In this study, we consider an optimization problem with uncertainty dependent on decision variables, which has recently attracted attention due to its importance in machine learning and pricing applications. In this problem, the gradient of the objective function cannot be obtained explicitly because the decision-dependent distribution is unknown. Therefore, several zeroth-order methods have been proposed, which obtain noisy objective values by sampling and update the iterates. Although these existing methods have theoretical convergence for optimization problems with decision-dependent uncertainty, they require strong assumptions about the function and distribution or exhibit large variances in their gradient estimators. To overcome these issues, we propose two zeroth-order methods under mild assumptions. First, we develop a zeroth-order method with a new one-point gradient estimator including a variance reduction parameter. The proposed method updates the decision variables while adjusting the variance reduction parameter. Second, we develop a zeroth-order method with a two-point gradient estimator. There are situations where only one-point estimators can be used, but if both one-point and two-point estimators are available, it is more practical to use the two-point estimator. As theoretical results, we show the convergence of our methods to stationary points and provide the worst-case iteration and sample complexity analysis. Our simulation experiments with real data on a retail service application show that our methods output solutions with lower objective values than the conventional zeroth-order methods.

In this study, we tackle an optimization problem with a known function and an unknown decision-dependent distribution, which arises in a variety of applications and is often referred to as a performative prediction problem. To solve the problem, several zeroth-order methods have been developed because the gradient of the objective function cannot be obtained explicitly due to the unknown distribution. Although these methods have theoretical convergence, they cannot utilize the information on the known function, which limits their efficiency in reducing the objective value. To overcome this issue, we propose new zeroth-order methods that generate effective update directions by utilizing information on the known function. As theoretical results, we show the convergence of our methods to stationary points and provide the worst-case sample complexity analysis. Our simulation experiments on multiple applications show that our methods output solutions with lower objective values than the existing zeroth-order methods do.

This paper proposes a novel concept of natural perturbations for black-box training of neural networks by zeroth-order optimization. When a neural network is implemented directly in hardware, training its parameters by backpropagation ends up with an inaccurate result due to the lack of detailed internal information. We instead employ zeroth-order optimization, where the sampling of parameter perturbations is of great importance. The sampling strategy we propose maximizes the entropy of perturbations with a regularization that the probability distribution conditioned by the neural network does not change drastically, by inheriting the concept of natural gradient. Experimental results show the superiority of our proposal on diverse datasets, tasks, and architectures.

Crowd-sourcing has attracted much attention due to its growing importance to society, and numerous studies have been conducted on task allocation and wage determination. Recent works have focused on optimizing task allocation and workers' wages, simultaneously. However, existing methods do not provide good solutions for real-world crowd-sourcing platforms due to the low approximation ratio or myopic problem settings. We tackle an optimization problem for wage determination and online task allocation in crowd-sourcing and propose a fast 1-1/(k+3)^(1/2)-approximation algorithm, where k is the minimum of tasks' budgets (numbers of possible assignments). This approximation ratio is greater than or equal to the existing method. The proposed method reduces the tackled problem to a non-convex multi-period continuous optimization problem by approximating the objective function. Then, the method transforms the reduced problem into a minimum convex cost flow problem, which is a well-known combinatorial optimization problem, and solves it by the capacity scaling algorithm. Synthetic experiments and simulation experiments using real crowd-sourcing data show that the proposed method solves the problem faster and outputs higher objective values than existing methods.

Online bipartite matching has attracted much attention due to its importance in various applications such as advertising, ride-sharing, and crowdsourcing. In most online matching problems, the rewards and node arrival probabilities are given in advance and are not controllable. However, many real-world matching services require them to be controllable and the decision-maker faces a non-trivial problem of optimizing them. In this study, we formulate a new optimization problem, Online Matching with Controllable Rewards and Arrival probabilities (OM-CRA), to simultaneously determine not only the matching strategy but also the rewards and arrival probabilities. Even though our problem is more complex than the existing ones, we propose a fast 1/2-approximation algorithm for OM-CRA. The proposed approach transforms OM-CRA to a saddle-point problem by approximating the objective function, and then solves it by the Primal-Dual Hybrid Gradient (PDHG) method with acceleration through the use of the problem structure. In simulations on real data from crowdsourcing and ride-sharing platforms, we show that the proposed algorithm can find solutions with high total rewards in practical times.

The research field of stochastic matching has yielded many developments for various applications. In most stochastic matching problems, the probability distributions inherent in the nodes and edges are set a priori, and are not controllable. However, many matching services have options, which we call control variables, that affect the probability distributions and thus what constitutes an optimum matching. Although several methods for optimizing the values of the control variables have been developed, their optimization in consideration of the matching problem is still in its infancy. In this paper, we formulate an optimization problem for determining the values of the control variables so as to maximize the expected value of matching weights. Since this problem involves hard to evaluate objective values and is non-convex, we construct an approximation algorithm via a minimum-cost flow algorithm that can find 3-approximation solutions rapidly. Simulations on real data from a ride-hailing platform and a crowd-sourcing market show that the proposed method can find solutions with high profits of the service provider in practical time.