Lunar Lander RL: Reward Shaping & Reward Hacking

An empirical reinforcement-learning study using Gymnasium LunarLander-v3 and Proximal Policy Optimization (PPO). It compares an untrained random policy, a baseline PPO agent, a deliberately flawed reward bonus that induces reward hacking (specification gaming), and a frame-to-frame potential-difference shaping wrapper with a per-step time penalty.

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Experimental Pipeline & Evaluation Discipline

A common mistake in reward-shaping experiments is evaluating shaped policies with their custom training wrappers still attached, which conflates artificial shaping bonuses with true task performance. In this repository, all checkpoints are evaluated strictly on the unwrapped LunarLander-v3 environment (custom_reward_wrappers = off).

flowchart LR
    subgraph Training["Training Variants (Gymnasium LunarLander-v3)"]
        B["Baseline PPO\nUnwrapped Environment\n(1,000,000 steps)"]
        H["Reward-Hacked PPO\nHoverHackWrapper (+1 airborne hover)\n(400,000 steps)"]
        F["Fixed-Shaped PPO\nFixedRewardShapingWrapper (ΔΦ - 0.05)\n(1,000,000 steps)"]
        C["Champion PPO\nContinuation Best Checkpoint\n(1,313,520 steps)"]
    end

    subgraph Eval["Unwrapped Evaluation Protocol (Wrappers OFF)"]
        Env["Standard LunarLander-v3\nDeterministic Policy Actions"]
        Metrics["Metrics & Bootstrap CI\nresults/*.json · results/*.csv"]
    end

    B --> Env
    H --> Env
    F --> Env
    C --> Env
    Env --> Metrics

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Results Summary

1. Four-Stage Ablation (results/benchmark_results.json)

All PPO scores below were evaluated on the unwrapped environment with custom reward wrappers OFF over 10 deterministic episodes (the random policy reference is 1 episode). LunarLander-v3 is conventionally considered solved around an average score of 200.

Agent	Training steps	Unwrapped evaluation score	Behavioral interpretation
Untrained random policy	0	29.92	Single-episode reference; crashes quickly
Baseline PPO	1,000,000	269.41 ± 14.90	Learns stable descent using the environment's native reward
Reward-hacked PPO (HoverHackWrapper)	400,000	-56.07 ± 20.20	Exploits the +1 airborne hover bonus instead of landing; true task score collapses
Fixed-shaped PPO (FixedRewardShapingWrapper)	1,000,000	266.54 ± 23.28	Eliminates hovering and lands reliably; mean is close to baseline in this run

The baseline and fixed-shaped means (269.41 vs. 266.54) are within one standard deviation in this 10-episode run; these results do not claim that the shaped agent outperforms baseline PPO. Full values are stored in results/benchmark_results.json and results/benchmark_summary.csv.

2. 500-Seed Champion Checkpoint Benchmark (results/final_champion_evaluation.json)

The periodic-best continuation checkpoint (models/ppo_lunar_lander_champion.zip, 1,313,520 timesteps) was evaluated across 500 deterministic episodes (seeds 600000–600499) with custom wrappers disabled:

Metric	Result
Evaluation episodes (seeds 600000–600499)	500
Mean unwrapped reward	274.98
Median unwrapped reward	276.92
Sample standard deviation	27.15
5th-percentile reward	239.09
10th-percentile reward	246.97
Episodes scoring ≥ 200	495 / 500 (99.0%)
Mean episode length	247.5 steps

A subsequent low-learning-rate fine-tuning candidate achieved a mean reward of 271.67 on the same 500 seeds (paired difference +3.31 in favor of the champion checkpoint, 95% bootstrap CI [0.33, 6.58]), so the fine-tuned candidate was not promoted. Full details are recorded in results/final_champion_evaluation.json.

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Visual Progression

Stage 1 — Random policy	Stage 2 — Baseline PPO
Original MP4	Original MP4

Stage 3 — Reward hacking (HoverHackWrapper)	Stage 4 — Fixed shaping (FixedRewardShapingWrapper)
Original MP4	Original MP4

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Mathematical Formulation of the Reward Wrappers (src/reward_wrappers.py)

Let the 8-dimensional observation vector at step $t$ be: $$s_t = [x_t, y_t, v_{x,t}, v_{y,t}, \theta_t, \omega_t, \ell_{1,t}, \ell_{2,t}]$$ where $(x_t, y_t)$ is lander position relative to the pad, $(v_{x,t}, v_{y,t})$ is linear velocity, $\theta_t$ is angle (tilt), $\omega_t$ is angular velocity, and $\ell_{1,t}, \ell_{2,t} \in {0, 1}$ are leg ground-contact indicators.

