Distributed Computing with Adaptive Heuristics

TL;DR

This paper investigates how simple adaptive heuristics in distributed systems converge to equilibrium in asynchronous environments, revealing fundamental non-termination results and implications for various applications.

Contribution

It introduces a general non-termination result for bounded-recall heuristics and explores their convergence and complexity in asynchronous distributed settings.

Findings

Non-termination results for bounded-recall heuristics

Implications for game theory, social networks, and routing

Insights into the complexity of asynchronous adaptive dynamics

Abstract

We use ideas from distributed computing to study dynamic environments in which computational nodes, or decision makers, follow adaptive heuristics (Hart 2005), i.e., simple and unsophisticated rules of behavior, e.g., repeatedly "best replying" to others' actions, and minimizing "regret", that have been extensively studied in game theory and economics. We explore when convergence of such simple dynamics to an equilibrium is guaranteed in asynchronous computational environments, where nodes can act at any time. Our research agenda, distributed computing with adaptive heuristics, lies on the borderline of computer science (including distributed computing and learning) and game theory (including game dynamics and adaptive heuristics). We exhibit a general non-termination result for a broad class of heuristics with bounded recall---that is, simple rules of behavior that depend only on recent history of interaction between nodes. We consider implications of our result across a wide variety of interesting and timely applications: game theory, circuit design, social networks, routing and congestion control. We also study the computational and communication complexity of asynchronous dynamics and present some basic observations regarding the effects of asynchrony on no-regret dynamics. We believe that our work opens a new avenue for research in both distributed computing and game theory.