相关论文: Finding a Multiple Follower Stackelberg Equilibriu…

This paper studies the complexity of finding approximate stationary points for the smooth nonconvex-strongly-concave (NC-SC) saddle point problem: $\min_x\max_yf(x,y)$. Under the standard first-order smoothness conditions where $f$ is…

This paper is concerned with the application of Stackelberg-Nash strategies to control fourth order linear and semi-linear parabolic equations. We assume that the system is acted through a hierarchy of distributed controls: one main control…

In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…

We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ (and possibly some labels ${\boldsymbol y}\in{\mathbb R}^n$) and would like to estimate a…

We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold. The proposed methods combine a function value reduction step with a proximal correction step. The former one searches…

In the first-order query model for zero-sum $K\times K$ matrix games, players observe the expected pay-offs for all their possible actions under the randomized action played by their opponent. This classical model has received renewed…

We study a two-player Stackelberg game with incomplete information such that the follower's strategy belongs to a known family of parameterized functions with an unknown parameter vector. We design an adaptive learning approach to…

This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term "overlapping" means that there are…

This paper characterizes optimal classification when individuals adjust their behavior in response to the classification rule. We model the interaction between a designer and a population as a Stackelberg game: the designer selects a…

Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…

Risk measures are commonly used to capture the risk preferences of decision-makers (DMs). The decisions of DMs can be nudged or manipulated when their risk preferences are influenced by factors such as the availability of information about…

We consider the classic stochastic linear quadratic regulator (LQR) problem under an infinite horizon average stage cost. By leveraging recent policy gradient methods from reinforcement learning, we obtain a first-order method that finds a…

Leader-follower tracking control design has received significant attention in recent years due to its important and wide applications. Considering a multi-agent system composed of a leader and multiple followers, this paper proposes and…

We study a stochastic anchored gradient scheme, namely HalpernSGD, which combines the classical Halpern iteration for finding a minimizer of a convex and $L$-smooth objective function with a stochastic {first-order} oracle. The algorithm is…

Agents rarely act in isolation -- their behavioral history, in particular, is public to others. We seek a non-asymptotic understanding of how a leader agent should shape this history to its maximal advantage, knowing that follower agent(s)…

We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…

First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…

Motivated by a product pricing problem, a linear-quadratic Stackelberg differential game for a regime switching system involving one leader and two followers is studied. The two followers engage in a zero-sum differential game, and both the…

Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…