Correlated Equilibria for Approximate Variational Inference in MRFs

by   Luis E. Ortiz, et al.

Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of recent advances in equilibrium computation for probabilistic inference. We present formulations of inference problems in Markov random fields (MRFs) as computation of equilibria in a certain class of game-theoretic graphical models. We concretely establishes the precise connection between variational probabilistic inference in MRFs and correlated equilibria. No previous work exploits recent theoretical and empirical results from the literature on algorithmic and computational game theory on the tractable, polynomial-time computation of exact or approximate correlated equilibria in graphical games with arbitrary, loopy graph structure. We discuss how to design new algorithms with equally tractable guarantees for the computation of approximate variational inference in MRFs. Also, inspired by a previously stated game-theoretic view of state-of-the-art tree-reweighed (TRW) message-passing techniques for belief inference as zero-sum game, we propose a different, general-sum potential game to design approximate fictitious-play techniques. We perform synthetic experiments evaluating our proposed approximation algorithms with standard methods and TRW on several classes of classical Ising models (i.e., with binary random variables). We also evaluate the algorithms using Ising models learned from the MNIST dataset. Our experiments show that our global approach is competitive, particularly shinning in a class of Ising models with constant, "highly attractive" edge-weights, in which it is often better than all other alternatives we evaluated. With a notable exception, our more local approach was not as effective. Yet, in fairness, almost all of the alternatives are often no better than a simple baseline: estimate 0.5.


page 1

page 2

page 3

page 4


Graphical Models for Game Theory

In this work, we introduce graphical modelsfor multi-player game theory,...

Inference in Probabilistic Graphical Models by Graph Neural Networks

A useful computation when acting in a complex environment is to infer th...

Learning Planar Ising Models

Inference and learning of graphical models are both well-studied problem...

Tutorial and Survey on Probabilistic Graphical Model and Variational Inference in Deep Reinforcement Learning

Probabilistic Graphical Modeling and Variational Inference play an impor...

Structured Stein Variational Inference for Continuous Graphical Models

We propose a novel distributed inference algorithm for continuous graphi...

Automorphism Groups of Graphical Models and Lifted Variational Inference

Using the theory of group action, we first introduce the concept of the ...

Graphical Potential Games

Potential games, originally introduced in the early 1990's by Lloyd Shap...

Please sign up or login with your details

Forgot password? Click here to reset