769 ± .009
0.510 ± .021
0.924 ± .003
1.272 ± .055
0.402 ± .022
0.870 ± .004
0.34 ± .08%
Advantage-level
0.298 ± .015
0.776 ± .007
0.485 ± .022
0.937 ± .010
1.387 ± .101
0.350 ± .010
0.865 ± .006
0.25 ± .06%
Loss-level
0.290 ± .012
0.771 ± .001
0.500 ± .030
0.937 ± .022
1.422 ± .082
0.352 ± .006
0.858 ± .005
0.32 ± .09%
Table 2: Fixed-direction preference-conditioned control in MimicKit, mean ± std over 3 training seeds at 1.2B environment steps. Column groups correspond to the five evaluation axes in Section 1 . Bold marks the best displayed mean, including ties; ↑ / ↓ indicate the preferred direction.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Dimension
Description
Bounds
energy
negative raw power (W)
(−800.0,0.0)
arm_swing
shoulder-pitch angular velocity (rad/s)
(0.0,3.0)
foot_clearance
swing-phase foot height (m)
(0.0,0.20)
step_width
lateral foot separation (m)
(0.0,0.40)
smoothness
negative ∥Δaction∥2
(−2.5,0.0)
Appendix
Table 3: Style reward dimensions and normalization bounds.
Horizon H
300
Axis-sweep points per dimension M
15
Axis-sweep range [αmin,αmax]
[0.05,0.95]
Full-simplex samples N
50
Dirichlet concentration α
0.5
Hypervolume Monte Carlo samples
2×105
Eval repeats
3 (seeds 1000/1001/1002 )
Appendix
Table 4: Evaluation hyperparameters, shared across all four methods and three training seeds.
Method
Dimension
Self-PRR ↑
Cross-PRR ↓
Rank acc. ↑
Reward-level
energy
0.295 ± .051
0.441 ± .042
0.791 ± .059
arm_swing
0.703 ± .080
0.152 ± .044
0.895 ± .054
foot_clearance
0.790 ± .003
0.290 ± .035
0.876 ± .026
step_width
0.315 ± .043
0.167 ± .040
0.778 ± .003
smoothness
0.165 ± .010
0.375 ± .059
0.893 ± .028
Loss-level
energy
0.048 ± .010
0.067 ± .018
0.678 ± .035
Appendix
Table 5: Per-dimension Self-PRR, Cross-PRR, and Rank Accuracy, mean ± std over 3 training seeds.
Hypervolume
Expected Utility
Method
Fixed
Alive
Fixed
Alive
Reward-level
0.316 ± .016
0.435 ± .021
0.763 ± .007
0.818 ± .008
Advantage-level
0.109 ± .011
0.158 ± .012
0.568 ± .014
0.610 ± .015
PCGrad
0.104 ± .016
0.154 ± .024
0.558 ± .029
0.601 ± .031
Loss-level
0.103 ± .007
0.149 ± .010
0.572 ± .010
0.615 ± .011
Appendix
Table 6: Hypervolume and Expected Utility under the Fixed and Alive conventions, mean ± std over 3 training seeds.
Setting
Value
Parallel training environments
4096
PPO rollout length
32 steps
Actor / critic / discriminator hidden widths
1024 / 1024 / 1024
Gaussian action standard deviation
0.05
Discount γ / GAE λ
0.99 / 0.95
PPO clipping coefficient
0.2
Appendix
Table 7: MimicKit optimization hyperparameters, shared across all methods and seeds.
Responsiveness
Monotonicity
Selectivity
Task preservation
Failure behavior
Method
Hypervolume ↑
Exp. Utility ↑
Self-PRR ↑
Rank acc. ↑
Selectivity ↑
Cross-PRR ↓
Jtask↑
Fall rate ↓
Reward-level
0.178 ± .005
0.728 ± .006
0.479 ± .020
0.966 ± .007
1.315 ± .034
0.365 ± .023
0.813 ± .010
0.26 ± .04%
Advantage-level
0.199 ± .004
0.732 ± .003
0.480 ± .004
0.971 ± .005
1.503 ± .015
0.319 ± .002
0.809 ± .003
0.22 ± .03%
Loss-level
0.201 ± .005
0.731 ± .003
0.471 ± .013
0.975 ± .008
1.498 ± .067
0.315 ± .007
0.807 ± .010
0.17 ± .03%
Appendix
Table 8: Reactive-steering preference-conditioned control in MimicKit, mean ± std over 3 training seeds at 1.2B environment steps. Bold marks the best mean; ↑ / ↓ indicate the preferred direction.
Method
Paired EU ↑
Mean Self-PRR ↑
Mean Cross-PRR ↓
Reward-level
0.608 ± .014
0.0028 ± .0027
0.0216 ± .0012
Advantage-level
0.634 ± .015
0.0263 ± .0017
0.0246 ± .0015
Loss-level
0.586 ± .020
0.0015 ± .0003
0.0112 ± .0005
Appendix
Table 9: MetaDrive environment ablation, mean ± std over three evaluation seeds. Bold marks the best value; ↑ / ↓ indicate the preferred direction.
Preference-based reinforcement learning learns policies from comparisons or rankings of behaviors instead of requiring hand-designed numerical rewards.