Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always

Key points

• In this setting, heterogeneous agents collaborate to solve distinct linear fixed-point equations, each corresponding to an agent-specific learning problem.1
• A central open question in personalized learning is whether a single method can adapt to an unknown level of heterogeneity by converging to each agent's personalized solution in all regimes while achieving a linear speedup in the number of agents when their learning problems are sufficiently similar.1
• We answer this question affirmatively by introducing PF-LSA, a minimalist algorithm that mixes each agent's local stochastic update with the average update across agents, at no additional computational cost relative to standard federated methods.1
• We prove that PF-LSA, achieves best-of-both-worlds guarantees without any prior knowledge on the level of heterogeneity.1

Sources (1)

• [1]Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 09:18 AM

  We study personalized federated linear stochastic approximation (LSA), a framework which notably encompass personalized temporal difference learning.

  In this setting, heterogeneous agents collaborate to solve distinct linear fixed-point equations, each corresponding to an agent-specific learning problem.

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