In many modern systems, the tasks of learning and decision-making must be carried out in a distributed and data-driven fashion. A collection of autonomous agents— whether they are sensors, robots, or individuals—each observe only a portion of the data and can communicate with a limited set of neighbors in a network. These agents are often required to operate in real time, processing information that arrives sequentially, and making decisions with no centralized controller or access to global information. This setting is increasingly common in applications such as distributed sensing, multi-robot coordination, financial networks, and social learning environments.
The central problem studied in this thesis is to examine the limits of performance of decentralized decision-making systems. Specifically, the dissertation considers a class of models in which agents aim to infer an unknown hypothesis by maintaining and updating probabilistic beliefs over time. At each time step, each agent receives a private signal drawn from a local observation model and exchanges beliefs with its neighbors in the network. The challenge is to design learning rules that allow each agent to improve its inference performance over time, while satisfying the structural and informational constraints imposed by the networked environment.
A natural and widely studied approach for this setting is distributed non-Bayesian social learning. In this framework, each agent performs a two-stage update at each time step: (i) an adaptation step, such as a local Bayesian update, that incorporates new private data using a known likelihood function, and (ii) a combination step, such as linear or geometric averaging, which pools beliefs from neighbors in the network.
This paradigm combines the strengths of two foundational ideas. From Bayesian learning, it inherits a principled method for incorporating data through likelihood-based updates. From non-Bayesian opinion dynamics, it adopts scalable and distributed mechanisms for aggregating information in a network. The resulting learning rule is both tractable and flexible: it requires no modeling of the full joint likelihood across agents, no recursive reasoning about others’ information, and is implementable in systems with limited computation and communication.
This thesis develops a rigorous theoretical framework for understanding distributed non-Bayesian social learning. The contributions are organized around two directions. In the first part, we study the impact of the aggregation strategy, focusing on how the structure and design of combination policies influence learning performance. In particular, we use the probability of decision error as our primary performance metric. We analyze two learning environments for the network: a non-stationary scenario that demands adaptive learning rules, and a stationary scenario where non-adaptive learning rules are preferable.
In the second part, we examine the role of the local likelihood models. In particular, we analyze scenarios where the likelihood models are unknown and must be learned from data. We characterize the generalization performance of the resulting distributed data-driven decision-making framework for two inference tasks: one with a stream of observations and the other with a single observation during the inference stage.