1. Flawed Bonus (HoverHackWrapper)

Adds a dense $+1.0$ step bonus whenever the lander is upright, moving slowly, and still airborne: $$r't = r_t + \mathbb{I}!\left(|\theta_t| < 0.25 ;\land; \sqrt{v{x,t}^2 + v_{y,t}^2} < 0.35 ;\land; (\ell_{1,t} + \ell_{2,t}) = 0\right)$$ Because touching down sets $\ell_{1,t} + \ell_{2,t} &gt; 0$ and terminates the episode, the agent discovers that hovering indefinitely collects more cumulative shaped return than landing—a textbook example of specification gaming.

2. Potential-Difference Shaping (FixedRewardShapingWrapper)

Defines a state potential function penalizing tilt, horizontal offset, and angular velocity: $$\Phi(s_t) = -15|\theta_t| - 10|x_t| - 5|\omega_t|$$ and modifies the step reward using the undiscounted frame-to-frame potential difference plus a constant per-step time fee ($c = -0.05$): $$r't = r_t + \bigl(\Phi(s_t) - \Phi(s{t-1})\bigr) - 0.05$$ Note on policy invariance: Classic potential-based reward shaping (Ng, Harada & Russell, 1999) uses $\gamma \Phi(s_t) - \Phi(s_{t-1})$ without an additive step penalty to guarantee strict optimal-policy invariance. Here, $\Delta \Phi = \Phi(s_t) - \Phi(s_{t-1})$ with a $-0.05$ step fee is tested empirically as a practical shaping heuristic and evaluated against the true unwrapped task reward.

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Repository Map

.
├── .github/workflows/ci.yml             # Automated unit tests for reward wrappers
├── README.md
├── requirements.txt
├── LICENSE
├── notebooks/
│   └── LunarLander_Reward_Shaping.ipynb # Interactive training & recording notebook
├── src/
│   └── reward_wrappers.py               # HoverHackWrapper & FixedRewardShapingWrapper
├── scripts/
│   ├── evaluate_models.py               # Reproducible multi-seed CLI evaluator
│   └── train_experiment.py              # Colab training & artifact export pipeline
├── tests/
│   └── test_reward_wrappers.py          # Unit tests for wrapper math & edge cases
├── models/
│   ├── ppo_lunar_lander_baseline.zip
│   ├── ppo_lunar_lander_hacked.zip
│   ├── ppo_lunar_lander_fixed.zip
│   └── ppo_lunar_lander_champion.zip
├── videos/                              # 4 MP4 originals + 4 GIF previews
└── results/                             # JSON + CSV evaluation benchmarks

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Run & Verify Locally

1. Install Dependencies

# Ubuntu/Debian system packages required for Box2D & video rendering
sudo apt-get update && sudo apt-get install -y swig ffmpeg
python -m pip install -r requirements.txt

2. Run Reward Wrapper Unit Tests

python -m unittest discover -s tests -p "test_*.py" -v

3. Reproduce Checkpoint Evaluations (scripts/evaluate_models.py)

Evaluate all four saved checkpoints over 10 deterministic seeds:

python scripts/evaluate_models.py --episodes 10 --start-seed 600000

Reproduce the 500-episode champion benchmark (seeds 600000–600499):

python scripts/evaluate_models.py \
  --models models/ppo_lunar_lander_champion.zip \
  --episodes 500 \
  --start-seed 600000 \
  --output-json results/reproduced_champion_eval.json

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Limitations & Evaluation Protocol

• Single training seed per variant: While the champion checkpoint is evaluated across 500 held-out environment seeds (600000–600499), training multiple independent random seeds per wrapper configuration is required to establish variance across training runs.
• Checkpoint selection vs. final evaluation: Periodic checkpoints during continuation training were monitored on validation rollouts, and the selected candidate (ppo_lunar_lander_champion.zip, 1,313,520 steps) was subsequently benchmarked against the low-learning-rate fine-tuning candidate on the disjoint 500-seed test range (seeds 600000–600499).
• Reward threshold vs. physical landing: A score of ≥ 200 is the standard Gymnasium performance threshold proxy, not a direct geometric check that both landing legs came to rest between the flags on every episode.
• Hardware/library sensitivity: Box2D physics and PyTorch floating-point reductions can exhibit minor cross-platform drift across library versions; scripts/evaluate_models.py records exact evaluation parameters in its JSON output.

References

• Schulman et al., Proximal Policy Optimization Algorithms, 2017.
• Ng, Harada & Russell, Policy Invariance Under Reward Transformations: Theory and Application to Reward Shaping, ICML 1999.

License

Code and experiment artifacts in this repository are released under the MIT License.