Related papers: On the Asymptotic Optimality of Work-Conserving Di…

In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

Stochastic policies (also known as relaxed controls) are widely used in continuous-time reinforcement learning algorithms. However, executing a stochastic policy and evaluating its performance in a continuous-time environment remain open…

We consider a simulation optimization problem for a context-dependent decision-making, which aims to determine the top-m designs for all contexts. Under a Bayesian framework, we formulate the optimal dynamic sampling decision as a…

In the contextual linear bandit setting, algorithms built on the optimism principle fail to exploit the structure of the problem and have been shown to be asymptotically suboptimal. In this paper, we follow recent approaches of deriving…

The consumption function maps current wealth and the exogenous state to current consumption. We prove the existence and uniqueness of a consumption function when the agent has a preference for wealth. When the period utility functions are…

We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…

In this paper, we analyze the preservation of asymptotic properties of partially dissipative hyperbolic systems when switching to a discrete setting. We prove that one of the simplest consistent and unconditionally stable numerical methods…

For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects,…

In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is…

We present novel results on the solution of a class of leavable, undiscounted optimal control problems in the minimax sense for nonlinear, continuous-state, discrete-time plants. The problem class includes entry-(exit-)time problems as well…

Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the…

For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…

We consider the problem of tracking a target whose dynamics is modeled by a continuous It\=o semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds…

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…

We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several…

For the stochastic multi-armed bandit (MAB) problem from a constrained model that generalizes the classical one, we show that an asymptotic optimality is achievable by a simple strategy extended from the $\epsilon_t$-greedy strategy. We…

Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received…

We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…

Integrated task and motion planning problems describe a multi-modal state space, which is often abstracted as a set of smooth manifolds that are connected via sets of transitions states. One approach to solving such problems is to sample…