arXiv:2609.14922v1 Announce Type: cross Abstract: For constant-stepsize stochastic approximation (SA), the iterates converge in distribution to a stationary law that depends on the stepsize $\alpha.$...
arXiv:2506. 07040v4 Announce Type: replace-cross Abstract: We study model-free methods for distributionally robust infinite-horizon average-reward Markov decision processes (MDPs).
arXiv:2608. 14401v1 Announce Type: cross Abstract: In offline RL, estimating the optimal action-value function $Q^*$ can be formulated as solving the optimal Bellman equation based solely on offline observations.
The paper introduces a Projected Riemannian Gradient Descent (RGD) algorithm for computing the Bures‑Wasserstein barycenter of positive definite matrices, achieving dimension‑independent linear convergence at unit step size. It resolves a previous dichotomy by showing that clipping eigenvalues to a fixed interval yields a closed‑form, non‑expansive projection in the BW metric, allowing the algorithm to match the empirical speed of unit‑step RGD while maintaining theoretical guarantees. The method also extends to the invariant matrix projection problem, providing a unified dimension‑independent analysis.
arXiv:2404.06023v3 Announce Type: replace-cross Abstract: Motivated by Q-learning, we study nonsmooth contractive stochastic approximation (SA) with constant stepsize. We focus on two important class...
arXiv:2606. 04834v1 Announce Type: new Abstract: Minimum Description Length (MDL) formalizes the principle of Occam's razor by optimizing the total description length: $L(\mathrm{model})+L(\mathrm{data} \ | \ \mathrm{model})$.
arXiv:2609. 03762v1 Announce Type: new Abstract: The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information.
arXiv:2606. 16846v1 Announce Type: cross Abstract: We study the operator-theoretic core of Q-learning in continuous-time stochastic control with continuous states and actions.
arXiv:2302.07477v4 Announce Type: replace Abstract: We study the optimal sample complexity of tabular reinforcement learning for infinite-horizon discounted Markov decision processes. The unrestricte...
arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.
The paper introduces proximal equilibrium operators (PEOs), a class of neural operators that can simultaneously solve infinitely many convex optimization problems over a separable Hilbert space. A short training algorithm is presented that constructs PEOs using finite‑dimensional deep equilibrium layers, and a theoretical guarantee shows that, for inputs from a suitable infinite‑dimensional set, the trained PEOs uniformly approximate the solutions to arbitrary precision with logarithmic rank and width and linear depth in the inverse error. The authors validate their approach on applications to nonlinear PDEs, stochastic optimal control, and portfolio optimization and hedging in mathematical finance.
arXiv:2610.14988v1 Announce Type: cross Abstract: The average-reward setting for reinforcement learning is challenging because its Bellman operator is known to contract in span only when the underlyi...