Related papers: Differentiable Game Mechanics

Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…

We consider decentralized machine learning over a network where the training data is distributed across $n$ agents, each of which can compute stochastic model updates on their local data. The agent's common goal is to find a model that…

We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The…

Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) algorithms used for policy evaluation in reinforcement learning. Here, we consider Gradient TD algorithms with an additional heavy…

Recent years have seen many insights on deep learning optimisation being brought forward by finding implicit regularisation effects of commonly used gradient-based optimisers. Understanding implicit regularisation can not only shed light on…

We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…

We consider surveillance-evasion differential games, where a pursuer must try to constantly maintain visibility of a moving evader. The pursuer loses as soon as the evader becomes occluded. Optimal controls for game can be formulated as a…

We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…

Multi-agent interactions are increasingly important in the context of reinforcement learning, and the theoretical foundations of policy gradient methods have attracted surging research interest. We investigate the global convergence of…

Learning in games provides a powerful framework to design control policies for self-interested agents that may be coupled through their dynamics, costs, or constraints. We consider the case where the dynamics of the coupled system can be…

This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based algorithms may vary depending on the learning task, they behave…

This paper proposes and studies a general form of dynamic $N$-player non-cooperative games called $\alpha$-potential games, where the change of a player's value function upon her unilateral deviation from her strategy is equal to the change…

From large-scale organizations to decentralized political systems, hierarchical strategic decision making is commonplace. We introduce a novel class of structured hierarchical games (SHGs) that formally capture such hierarchical strategic…

We show by counterexample that policy-gradient algorithms have no guarantees of even local convergence to Nash equilibria in continuous action and state space multi-agent settings. To do so, we analyze gradient-play in N-player general-sum…

Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks has attracted continuing studies for the theoretical principles behind its success. A recent work reports an anomaly (inverse) relation between the…

Distributed machine learning algorithms play a significant role in processing massive data sets over large networks. However, the increasing reliance on machine learning on information and communication technologies (ICTs) makes it…

Generative adversarial networks (GANs), modeled as a zero-sum game between a generator (G) and a discriminator (D), allow generating synthetic data with formal guarantees. Noting that D is a classifier, we begin by reformulating the GAN…

Nash equilibrium is a central concept in game theory. Several Nash solvers exist, yet none scale to normal-form games with many actions and many players, especially those with payoff tensors too big to be stored in memory. In this work, we…

Stochastic gradient descent (SGD) is central to deep learning, yet the dynamical origin of its preference for flatter, more generalizable solutions remains unclear. Here, by analyzing SGD learning dynamics, we identify a nonequilibrium…

Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space…