Online discrete optimization in social networks in the presence of Knightian uncertainty

TL;DR

This paper introduces a decentralized online decision-making strategy for social networks operating under Knightian uncertainty, where agents learn and adapt without prior probabilistic models, achieving low regret over time.

Contribution

It proposes a novel decentralized approach for collective decision-making in uncertain environments, with regret bounds that scale polylogarithmically with time.

Findings

Strategy achieves polylogarithmic regret in time horizon

Decentralized actions depend only on local costs and neighbor decisions

Applicable to social networks with arbitrary local interaction structures

Abstract

We study a model of collective real-time decision-making (or learning) in a social network operating in an uncertain environment, for which no a priori probabilistic model is available. Instead, the environment's impact on the agents in the network is seen through a sequence of cost functions, revealed to the agents in a causal manner only after all the relevant actions are taken. There are two kinds of costs: individual costs incurred by each agent and local-interaction costs incurred by each agent and its neighbors in the social network. Moreover, agents have inertia: each agent has a default mixed strategy that stays fixed regardless of the state of the environment, and must expend effort to deviate from this strategy in order to respond to cost signals coming from the environment. We construct a decentralized strategy, wherein each agent selects its action based only on the costs directly affecting it and on the decisions made by its neighbors in the network. In this setting, we quantify social learning in terms of regret, which is given by the difference between the realized network performance over a given time horizon and the best performance that could have been achieved in hindsight by a fictitious centralized entity with full knowledge of the environment's evolution. We show that our strategy achieves the regret that scales polylogarithmically with the time horizon and polynomially with the number of agents and the maximum number of neighbors of any agent in the social network.