相关论文: Sequential test sampling for stochastic derivative…

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…

This work presents the convergence rate analysis of stochastic variants of the broad class of direct-search methods of directional type. It introduces an algorithm designed to optimize differentiable objective functions $f$ whose values can…

This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…

In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic…

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…

This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the…

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…

A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…

Financial statement auditing is conducted under a risk-based evidence approach to obtain reasonable assurance. In practice, auditors often perform additional sampling or related procedures when an initial sample does not provide a…

Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure…

The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice…

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…

We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…

This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…

Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and adversarial machine learning. While…

We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…

Stochastic constraints, which incorporate both deterministic parameters and random variables, extend classical deterministic constraints by explicitly accounting for uncertainty. These constraints are increasingly prevalent in data science,…