Reinforcement learning algorithms assume that observations satisfy the Markov property, yet real-world sensors frequently violate this assumption through correlated noise, latency, or partial observability. Standard performance metrics conflate Markov breakdowns with other sources of suboptimality, leaving practitioners without diagnostic tools for such violations. This paper introduces a prediction-based scoring method that quantifies non-Markovian structure in observation trajectories. A random forest first removes nonlinear Markov-compliant dynamics; ridge regression then tests whether historical observations reduce prediction error on the residuals beyond what the current observation provides. The resulting score is bounded in [0, 1] and requires no causal graph construction. Evaluation spans six environments (CartPole, Pendulum, Acrobot, HalfCheetah, Hopper, Walker2d), three algorithms (PPO, A2C, SAC), controlled AR(1) noise at six intensity levels, and 10 seeds per condition. In post-hoc detection, 7 of 16 environment-algorithm pairs, primarily high-dimensional locomotion tasks, show significant positive monotonicity between noise intensity and the violation score (Spearman rho up to 0.78, confirmed under repeated-measures analysis); under training-time noise, 13 of 16 pairs exhibit statistically significant reward degradation. An inversion phenomenon is documented in low-dimensional environments where the random forest absorbs the noise signal, causing the score to decrease as true violations grow, a failure mode analyzed in detail. A practical utility experiment demonstrates that the proposed score correctly identifies partial observability and guides architecture selection, fully recovering performance lost to non-Markovian observations. Source code to reproduce all results is provided at https://github.com/NAVEENMN/Markovianes.

In this section, we describe details about hyperparameter setting of RD. SAC-N-Unc and TD3-N-Unc, M is set to 1/10 of the total training steps. To ensure fairness, algorithms employing RD are implemented using CORL repository [54]. By modifying the original SAC/TD3 algorithm to employ a critic ensemble of number N and incorporate an uncertainty regularization term within the policy update process, we derive these backbone algorithms. Additionally, using RD with fewer Q ensembles can achieve similar or even better results than the backbone methods using more Q ensembles, indicating its potential in reducing computing resource consumption.

Thus written = argm JR( ).

Traditional robust reinforcement learning often depends on rectangularity assumptions, where adverse probability measures of outcome states are assumed to be independent across different states and actions.

Theorem B.1 (Performance difference bound for Model-based RL). Mi denote the inconsistency between the learned dynamics PMi and the true dynamics, i.e. ϵ For L1 L3, with the performance gap approximation of M1 and π1, we apply Lemma C.2, and Here, dπMi denotes the distribution of state-action pair induced by policy π under the dynamical modelMi. Theorem B.3 (Refined bound with constraints). Let µ and v be two probability distributions on the configuration space X, according to LemmaC.1,thenwehaveDTV(µ Under these definitions, we can yield the following intermediate outcome by applying the results from B.2and B.1 Here, we take the time-varying linear quadratic regulator as an instance for illustrating the rationality of our assumption on α.

Note that ˆφ is feasible for the constrained optimization problem. We refer to it as an "early stopping scheme" because the key idea is to return to the parameter values which gave the lowest validation error (see Section 7.8 of Goodfellow et al.[3]). In our implementation, we initialize two upper envelope networks with parametersφ and φ0, where φ is trained using the penalty loss, andφ0 records the parameters with the lowest validation error encounteredsofar. IfLφ > Lφ0, we count the number of consecutive times this occurs. Notonlyis this not standard practice, but to makeafair comparison across all algorithms, this would require, foreachofthe fivealgorithms, performing aseparate hyper-parameter search foreachofthe five environments.