Prediction-Based Markov Violation Scores for Detecting Non-Markovian Observations in Reinforcement Learning

We study the closed-loop properties of a recurrent state-space model (RSSM) world model trained on human demonstrations in Gymnasium's LunarLander-v3. We use the trained world model for zero-shot CEM model-predictive control (MPC) and for actor-critic (A2C) training in imagination. Scored on 100 held-out episodes, the selected model-based A2C policy (trained on world-model checkpoint 280) reaches a mean return of +189.5, matching the best model-free A2C checkpoint (+183.7; 600- and 1000-step episode caps respectively) with ~65x fewer real training transitions. We also compare world-model MPC with a behaviour-cloning (BC) policy trained on the successful demonstrations. The BC policy matches MPC's mean return only under stochastic action selection, and on the same 20 episodes it has one catastrophic episode where MPC has none. We then introduce the Reward Observability Fraction (ROF), the Euclidean fraction of the reward gradient in the observable subspace of the linearized latent dynamics, and show that the next H observations carry Fisher information about every direction in this subspace and none about directions orthogonal to it. ROF itself however depends on how the latent is scaled: rescaling it changes ROF but not the model, so raw levels are not comparable across models. Forcing the reward head onto the posterior-corrected latent z raises ROF, and the rise survives a coordinate-invariant check on the pair of runs we tested. Finally, we test whether ROF or other offline metrics can predict the closed-loop collapse of MPC. Collapse varies between training runs with identical data and configuration. ROF does not predict it, none of the 108 offline summaries we screened passes a permutation test, and the best candidate fails on new runs. Predicting collapse offline from the model and logged data alone remains open.

Reinforcement learning algorithms are commonly analyzed (and designed) under the Markov assumption. This is unrealistic, as most environments encountered in practice are either partially observable, or require function approximation that restricts the agent to access non-Markovian state features. We consider the problem of learning an optimal reactive policy in a finite environment with deterministic observations (or equivalently, hard state aggregation). We introduce a new algorithm, Committed Q-learning, and prove almost-sure convergence to the optimal reactive policy under an intuitive assumption we call rewire-robustness. This assumption is strictly weaker than the $q_\star$-realizability condition used in prior work. Our algorithm is a variant of classical Q-learning in which the behavior policy commits to a single action upon entering a feature, and only resamples actions when the observed feature changes. A crucial part of our analysis is the introduction of quasi-Markov environments.

This paper addresses the problem of training a reinforcement learning (RL) policy under partial observability by exploiting a privileged, anytime-feasible planner agent available exclusively during training. We formalize this as a Partially Observable Markov Decision Process (POMDP) in which a planner agent with access to an approximate dynamical model and privileged state information guides a learning agent that observes only a lossy projection of the true state. To realize this framework, we introduce an anytime-feasible Model Predictive Control (MPC) algorithm that serves as the planner agent. For the learning agent, we propose Planner-to-Policy Soft Actor-Critic (P2P-SAC), a method that distills the planner agent's privileged knowledge to mitigate partial observability and thereby improve both sample efficiency and final policy performance. We support this framework with rigorous theoretical analysis. Finally, we validate our approach in simulation using NVIDIA Isaac Lab and successfully deploy it on a real-world Unitree Go2 quadruped navigating complex, obstacle-rich environments.