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Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
Bilevel optimization problems involve two nested objectives, where an upper-level objective depends on a solution to a lower-level problem. When the latter is non-convex, multiple critical points may be present, leading to an ambiguous…
Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…
Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…
Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems. However, computing gradients via implicit differentiation requires solving a linear system with Hessian terms, which is…
This paper is concerned with a three-level multi-leader-follower incentive Stackelberg game with $H_\infty$ constraint. Based on $H_2/H_\infty$ control theory, we firstly obtain the worst-case disturbance and the team-optimal strategy by…
This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This…
Large scale systems are forecasted to greatly impact our future lives thanks to their wide ranging applications including cooperative robotics, mobility on demand, resource allocation, supply chain management. While technological…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
A crucial task in system identification problems is the selection of the most appropriate model class, and is classically addressed resorting to cross-validation or using asymptotic arguments. As recently suggested in the literature, this…
Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained bilevel problems, the constrained setting remains relatively…
We consider an N-player hierarchical game in which the i-th player's objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of…
In this study, we explore the application of game theory, in particular Stackelberg games, to address the issue of effective coordination strategy generation for heterogeneous robots with one-way communication. To that end, focusing on the…
This paper investigates the convergence of learning dynamics in Stackelberg games. In the class of games we consider, there is a hierarchical game being played between a leader and a follower with continuous action spaces. We establish a…
Stochastic bilevel optimization finds widespread applications in machine learning, including meta-learning, hyperparameter optimization, and neural architecture search. To extend stochastic bilevel optimization to distributed data, several…
This paper studies a class of dynamic Stackelberg games under open-loop information structure with constrained linear agent dynamics and quadratic utility functions. We show two important properties for this class of dynamic Stackelberg…
Many strategic decision-making problems, such as environment design for warehouse robots, can be naturally formulated as bi-level reinforcement learning (RL), where a leader agent optimizes its objective while a follower solves a Markov…
Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…
Gradient-based algorithms have shown great promise in solving large (two-player) zero-sum games. However, their success has been mostly confined to the low-precision regime since the number of iterations grows polynomially in $1/\epsilon$,…