Related papers: Nash Equilibria, Regularization and Computation in…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
We analyze the robustness of (pure strategy) Nash equilibria for network games against perturbations of the players' utility functions. We first derive a simple characterization of the margin of robustness, defined as the minimum magnitude…
The distributed task allocation problem, as one of the most interesting distributed optimization challenges, has received considerable research attention recently. Previous works mainly focused on the task allocation problem in a population…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
We consider the problem of finding an optimal history-dependent routing strategy on a directed graph weighted by stochastic arc costs when the objective is to minimize the risk of spending more than a prescribed budget. To help mitigate the…
We introduce graphs associated to transport problems between discrete marginals, that allow to characterize the set of all optimizers given one primal optimizer. In particular, we establish that connectivity of those graphs is a necessary…
While progress has been made in understanding the robustness of machine learning classifiers to test-time adversaries (evasion attacks), fundamental questions remain unresolved. In this paper, we use optimal transport to characterize the…
-In this paper, a novel resource allocation scheme based on discrete Cournot-Nash equilibria and optimal transport theory is proposed. The originality of this framework lies in the joint optimization of downlink bandwidth allocation and…
We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…
We propose a data-driven portfolio selection model that integrates side information, conditional estimation and robustness using the framework of distributionally robust optimization. Conditioning on the observed side information, the…
We propose a new dynamics for equilibrium selection of finite player discrete strategy games. The dynamics is motivated by optimal transportation, and models individual players' myopicity, greedy and uncertainty when making decisions. The…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
Distributionally robust offline reinforcement learning (RL), which seeks robust policy training against environment perturbation by modeling dynamics uncertainty, calls for function approximations when facing large state-action spaces.…
We consider a class of games with continuum of players where equilibria can be obtained by the minimization of a certain functional related to optimal transport as emphasized in [7]. We then use the powerful entropic regularization…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
Motivated by emerging resource allocation and data placement problems such as web caches and peer-to-peer systems, we consider and study a class of resource allocation problems over a network of agents (nodes). In this model, nodes can…
This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…
We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…
We introduce Cut-and-Play, a practically-efficient algorithm for computing Nash equilibria in simultaneous non-cooperative games where players decide via nonconvex and possibly unbounded optimization problems with separable payoff…