Provably Efficient Sample Complexity for Robust CMDP

arXiv — stat.MLWednesday, November 12, 2025 at 5:00:00 AM
The recent paper on robust constrained Markov decision processes (RCMDPs) addresses the challenge of learning policies that maximize cumulative rewards while satisfying safety constraints, particularly when real environments differ from simulations. The authors introduce the Robust Constrained Value Iteration (RCVI) algorithm, which incorporates an augmented state space to enhance policy optimization. This approach is crucial as it marks the first sample complexity guarantee for RCMDPs, revealing that traditional Markovian policies may not be optimal in all scenarios. The RCVI algorithm boasts a sample complexity of O(|S||A|H^5/ε²), which is a significant advancement in ensuring that cumulative utility exceeds safety thresholds with minimal violation. Empirical results further validate the effectiveness of this approach, highlighting its potential impact on the field of artificial intelligence and decision-making under uncertainty.
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