Polynomial-Time Algorithm for Optimal Stopping with Fixed Accuracy

On the Slow Convergence to Trivial Solutions of Algorithms for Hard Optimization Problems

It is demonstrated that while algorithms do eventually converge to theoretically predicted bounds, this convergence can be remarkably slow; in the intermediate regime where instances are already highly constrained, local algorithms achieve solutions substantially better than their predicted performance in the high-cons...

Anytime Last Iterates in Fixed Dimension

Optimal Krylov on Average

Abstract. We propose an adaptive randomized truncation estimator for Krylov subspace methods that optimizes the trade-off between the solution variance and the computational cost while remaining unbiased. The estimator solves a constrained optimization problem to compute the truncation probabilities on the fly with mi...

Finite-Time Analysis of the Natural Policy Gradient in Finite-Horizon Markov Decision Processes

This paper provides the first finite-time convergence guarantees for this algorithm in this setting, for which it is proved that NPG converges sublinearly with a rate of $\mathcal{O}(H^{2}/t)$ after $t$ iterations, where $H$ is the horizon length.

Finite-Time Analysis of Discounted Exponential-Utility Reinforcement Learning

This work establishes finite-time rates of $\tilde{O} (1/\sqrt{n})$ for the aforementioned two algorithms under asynchronous Markovian sampling, where $n$ is the iteration index and $\tilde{O}$ hides logarithmic expressions.

Beyond Optimal Rates in Stochastic Optimization: Trajectory-Adaptive Stopping Rules

This work treats the evolving SGD trajectory as a sequential experiment whose observations provide evidence about the unknown optimization error, and develops new recursive confidence-sequence techniques and a general time-uniform empirical Bernstein inequality for adapted processes with time-varying conditional means...