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Highly Efficient Self-Adaptive Reward Shaping for Reinforcement Learning
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Proposes SASR, a self-adaptive reward shaping method that samples shaped rewards from Beta distributions parameterized by KDE/RFF-estimated success and failure state counts, evaluated with SAC on extremely sparse-reward MuJoCo, robotics and Atari tasks.
Problem
Extremely sparse rewards in RL make exploration slow; existing reward shaping methods either overlook state values (intrinsic novelty bonuses) or struggle early in training (value-based heuristics), and count-based shaping is hard in continuous, high-dimensional state spaces.
Approach
Derive shaped rewards from success rates of states computed from historical successful vs. failed trajectories, sampled from Beta distributions whose variance shrinks as data accumulates; KDE with random Fourier features efficiently estimates the success and failure counts in continuous spaces.
Key results
- SASR achieves the highest average episodic return on most of the 14 tasks, e.g. 94.9 on AntStand versus 67.3 for DRND-online and 31.6 for SAC.
- On Montezuma's Revenge, SASR scores 6737.9 versus 6828.5 for DRND-online, so DRND-online is slightly higher there.
- Removing Beta sampling drops AntStand from 94.92 to 54.48 and HumanStand from 79.83 to 9.77.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SASR self-adaptive success-rate reward shaping with Beta sampling rather than the listed baselines | SAC · AntStand, AntFar, HumanStand, HumanKeep, RobotSlide, RobotPush, RobotPickPlace, Pitfall, Frogger, Solaris, Freeway, MountainCar | average episodic return: 94.9$\pm$0.0 vs 90.5$\pm$1.7 (AntStand); 139.8$\pm$0.0 vs 115.7$\pm$0.0 (AntFar) | Helped |
| Use SASR rather than DRND-online | SAC · Montezuma | average episodic return: 6737.9$\pm$0.0 vs 6828.5$\pm$0.0 | Hurt |
| Replace state-only reward with a state-action-pair reward (ablation) | SASR · RobotReach and RobotPush | average episodic return: 170.18$\pm$0.00 -> 151.95$\pm$5.74 (RobotReach); 167.14$\pm$0.00 -> 179.76$\pm$1.66 (RobotPush) | Mixed |
| Omit Beta sampling and directly use the success rate (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 54.48 $\pm$ 1.29 | Hurt |
| Increase retention rate from φ=0.1 to φ=1 (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 45.71$\pm$7.57 | Hurt |
| Decrease retention rate from φ=0.1 to φ=0.01 (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 62.85$\pm$3.49 | Hurt |
| Reduce RFF feature dimension from M=1000 to M=50 (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 5.21$\pm$0.45 | Hurt |
| Increase RFF feature dimension from M=1000 to M=2000 (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 96.80$\pm$8.42 | No clear effect |
| Reduce shaped reward weight from λ=0.6 to λ=0.2 (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 35.71$\pm$0.92 | Hurt |
| Increase shaped reward weight from λ=0.6 to λ=1.0 (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 3.16$\pm$0.35 | Hurt |
| Reduce Gaussian kernel bandwidth from h=0.2 to h=0.01 (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 10.71$\pm$2.52 | Hurt |
| Increase Gaussian kernel bandwidth from h=0.2 to h=1 (ablation) | SASR · AntStand | average episodic return: 94.92$\pm$0.00 -> 17.74$\pm$2.53 | Hurt |
Surprising findings
- Using a fixed deterministic success rate instead of Beta sampling sharply degrades performance, showing stochastic reward sampling matters for exploration.
- Using a retention rate of 1 (storing all states) causes premature overconfidence and large drops, e.g. RobotPush falls from 167.14 to 2.96.
Limitations
- Sensitive to the retention rate; the method does not account for varying importance of states within a trajectory.
- Designed for sparse-reward settings; extra shaped rewards may be unnecessary in dense-reward settings.
- ReLara outperforms SASR on RobotReach, which the authors attribute to access to action information.
Experimental setup
Datasets: MuJoCo tasks robotic tasks Atari games MountainCar
Benchmarks: AntStand AntFar HumanStand HumanKeep RobotReach RobotSlide RobotPush RobotPickPlace Pitfall Frogger Montezuma's Revenge Solaris
Metrics: average episodic return standard error sample efficiency training time peak memory
Baselines: DRND ReLara GFA-RFE ROSA ExploRS #Explo RND SAC TD3 PPO
Builds on: soft actor-critic random fourier features thompson sampling random network distillation
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