Risk and Anomaly Identification for Distribution Network Optimal Operation Based on Reinforcement Learning and Uncertainty Quantification

Distributional reinforcement learning agents learn full return distributions that are increasingly read at face value: for interpretability, risk-sensitive control, and safety monitoring. We ask a question theory anticipates but that has not been measured directly: are the risk claims of a trained distributional agent true? Our audit combines a decision-relevant screening metric (the excess Wasserstein gap between the top two actions, which equals the mass by which first-order stochastic dominance is violated), ground truth from snapshot-restart Monte Carlo, and a statistical harness (permutation nulls, bootstrap refutation, FDR control) without which the audit itself manufactures false conclusions. Across QR-DQN, C51, and IQN on MinAtar (33 runs), 40-95% of the strongest claimed risk trade-offs are refuted at 95% confidence, the placement of the strongest claims is statistically indistinguishable from truth-blind, and essentially no claim is confirmable: for these agents, the learned "risk" reflects a training artifact rather than environment stochasticity. The artifact is structural (fully formed early in training, uncorrelated with final score, idiosyncratic to each seed) and appears unchanged at full-Atari scale, with every top Breakout claim of a pretrained near-state-of-the-art QR-DQN refuted. Positive controls of known magnitude confirm 96-100% of real claims (correlation 0.89-0.92): the reading measures the agents, not the audit. Acting on the heads' CVaR advice at their most-flagged states ranges from beneficial to significantly worse than chance. Neither training for risk nor ensembling removes the artifact, and recalibration passes the audit only by nullifying the claims: the head is uninformative, not merely miscalibrated. We release the toolkit and document two silent pitfalls that produced convincing but wrong audits of our own.

Effective model-based reinforcement learning in stochastic environments requires planning that accounts for predictive uncertainty. Propagating full state distributions analytically offers a principled way to do this, but has traditionally required restrictive policy or reward structures to remain tractable. Consequently, modern deep reinforcement learning has largely retreated to either stochastic sampling, which introduces significant target variance, or deterministic point estimates that ignore predictive covariance entirely. We investigate whether distribution-aware planning is possible without these constraints. Using a quadratic action-value parameterization, we first reduce the Bellman backup to an expectation over the state-value function alone; the key idea is then a compatibility principle between the predictive transition distribution and the value function class, under which this expectation is analytic in the distribution's moments. We instantiate this principle with a Gaussian transition model paired with a radial-basis value function, yielding a closed-form backup that propagates both predictive mean and covariance. Empirically, our approach reduces target variance and yields well-calibrated predictive uncertainty under stochastic observations in continuous control, providing a principled framework for planning with learned distribution models.

Offline-to-Online Reinforcement Learning (O2O-RL) leverages an offline, pre-trained policy to minimize costly online interactions. Although data-efficient, O2O-RL is susceptible to shifts between offline and online distributions. Existing work aims to mitigate the harm of this shift by finetuning the policy on trajectory data sampled from a diffusion model. Inspired by this line of work, we propose DUAL: an efficient \textbf{D}iffusion \textbf{U}ncertainty-\textbf{A}ware framework for offline-to-online reinforcement \textbf{L}earning. DUAL utilizes the prior knowledge of the diffusion model to distill a fast-sampling diffusion actor policy and transition model in the offline phase. DUAL also employs a Laplace approximation and distance transition-state-shift detection, thereby using uncertainty quantification to improve exploration versus exploitation in the online phase. We formally show that our actor loss with the Laplace approximation provides a proxy for a principled estimate of epistemic uncertainty. Empirically, DUAL improves the online expected return over O2O-RL baselines across multiple settings and environments.