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Multiplayer Federated Learning: Reaching Equilibrium with Less Communication

NeurIPS 2025 · Federated learning and privacy › Communication-efficient FL · approach: Local drift correction · 0 citations (OpenAlex)

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Introduces Multiplayer Federated Learning (MpFL), casting FL clients as game players seeking equilibrium, and proposes PEARL-SGD (per-player local SGD) with convergence guarantees showing fewer communication rounds than the non-local variant, verified on quadratic games and robot control simulations.

Problem

Federated learning assumes cooperative clients with aligned objectives, but in many settings clients are strategic players with individual utilities; finding a Nash-type equilibrium among heterogeneous, possibly competing clients with limited communication is not addressed by existing FL methods.

Approach

Model each client as a player in an n-player game whose action is its local model; each player runs local SGD on its own objective with other players' actions fixed, synchronizing via a server every tau steps (PEARL-SGD), with step-sizes scaled by 1/tau to avoid player drift.

Key results

• Deterministic PEARL-SGD converges linearly to an exact equilibrium for any tau>1 with step-size gamma scaled as O(1/tau); all tau give indistinguishable curves in the deterministic experiment.
• In the stochastic setting with constant step-size, PEARL-SGD converges linearly to a neighborhood whose size shrinks by a factor of order 1/tau + 1/sqrt(kappa), so with tau=Omega(sqrt(kappa)) it reaches a sqrt(kappa)-times smaller neighborhood in the same number of rounds.
• Experiments on quadratic games with stochastic gradients (5 runs) show larger tau achieves smaller relative error for the same number of communication rounds.

Measured effects reported in the paper

Surprising findings

• Local SGD on the summed objective can diverge in a simple two-player example, so classical FL algorithms do not solve MpFL equilibria.
• Player drift can cause divergence under large step-sizes, unlike client drift in classical FL.

Limitations

• Assumes convexity, smoothness, bounded variance, quasi-strong monotonicity and star-cocoercivity; no assumptions relaxed beyond these.
• Communication of high-dimensional joint action vectors (dimension sum of d_i) per synchronization is expensive; gradient compression left to future work.
• Player drift requires step-size scaling with tau, so no communication gain in the deterministic setting, and it is suited to cross-silo setups with few organizations.

Experimental setup

Datasets: synthetic quadratic n-player games synthetic mobile robot control problem

Benchmarks: quadratic n-player game distributed mobile robot control

Metrics: relative squared distance to equilibrium communication rounds to accuracy

Baselines: Local SGD (tau=1, non-local counterpart) Local SGDA Local SEG

Builds on: Local SGD (FedAvg) gradient descent-ascent stochastic gradient play Decoupled SGD

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