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We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands…

In this work, we develop a novel fairness learning approach for multi-task regression models based on a biased training dataset, using a popular rank-based non-parametric independence test, i.e., Mann Whitney U statistic, for measuring the…

Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial…

We extend the classic regret minimization framework for approximating equilibria in normal-form games by greedily weighing iterates based on regrets observed at runtime. Theoretically, our method retains all previous convergence rate…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

Estimating the unknown reward functions driving agents' behaviors is of central interest in inverse reinforcement learning and game theory. To tackle this problem, we develop a unified framework for reward function recovery in two-player…

Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…

We present polynomial-time algorithms as well as hardness results for equilibrium computation in atomic splittable routing games, for the case of general convex cost functions. These games model traffic in freight transportation, market…

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method…

We consider the traffic assignment problem in nonatomic routing games where the players' cost functions may be subject to random fluctuations (e.g., weather disturbances, perturbations in the underlying network, etc.). We tackle this…

We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…

This work introduces a unified framework for analyzing games in greater depth. In the existing literature, players' strategies are typically assigned scalar values, and equilibrium concepts are used to identify compatible choices. However,…

Within the context of video games the notion of perfectly rational agents can be undesirable as it leads to uninteresting situations, where humans face tough adversarial decision makers. Current frameworks for stochastic games and…

Considering a class of gradient-based multi-agent learning algorithms in non-cooperative settings, we provide local convergence guarantees to a neighborhood of a stable local Nash equilibrium. In particular, we consider continuous games…

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…

This paper considers games where the utilities for agents are the sum of a term proportional to a social utility, and another term that is an individual cost or reward. The agents are assumed to be irrational in their perception of the…

The literature on game-theoretic equilibrium finding predominantly focuses on single games or their repeated play. Nevertheless, numerous real-world scenarios feature playing a game sampled from a distribution of similar, but not identical…