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Rich-Observation Reinforcement Learning with Continuous Latent Dynamics
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Proposes RichCLD, a theoretical framework for rich-observation RL with continuous Lipschitz latent dynamics, with a GOLF-based upper bound, a lower bound showing Q*/V*-Lipschitzness is insufficient, a Lipschitz-constrained min-max-min representation learner (BCRL.C), and an exploration algorithm CRIEE.
Problem
Reinforcement learning from high-dimensional observations where the latent state is continuous and governed by Lipschitz nonlinear dynamics; existing rich-observation theory covers only tabular or linear latent dynamics, and representation learning must be interleaved with exploration.
Approach
A min-max-min representation objective with a Lipschitz-constrained prediction head (enforced via spectral normalization) and double-sampling debiasing, which learns decoders that respect the Lipschitz structure of latent dynamics; combined with discretized optimistic DP and count-based bonuses in the learned latent space.
Key results
- On visual D4RL walker and cheetah, BCRL.C representations with TD3-BC are competitive with the PCLaSt baseline and significantly better than a random decoder.
- In maze environments with K-means (K=16), BCRL.C learned latents respect walls and boundaries, while the variant without Lipschitz prediction heads does not.
- Theory: GOLF.DBR gives sample complexity O(eps^-(2dim_SA+dim_A+2)) and CRIEE gives O(eps^-O(dim_SA^2)); Q*/V*-Lipschitz latent dynamics require exponential-in-H or |X|^{1/2} sample complexity lower bound.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Enforce Lipschitzness of the prediction heads with spectral normalization (ablation) | BCRL.C · Maze environments | latent dynamics structure | Helped |
| Learn representations with BCRL.C instead of a randomly initialized decoder | TD3-BC on visual D4RL · Walker and cheetah | reward | Helped |
| Use BCRL.C representations instead of PCLaSt representations | TD3-BC on visual D4RL · Walker and cheetah | reward | No clear effect |
Surprising findings
- Q*/V*-Lipschitzness, a weaker assumption sufficient for sample-efficient Lipschitz MDPs without rich observations, is insufficient in the rich-observation setting.
- Standard representation objectives (contrastive learning and multistep inverse kinematics) do not readily extend to continuous latent dynamics, since their optimal predictors need not be Lipschitz in the latent state.
Limitations
- Sample complexity is nonparametric, exponential in latent dimension, and has worse exponents than Lipschitz MDP minimax rates.
- Experiments focus on representation learning in isolation; full CRIEE algorithm is not empirically evaluated.
- Experiments remove exogenous noise from observations, so robustness to distractors is not tested.
Experimental setup
Datasets: visual D4RL walker visual D4RL cheetah maze environments (synthetic, 500k random-policy steps each)
Benchmarks: visual D4RL walker visual D4RL cheetah point-mass maze environments (qualitative)
Metrics: episode return K-means cluster visualization
Baselines: PCLaSt Random decoder Baseline without Lipschitz constraint
Builds on: GOLF Block MDP representation learning (RepLearn) disagreement-based regression TD3-BC coverability
Closest papers by meaning
- Reinforcement Learning Under Latent Dynamics: Toward Statistical and Algorithmic Modularity (NeurIPS 2024 · similarity 0.90)
- Provable Rich Observation Reinforcement Learning with Combinatorial Latent States (ICLR 2021 · similarity 0.90)
- Kinematic State Abstraction and Provably Efficient Rich-Observation Reinforcement Learning (ICML 2020 · similarity 0.89)
- Extracting Latent State Representations with Linear Dynamics from Rich Observations (ICML 2022 · similarity 0.89)
- PAC Reinforcement Learning with Rich Observations (NeurIPS 2016 · similarity 0.89)
- Towards Principled Representation Learning from Videos for Reinforcement Learning (ICLR 2024 · similarity 0.88)
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