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The Stackelberg prediction game (SPG) has been extensively used to model the interactions between the learner and data provider in the training process of various machine learning algorithms. Particularly, SPGs played prominent roles in…
Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…
We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of…
We consider the problem of learning to exploit learning algorithms through repeated interactions in games. Specifically, we focus on the case of repeated two player, finite-action games, in which an optimizer aims to steer a no-regret…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
We use matrix iteration theory to characterize acceleration in smooth games. We define the spectral shape of a family of games as the set containing all eigenvalues of the Jacobians of standard gradient dynamics in the family. Shapes…
In this paper, we investigate a prescribed-time and fully distributed Nash Equilibrium (NE) seeking problem for continuous-time noncooperative games. By exploiting pseudo-gradient play and consensus-based schemes, various distributed NE…
The complexity in large-scale optimization can lie in both handling the objective function and handling the constraint set. In this respect, stochastic Frank-Wolfe algorithms occupy a unique position as they alleviate both computational…
In this work, a novel Stackelberg game theoretic framework is proposed for trading energy bidirectionally between the demand-response (DR) aggregator and the prosumers. This formulation allows for flexible energy arbitrage and additional…
The optimal policy in various real-world strategic decision-making problems depends both on the environmental configuration and exogenous events. For these settings, we introduce Contextual Bilevel Reinforcement Learning (CB-RL), a…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has…
We consider the multi-agent spatial navigation problem of computing the socially optimal order of play, i.e., the sequence in which the agents commit to their decisions, and its associated equilibrium in an N-player Stackelberg trajectory…
Motivated by the complex dynamics of cooperative and competitive interactions within networked agent systems, multi-cluster games provide a framework for modeling the interconnected goals of self-interested clusters of agents. For this…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for…
Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…
Interdicting a criminal with limited police resources is a challenging task as the criminal changes location over time. The size of the large transportation network further adds to the difficulty of this scenario. To tackle this issue, we…