Near-Constant Strong Violation and Last-Iterate Convergence for Online CMDPs via Decaying Safety Margins

The FlexDOME algorithm represents a landmark advancement in safe online reinforcement learning, achieving provable near-constant strong constraint violation (scaling as Õ(1)) alongside sublinear strong reward regret and non-asymptotic last-iterate convergence for Constrained Markov Decision Processes. This breakthrough addresses critical limitations in existing primal-dual methods that previously suffered from growing constraint violations or were restricted to average-iterate convergence. The algorithm's innovative use of decaying safety margins and regularization enables practical deployment in safety-critical applications like autonomous systems and medical decision-making.

Near-Constant Strong Violation and Last-Iterate Convergence for Online CMDPs via Decaying Safety Margins

FlexDOME Algorithm Achieves Breakthrough in Safe Online Reinforcement Learning

Researchers have introduced a novel algorithm, Flexible safety Domain Optimization via Margin-regularized Exploration (FlexDOME), which achieves a landmark result in safe online reinforcement learning. The algorithm is the first to provably deliver near-constant strong constraint violation—scaling as $\tilde{O}(1)$—alongside sublinear strong reward regret and non-asymptotic last-iterate convergence, addressing critical limitations in existing methods for Constrained Markov Decision Processes (CMDPs).

The Challenge of Strong Regret and Violation Metrics

In safe online RL, agents must learn optimal policies while strictly adhering to safety constraints over time. Prior primal-dual methods designed to achieve sublinear strong reward regret often suffer from a fundamental trade-off: they inevitably incur growing strong constraint violation or are restricted to average-iterate convergence. This limitation stems from inherent oscillations in the optimization process, where errors do not cancel out over time under strong metrics, posing a significant barrier to deploying RL in safety-critical applications like autonomous driving or medical systems.

How FlexDOME Solves the Problem

The FlexDOME algorithm innovates by incorporating carefully designed, time-varying safety margins and regularization terms into the established primal-dual optimization framework. This design allows the algorithm to actively manage the trade-off between exploration and constraint satisfaction dynamically. The core theoretical advancement is a novel term-wise asymptotic dominance strategy, where the safety margin is rigorously scheduled to asymptotically majorize the functional decay rates of both optimization and statistical errors. This mechanism effectively "clamps" cumulative safety violations to a near-constant level, a previously unattained guarantee.

Theoretical Guarantees and Experimental Validation

The research provides rigorous theoretical proofs for FlexDOME's performance. Beyond the $\tilde{O}(1)$ strong violation bound, the team established non-asymptotic last-iterate convergence guarantees using a sophisticated policy-dual Lyapunov argument. This ensures the algorithm's policy iterates converge to a solution point, not just on average, providing stronger stability assurances. Furthermore, experimental results across various CMDP benchmarks corroborate the theoretical findings, demonstrating FlexDOME's practical efficacy in maintaining safety while efficiently learning.

Why This Matters: Key Takeaways

  • Landmark Safety Guarantee: FlexDOME is the first algorithm to achieve provably near-constant strong constraint violation ($\tilde{O}(1)$) in online CMDPs, a critical step toward truly safe RL.
  • Solves a Fundamental Trade-off: It breaks the existing barrier where sublinear strong regret came at the cost of growing violation or weak convergence, using a novel term-wise asymptotic dominance strategy.
  • Stronger Convergence: The algorithm provides non-asymptotic last-iterate convergence guarantees, offering more reliable and stable policy performance than average-iterate methods.
  • Practical Implications: This advancement significantly enhances the feasibility of deploying reinforcement learning in real-world, safety-critical domains where constraints cannot be violated over time.

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