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Distributed Learning with Partial Information Sharing

P Raghavendra Rao, Pooja Vyavahare

TL;DR

This work presents and analyzes a distributed learning algorithm in which agents share belief on only one randomly chosen hypothesis at a time, and shows that agents learn the true hypothesis almost surely under standard network connectivity and observation model assumptions.

Abstract

This work studies the distributed learning process on a network of agents. Agents make partial observation about an unknown hypothesis and iteratively share their beliefs over a set of possible hypotheses with their neighbors to learn the true hypothesis. We present and analyze a distributed learning algorithm in which agents share belief on only one randomly chosen hypothesis at a time. Agents estimate the beliefs on missed hypotheses using previously shared beliefs. We show that agents learn the true hypothesis almost surely under standard network connectivity and observation model assumptions if belief on each hypothesis is shared with positive probability at every time. We also present a memory-efficient variant of the learning algorithm with partial belief sharing and present simulation results to compare rate of convergence of full and partial information sharing algorithms.

Distributed Learning with Partial Information Sharing

TL;DR

This work presents and analyzes a distributed learning algorithm in which agents share belief on only one randomly chosen hypothesis at a time, and shows that agents learn the true hypothesis almost surely under standard network connectivity and observation model assumptions.

Abstract

This work studies the distributed learning process on a network of agents. Agents make partial observation about an unknown hypothesis and iteratively share their beliefs over a set of possible hypotheses with their neighbors to learn the true hypothesis. We present and analyze a distributed learning algorithm in which agents share belief on only one randomly chosen hypothesis at a time. Agents estimate the beliefs on missed hypotheses using previously shared beliefs. We show that agents learn the true hypothesis almost surely under standard network connectivity and observation model assumptions if belief on each hypothesis is shared with positive probability at every time. We also present a memory-efficient variant of the learning algorithm with partial belief sharing and present simulation results to compare rate of convergence of full and partial information sharing algorithms.

Paper Structure

This paper contains 8 sections, 6 theorems, 15 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System model
  3. Learning with full information sharing
  4. Learning with partial information sharing
  5. Proof of Theorem \ref{['th:partial_previous']}
  6. Memory-efficient learning
  7. Numerical simulations
  8. Conclusion

Key Result

Theorem 1

Let the communication graph $G$ be strongly connected, and observation model satisfies Assumption as:global. If every agent shares belief on only one randomly chosen hypothesis at a time and uses estimates from eq:estimate_previous to update beliefs in eq:local_belief, eq:public_previous, then the t

Figures (2)

  • Figure 1: Distributed learning algorithm at agent $i \in V$ with partial information sharing.
  • Figure 2: Simulation results for a $100$ agents $4$-regular network using various update rules. (a) Evolution of $\beta_{i,t}(h^*)$ for a typical non-discriminating agent. (b) Rate of rejection of a false hypothesis, $h_4,$ namely $r_{i,t}(h_4) = -\frac{\log \beta_{i,t}(h_4)}{t}$ for a non-discriminating agent.

Theorems & Definitions (10)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • proof : Proof of Theorem \ref{['th:partial_previous']}
  • Corollary 1
  • Theorem 2
  • proof