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Regularized Parameter Uncertainty for Improving Generalization in Reinforcement Learning
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Proposes SNR PUN, a Bayesian parameter-uncertainty PPO policy whose parameters are regularized by capping each weight's mean-to-std ratio, improving out-of-distribution generalization on mutated control environments and transferring to a physical cartpole.
Problem
RL agents overfit to their training environment and generalize poorly to unseen environment configurations; standard KL-based regularization of parameter-uncertainty networks is hard to apply in noisy RL training.
Approach
Replace the KL-to-prior term in Bayes-by-backprop with a loss that penalizes each parameter's signal-to-noise ratio |mu|/sigma above a maximum threshold, shown to be equivalent to a KL against a family of priors; combined with per-timestep resampling, a deterministic critic, and a larger sigma initialization inside PPO.
Key results
- SNR PUN achieves ATP of 670.48 on CartPoleSwingUp, 421.77 on Acrobot, 750.47 on Quadruped and 310.96 on Walker, outperforming the MLP, dropout, gSDE, entropy, weight decay, VIB and PUN baselines in all environments.
- On the physical cartpole, only SNR PUN successfully transferred the policy; its successful swingup percentage is reported as 43% higher than the state-of-the-art.
- Removing the SNR loss (PUN) leaves 2.12% (CartPole) and 10.2% (Quadruped) of SNR values above the max threshold, while SNR PUN has none.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add SNR regularization to PUN (ablation) | PUN · CartPoleSwingUp | ATP: 534.43 ± 48.40 -> 670.48 ± 13.42 | Helped |
| add SNR regularization to PUN (ablation) | PUN · Acrobot-v1 | ATP: 246.57 ± 22.55 -> 421.77 ± 32.74 | Helped |
| add SNR regularization to PUN (ablation) | PUN · Quadruped | ATP: 738.95 ± 3.91 -> 750.47 ± 3.23 | Helped |
| add SNR regularization to PUN (ablation) | PUN · Walker | ATP: 250.11 ± 16.28 -> 310.96 ± 16.96 | Helped |
| sample parameters once per simulation rollout instead of resampling every timestep (ablation) | SNR PUN · CartPoleSwingUp, Acrobot-v1, Quadruped, Walker | ATP: 670.48 ± 13.42 -> 664.88 ± 24.35; 421.77 ± 32.74 -> 423.43 ± 50.98; 750.47 ± 3.23 -> 751.21 ± 3.44; 310.96 ± 16.96 -> 30 | Mixed |
| use the parameter mean instead of sampling parameters (ablation) | SNR PUN · CartPoleSwingUp, Acrobot-v1, Quadruped, Walker | ATP: 670.48 ± 13.42 -> 693.86 ± 12.21; 421.77 ± 32.74 -> 417.32 ± 31.97; 750.47 ± 3.23 -> 749.13 ± 3.41; 310.96 ± 16.96 -> 31 | Mixed |
Surprising findings
- Dropout performs well on Quadruped but not on the other environments, and combining PUN with dropout helps only on Acrobot.
Limitations
- Gains on the physical cartpole are reported only for a single simple task and small margins in average reward.
- Max SNR hyperparameter is environment-sensitive and must be tuned per environment.
- Evaluation is restricted to control tasks with mutated parameters; other domains such as supervised continual learning are not tested.
Experimental setup
Datasets: CartPoleSwingUp Acrobot-v1 Quadruped Walker
Benchmarks: CartPoleSwingUp Acrobot-v1 Quadruped Walker physical cartpole
Metrics: average task performance (ATP) successful swingup percentage
Baselines: MLP dropout gSDE maximum entropy RL weight decay VIB PUN
Builds on: Bayes-by-backprop proximal policy optimization variational information bottleneck gSDE
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