Conformal Test Martingales

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Supermartingale Certificates for Parametric MDPs
Sep 14, 2026Kaushik Mallik, \DHorj̣e ŽikelićMarkov Decision Processes Conformal Test Martingales
Gaussian Approximation for Multivariate Martingale Sums from Uniformly Ergodic Markov Chains
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When the Martingale Never Stops Firing: Anytime-Valid Gating on Real Forecast Streams
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Denoising growth complexity: Data geometry and certified schedules for diffusion sampling
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Betting on Moments: Legendre Jumper Martingales for Online Exchangeability Testing
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Anytime-Valid Confirmation of Label-Shift Corrections
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Noise-Adaptive High-Probability Regret Bounds for Online Convex Optimization
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Value Functions as Supermartingale Certificates
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Federated Martingale Posterior Samping
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Unified High-Probability Analysis of Stochastic Variance-Reduced Estimation
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Martingale-Consistent Self-Supervised Learning
May 12, 2026Moritz Gögl, Hanwen Xing, Christopher YauSelf-Supervised Conformal Test Martingales
Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means
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Self-Normalized Martingales and Uniform Regret Bounds for Linear Regression
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Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithms
Apr 30, 2026Zhenjie Ren, Xiaoli Wei, Xiang Yu +1Q-Learning Soft Actor-Critic

Sep 14, 2026 · cs.LOJ/K move · Enter open · S save

Supermartingale Certificates for Parametric MDPs

Kaushik Mallik, \DHorj̣e Žikelić

We consider the problems of formal verification and synthesis in parametric Markov decision processes (MDPs) with general measurable state and action spaces. The heart of our approach is a parameter flattening transformation, which allows us to transform parametric MDPs into semantically equivalent non-parametric MDPs. Building on this transformation, we introduce the novel notion of parametric supermartingale certificates, which generalize the traditional supermartingale certificates---used for non-parametric MDPs---to the parametric setting. We use our parametric supermartingale certificates to design algorithms for verification and approximate synthesis in polynomial arithmetic parametric MDPs. This leads to the first verification and synthesis algorithms for parametric MDPs with general state and action spaces. We implement our algorithms and experimentally evaluate them on several continuous parametric random walk benchmarks.

Markov Decision Processes Conformal Test Martingales Finite-Sample Certificates Formal Verification Constraint-Aware Synthesis

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