# RE-SAC: Disentangling aleatoric and epistemic risks in bus fleet control: A stable and robust ensemble DRL approach

arXiv: https://arxiv.org/abs/2603.18396 · HTML: https://mlsanity.com/paper/2603.18396/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 24 of 24)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [Uncertainty-Based Offline Reinforcement Learning with Diversified Q-Ensemble](https://mlsanity.com/paper/2110.01548/) (2021)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Deep Reinforcement Learning and the Deadly Triad](https://mlsanity.com/paper/1812.02648/) (2018)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Algorithms for CVaR Optimization in MDPs](https://mlsanity.com/paper/1406.3339/) (2014)
- [Dealing with Non-Stationarity in Multi-Agent Deep Reinforcement Learning](https://mlsanity.com/paper/1906.04737/) (2019)
- [Lipschitz Continuity in Model-based Reinforcement Learning](https://mlsanity.com/paper/1804.07193/) (2018)
- [RORL: Robust Offline Reinforcement Learning via Conservative Smoothing](https://mlsanity.com/paper/2206.02829/) (2022)
- [Estimating Risk and Uncertainty in Deep Reinforcement Learning](https://mlsanity.com/paper/1905.09638/) (2019)
- [Risk-Sensitive Reinforcement Learning: Near-Optimal Risk-Sample Tradeoff in Regret](https://mlsanity.com/paper/2006.13827/) (2020)
- [Natural Actor-Critic for Robust Reinforcement Learning with Function Approximation](https://mlsanity.com/paper/2307.08875/) (2023)
- [A Bayesian Approach to Robust Reinforcement Learning](https://mlsanity.com/paper/1905.08188/) (2019)
- [Seizing Serendipity: Exploiting the Value of Past Success in Off-Policy Actor-Critic](https://mlsanity.com/paper/2306.02865/) (2023)
- [Single Agent Robust Deep Reinforcement Learning for Bus Fleet Control](https://mlsanity.com/paper/2508.20784/) (2025)

## Built on by (most cited first, 2 of 2)

- [BAPR: Bayesian amnesic piecewise-robust reinforcement learning for non-stationary continuous control](https://mlsanity.com/paper/2605.16170/) (2026)
- [Arithmetic Actor Heads and Training Stabilization for Out-of-Distribution Reinforcement Learning](https://mlsanity.com/paper/2610.05143/) (2026)

## Abstract (arXiv)

Bus holding control is challenging due to stochastic traffic and passenger demand. While deep reinforcement learning (DRL) shows promise, standard actor-critic algorithms suffer from Q-value instability in volatile environments. A key source of this instability is the conflation of two distinct uncertainties: aleatoric uncertainty (irreducible noise) and epistemic uncertainty (data insufficiency). Treating these as a single risk leads to value underestimation in noisy states, causing catastrophic policy collapse. We propose a robust ensemble soft actor-critic (RE-SAC) framework to explicitly disentangle these uncertainties. RE-SAC applies Integral Probability Metric (IPM)-based weight regularization to the critic network to hedge against aleatoric risk, providing a smooth analytical lower bound for the robust Bellman operator without expensive inner-loop perturbations. To address epistemic risk, a diversified Q-ensemble penalizes overconfident value estimates in sparsely covered regions. This dual mechanism prevents the ensemble variance from misidentifying noise as a data gap, a failure mode identified in our ablation study. Experiments in a realistic bidirectional bus corridor simulation demonstrate that RE-SAC achieves the highest cumulative reward (approx. -0.4e6) compared to vanilla SAC (-0.55e6). Mahalanobis rareness analysis confirms that RE-SAC reduces Oracle Q-value estimation error by up to 62% in rare out-of-distribution states (MAE of 1647 vs. 4343), demonstrating superior robustness under high traffic variability.