PAC-Bayesian Certificates for Quadratic Closed-Loop Control

• URL: http://arxiv.org/abs/2606.28281v1
• Date: Fri, 26 Jun 2026 17:24:21 GMT
• Title: PAC-Bayesian Certificates for Quadratic Closed-Loop Control
• Abstract summary: PAC-Bayesian bounds provide finite-sample guarantees for data-dependent predictors.<n>Applying them to learning-based control is difficult because the natural objective is a quadratic trajectory cost.<n>We provide a set of PAC-Bayes-Chernoff certificates for posterior distributions over feasible closed-loop responses.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: PAC-Bayesian bounds provide finite-sample guarantees for data-dependent randomized predictors, but applying them to learning-based control is difficult because the natural objective is a quadratic trajectory cost. Such losses are unbounded, non-Lipschitz , and lead to response-dependent Chernoff terms. We employ System Level Synthesis parameterization, which exposes the closed-loop trajectory map of a linear system directly and makes the quadratic control loss amenable to explicit certification. Moreover, we provide a set of PAC-Bayes-Chernoff certificates for posterior distributions over feasible closed-loop responses. For Gaussian disturbance trajectories with arbitrary covariance, we derive an exact one-sided Gaussian transform and a tractable quadratic upper bound expressed through closed-loop sensitivity quantities. We also derive a posterior-localized surrogate for settings where pointwise closed-loop response certificates are unavailable or have support related admissibility issues. Although PAC-Bayes certifies a non-degenerate posterior, the convex quadratic form of the SLS loss transfers the certificate to the posterior mean response. We present a deterministic mean response deployment result that is particularly suitable for control while retaining the stochastic posterior in the bound. Additionally, we provide a data-driven bound for this deployment, transitioning away from an oracle bound. Minimizing this bound naturally results in a learning algorithm for control selection from data. Numerical experiments on a double integrator show that the algorithm acts as a sensitivity-aware finite-sample regularizer, improving held-out cost and reducing closed-loop sensitivity in the low-data regime

Related papers

• Certifying Plans under Model Mismatch: A Trilemma for Reachability from Scarce Data [5.455772242709494]
  Sim-to-real policies are designed under nominal dynamics, but target-system trials may yield only a few isolated one-step transitions.<n>We study pre-execution certification of a fixed control sequence, such as an action chunk produced by a learned policy.
  arXiv  Detail & Related papers  (2026-08-03T16:28:26Z)
• Closing the Null Space: Guidance-Aware Quantization for Classifier-Free Diffusion [0.0]
  Two-pass CFG execution pattern imposes a latency overhead that parameter-count and bit-operation metrics conceal entirely.<n>Guidance-Aware Mixed Precision (GAMP) is proposed, which calibrates directly on the guided prediction.
  arXiv  Detail & Related papers  (2026-07-09T08:42:07Z)
• Controller-Augmented Hidden Markov Models: A Computational Framework for Constrained Sequential Inference [0.0]
  We present Controller-Augmented Hidden Markov Models (CHMMs)<n>CHMMs is a framework that compiles each constraint into a finite-state controller tracking the minimal sufficient history.<n>We evaluate CHMMs against 6 alternative decoders on 3 real-world sequence-labeling tasks.
  arXiv  Detail & Related papers  (2026-06-11T19:29:09Z)
• Score-Guided Proximal Projection: A Unified Geometric Framework for Rectified Flow Editing [1.0312968200748118]
  Rectified Flow models achieve state-of-the-art generation quality, yet controlling them for precise tasks remains a challenge.<n>Current approaches bifurcate into inversion-based guidance, which suffers from "geometric locking"<n>We propose Score-Guided Proximal Projection, a unified framework that bridges the gap between deterministic optimization and contraction sampling.
  arXiv  Detail & Related papers  (2026-03-05T23:44:45Z)
• Coverage Guarantees for Pseudo-Calibrated Conformal Prediction under Distribution Shift [1.5861469511290378]
  Conformal prediction offers marginal coverage guarantees if the data distribution shifts.<n>We analyze the use of pseudo-calibration as a tool to counter this performance loss.<n>We propose a source-tuned pseudo-calibration algorithm that interpolates between hard pseudo-labels and randomized labels.
  arXiv  Detail & Related papers  (2026-02-16T16:48:39Z)
• Learnable Chernoff Baselines for Inference-Time Alignment [64.81256817158851]
  We introduce Learnable Chernoff Baselines as a method for efficiently and approximately sampling from exponentially tilted kernels.<n>We establish total-variation guarantees to the ideal aligned model, and demonstrate in both continuous and discrete diffusion settings that LCB sampling closely matches ideal rejection sampling.
  arXiv  Detail & Related papers  (2026-02-08T00:09:40Z)
• Verifying Closed-Loop Contractivity of Learning-Based Controllers via Partitioning [52.23804865017831]
  We address the problem of verifying closed-loop contraction in nonlinear control systems whose controller and contraction metric are both parameterized by neural networks.<n>We derive a tractable and scalable sufficient condition for closed-loop contractivity that reduces to checking that the dominant eigenvalue of a symmetric Metzler matrix is nonpositive.
  arXiv  Detail & Related papers  (2025-12-01T23:06:56Z)
• LEC: Linear Expectation Constraints for False-Discovery Control in Selective Prediction and Routing Systems [95.35293543918762]
  Large language models (LLMs) often generate unreliable answers, while uncertainty methods fail to fully distinguish correct from incorrect predictions.<n>We address this issue through the lens of false discovery rate (FDR) control, ensuring that among all accepted predictions, the proportion of errors does not exceed a target risk level.<n>We propose LEC, which reinterprets selective prediction as a constrained decision problem by enforcing a Linear Expectation Constraint.
  arXiv  Detail & Related papers  (2025-12-01T11:27:09Z)
• Unsupervised Conformal Inference: Bootstrapping and Alignment to Control LLM Uncertainty [49.19257648205146]
  We propose an unsupervised conformal inference framework for generation.<n>Our gates achieve close-to-nominal coverage and provide tighter, more stable thresholds than split UCP.<n>The result is a label-free, API-compatible gate for test-time filtering.
  arXiv  Detail & Related papers  (2025-09-26T23:40:47Z)
• Decision from Suboptimal Classifiers: Excess Risk Pre- and Post-Calibration [52.70324949884702]
  We quantify the excess risk incurred using approximate posterior probabilities in batch binary decision-making.<n>We identify regimes where recalibration alone addresses most of the regret, and regimes where the regret is dominated by the grouping loss.<n>On NLP experiments, we show that these quantities identify when the expected gain of more advanced post-training is worth the operational cost.
  arXiv  Detail & Related papers  (2025-03-23T10:52:36Z)
• Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems [79.67879934935661]
  We study the problem of system identification and adaptive control of unknown ARX systems. We provide finite-time learning guarantees for the ARX systems under both open-loop and closed-loop data collection.
  arXiv  Detail & Related papers  (2021-08-26T18:00:00Z)
• Closed-loop Parameter Identification of Linear Dynamical Systems through the Lens of Feedback Channel Coding Theory [0.0]
  This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise. We show that the learning rate is fundamentally upper bounded by the capacity of the corresponding AWGN channel. Although the optimal design of the feedback policy remains challenging, we derive conditions under which the upper bound is achieved.
  arXiv  Detail & Related papers  (2020-03-27T17:30:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.