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Identifying Latent State-Transition Processes for Individualized Reinforcement Learning
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Proposes individualized MDPs with time-invariant latent individual factors, proves identifiability under finite-mixture (group determinacy) and post-nonlinear conditions, and uses a VQ-VAE-style estimator plus latent-conditioned RL to learn individualized policies.
Problem
Identifying time-invariant latent individual-specific factors that causally shape state transitions from observed state-action trajectories, so that individualized RL policies can be learned and adapted to newcomers.
Approach
Models individual heterogeneity as a time-invariant latent factor in the transition process (iMDP), proves identifiability via finite-mixture group-wise arguments (group determinacy, sample sufficiency) and via a rank-based post-nonlinear temporal result, and estimates the factor with a vector-quantized sequential encoder and conditional decoder that feeds the estimate into the policy.
Key results
- On synthetic finite-latent data, the full model reaches PCC 0.942 ± 4.0e-05 with bias 0.072, improving over quantized encoding alone (PCC 0.646).
- On Pendulum, HeartPole and Half Cheetah, the proposed latent-conditioned policy outperforms baselines in jumpstart and accumulative reward, per training curves.
- Identifiability performance improves with trajectory length and requires enough individuals per group (sample sufficiency) to recover latent factors.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add a sequential encoder to quantized encoding (ablation) | Latent estimation framework · Synthetic Case 1 | PCC: 0.646 -> 0.910 | Helped |
| add a sequential encoder to quantized encoding (ablation) | Latent estimation framework · Synthetic Case 1 | Bias: 0.099 -> 0.077 | Helped |
| add a noise estimator to quantized encoding with a sequential encoder (ablation) | Latent estimation framework · Synthetic Case 1 | PCC: 0.910 -> 0.942 | Helped |
| add a noise estimator to quantized encoding with a sequential encoder (ablation) | Latent estimation framework · Synthetic Case 1 | Bias: 0.077 -> 0.072 | Helped |
Surprising findings
- Cross-individual transfer (pre-trained policy on other individuals) yields worse initial performance than training from scratch in some environments because it ignores individual-specific information.
- Random group embedding alone improves generalization over no-embedding baselines in HeartPole, suggesting group structure helps even without accurate estimates.
Limitations
- Does not model instantaneous causal dependencies among state variables.
- Continuous latent factors are supported empirically but lack a formal nonparametric identifiability proof.
- Assumes latent factors are time-invariant; time-varying extension is non-trivial.
Experimental setup
Datasets: PersuasionForGood corpus Pendulum HeartPole Half Cheetah synthetic post-nonlinear data
Benchmarks: Pendulum HeartPole Half Cheetah PersuasionForGood corpus synthetic post-nonlinear data
Metrics: Pearson correlation coefficient kernel canonical correlation analysis jumpstart accumulative reward initial reward final reward
Baselines: Disentangled Sequential Autoencoder Population-level component Aligned Latent Models SAC DDPG D3QN Rainbow DQN Cross-individual transfer
Builds on: VQ-VAE Disentangled Sequential Autoencoder DDPG Lemma of identifiability of mixture models from grouped samples post-nonlinear causal model
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