mlsanityData to 14 Oct 2026

SDE Guided Monte Carlo Reinforcement Learning: A Stochastic Maximum Principle Approach for Robust Decision Making in Noisy Environments

arXiv 2607.22541 ↗First posted 26 Apr 2026math.OC cs.NA math.NAcited by 0

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

This work investigates whether the qualitative optimality conditions of the SMP can serve as guiding heuristics for designing robust tabular RL algorithms. We propose the SDE-MC-AC framework, which establishes a set of SMP-inspired correspondences: the potential field gradient is mapped to potential-based reward shaping, the diffusion coefficient to a softmax temperature, and the value function gradient magnitude to the episode-averaged absolute temporal-difference (TD) error. Crucially, we derive an SMP-motivated adaptive temperature schedule that scales exploration stochastically in response to local value uncertainty. The resulting Monte Carlo Actor-Critic agent integrates potential-shaped rewards, entropy regularization, and adaptive temperature control within episodic updates. We conduct a set of five principled experiments in a minimal, fixed maze testbed under three canonical noise regimes (perceptual, dynamic goal, action) to test five falsifiable hypotheses derived from the SMP. Our results provide evidence for (i) an inverted-U optimal stochasticity curve, (ii) the robust failure prevention of the adaptive schedule under non-stationary noise, (iii) convergence acceleration by potential field guidance, (iv) cross-noise generalization, and (v) the indispensability of the combined SDE components through systematic ablation. Trajectory visualizations reveal a characteristic ``macroscopically deterministic, microscopically stochastic'' navigation pattern consistent with the SDE model. The study demonstrates that even a heuristic transposition of the SMP into a discrete MDP can yield significant empirical gains, thereby opening a bridge between rigorous stochastic optimal control and practical robust reinforcement learning.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 9 of its 34 references that are in the map. First posted on arXiv 26 Apr 2026.

Builds on

9 of 34 references.

References · 9

  1. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,885
  2. 2017Noisy Networks for Explorationcited by 266
  3. 2015Learning Continuous Control Policies by Stochastic Value Gradientscited by 162
  4. 2017Parameter Space Noise for Explorationcited by 161
  5. 2023An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systemscited by 38
  6. 2025Stochastic Operator Network: A Stochastic Maximum Principle Based Approach to Operator Learningcited by 4
  7. 2020An efficient numerical algorithm for solving data driven feedback control problemscited by 3
  8. 2024An Online Algorithm for Solving Feedback Optimal Control Problems with Partial Observationscited by 2
  9. 2025Batch Sample-wise Stochastic Optimal Control via Stochastic Maximum Principlecited by 1

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  1. 2026Agentic Monte Carlo: Simulating Reinforcement Learning for Black-Box Agents
  2. 2022On Practical Reinforcement Learning: Provable Robustness, Scalability, and Statistical Efficiency
  3. 2021Robust Entropy-regularized Markov Decision Processes
  4. 2026Uncertainty-Aware LLM-Guided Policy Shaping for Sparse-Reward Reinforcement Learning
  5. 2026DARLING: Detection Augmented Reinforcement Learning with Non-Stationary Guarantees
  6. 2026Online Robust Reinforcement Learning Through Monte-Carlo Planning
  7. 2025Exploration by Random Reward Perturbation
  8. 2026Exploring Starts Are Not Enough: Counterexamples and a Fix for Monte Carlo Exploring Starts