arXiv:2606. 28281v1 Announce Type: cross 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.
arXiv:2601. 07094v2 Announce Type: replace-cross Abstract: Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function.
arXiv:2608.30431v1 Announce Type: cross Abstract: By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization...
The paper introduces a new approach to learning chance-constrained Markov decision processes (CCMDPs) using a Bellman distributional certificate. It provides both model-based and model-free algorithms with theoretical guarantees, including matching upper and lower bounds for tabular discounted CCMDPs with bounded successor support. Numerical experiments on synthetic CCMDPs and an IEEE 14-bus energy storage benchmark demonstrate the safety and effectiveness of the proposed methods.
arXiv:2605. 20145v2 Announce Type: replace-cross Abstract: Gaussian process (GP) predictive distributions are commonly used in Bayesian optimization (BO) to guide the selection of evaluation points for expensive objective functions.
arXiv:2603. 08287v2 Announce Type: replace-cross Abstract: We analyze the Bayesian regret of the Gaussian process posterior sampling reinforcement learning (GP-PSRL) algorithm.
arXiv:2608. 10777v1 Announce Type: new Abstract: Linear Quadratic Stochastic Optimal Control (LQ-SOC) establishes a fundamental framework for steering noisy dynamical systems and has recently gained renewed interest in the machine learning community.
The paper presents a finite‑sample learning‑to‑control framework for geometrically supervised latent models of nonlinear deterministic systems. It introduces an encoder‑only local–global metric hinge that ensures directional resolution and state discrimination, and proves that any approximate empirical minimizer is pointwise co‑Lipschitz and uniformly approximately semiconjugate to the true dynamics under regularity assumptions. The results provide explicit bounds on approximation, sampling, and optimization errors, and demonstrate through controlled experiments that restoring metric resolution improves control performance.
arXiv:2609.39837v1 Announce Type: new Abstract: Policy mirror descent (PMD) enjoys fast convergence in regularized Markov decision processes (MDPs), but existing guarantees often rely on exact or inc...
The paper introduces penalized nonreversible Langevin algorithms for sampling from a target distribution constrained to a compact convex set. It combines a squared distance penalty with skew-symmetric perturbations that preserve the penalized Gibbs distribution, and provides nonasymptotic total variation and Wasserstein bounds under various smoothness and contraction assumptions. Numerical experiments demonstrate the methods on constrained Bayesian regression, classification, neural networks, and truncated sampling, highlighting acceleration in a stochastic quadratic model.
arXiv:2606. 15359v1 Announce Type: new Abstract: Diffusion models have emerged as powerful tools for planning and control by learning multimodal distributions over actions and trajectories.
The paper presents a convergence framework for deep $V$‑learning over a finite horizon $H$, deriving explicit bounds on policy loss by decomposing the Bellman update error into six residuals. It shows how $L^s$ concentrability controls expected $L^1$ loss, quantifies the impact of shared sampling across horizon levels, and provides optimal and near‑optimal sample allocations for statistical error rates. The work also establishes sharp action‑gap bounds under a margin condition, transfers optimal‑gap results to frozen‑iterate gaps, and offers consistency guarantees for generative‑reset approximate‑ERM procedures with exact action scores.
arXiv:2608. 25551v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory.