cs.LGSep 18, 2026

IncentRL: The Trade-Off Between Preference Guidance and Task Performance

Authors: Xuening Wu, Yanlan Kang, Shenqin Yin

Organizations: Fudan University

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Abstract

Preference-based reward shaping can guide reinforcement learning, but adding preference signals to the reward may unintentionally change the task being optimized. We address this problem with IncentRL, a framework that introduces preference guidance while explicitly characterizing its effect on external-task performance. IncentRL adds a Kullback--Leibler (KL) penalty between a specified outcome distribution and a preferred distribution. For finite discounted Markov decision processes with bounded shaping costs, we derive an external-value perturbation bound, establish a sufficient strict-action-gap condition for preserving the original optimal policy, and characterize the large-weight regime through discounted cumulative preference cost. Exact examples clarify the limits of these guarantees, including tied optima and support mismatch. We study a practical implementation using a hand-designed, distance-based outcome proxy, a fixed preference distribution, and score-weighted coefficient search. On MiniGrid DoorKey-8x8, the reported three-seed mean success rate after two million training steps reaches 98% with coefficient 0.01, compared with 90.5% for the reported zero-coefficient baseline, while the search progressively shifts toward smaller coefficients. Together, these results provide a principled view of the central trade-off in preference-based RL: using additional guidance to improve learning without excessively distorting the original task objective. The current experiments remain descriptive and do not yet isolate KL shaping from simpler alternatives.

Figures & tables

ItemAvailable information
EnvironmentMiniGrid DoorKey-8x8
Fixed coefficientsβ=0\beta=0 (reported baseline) and β=0.01\beta=0.01
Training budgetTwo million reported steps per agent
Training seedsThree for the fixed-coefficient comparison; identifiers not supplied. Search plots show seeds 42 and 43.
Architecture and optimizerReported as shared across fixed-coefficient conditions; exact network and optimizer settings are not recorded in the available experiment documentation.
Observations and versionsObservation encoding, wrappers, and environment/library versions are not documented for the figure-generating runs.
Table 1: Documented settings and reporting gaps for the MiniGrid experiments. Unavailable details are not inferred from library defaults or from the prospective protocol.
Figure 1: Learning curves on MiniGrid DoorKey-8x8 for β=0\beta=0 and β=0.01\beta=0.01 , averaged over three seeds with two million training steps per agent. The shared vertical axis combines success rate in percent and episode length in steps. No uncertainty bands are shown; the plot supports a descriptive comparison of the mean trajectories.
RoundMean β\betaSDMinimumMaximum
10.10570.05730.00780.1805
20.04540.03220.00740.0977
30.01940.00980.00350.0351
40.01730.01820.00000.0587
Table 2: Summary statistics of sampled coefficients across four search rounds. Values are shown to four decimal places. The available aggregates do not specify the exact pooling or averaging rule across seeds.
Figure 2: Mean and standard deviation of sampled coefficients across search rounds, using the values in Table 2 . Bars denote the reported standard deviation of sampled coefficients, not uncertainty in the mean or a Bayesian credible interval. A symmetric mean-plus/minus-SD bar can extend below zero even when all samples are nonnegative. No raw samples are reconstructed.
Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

β\betaOptimal actionExternal returnPreference costShaped return
0.00Reward-seeking11.386291.00000
0.25Reward-seeking11.386290.65343
0.50Reward-seeking11.386290.30685
0.75Aligned00.000000.00000
1.00Aligned00.000000.00000
Appendix
Table 3: Exact values for Example 1 . No agent is trained. The external reward is sacrificed once the weight exceeds 1/log⁡41/\log 4 .
Figure 3: Sampled-coefficient distributions for seeds 42 and 43 across four search rounds. The red line marks β=0.1\beta=0.1 as a visual reference, not an empirically established optimum. The plot shows a shift toward smaller sampled values and variation between seeds; it does not establish Bayesian posterior concentration. Sample counts and the precise boxplot convention are not available in the accompanying aggregate records.
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