Paper finds a spectral threshold for multi-agent performative prediction
Original title: The Reflexivity Threshold: A Phase Transition for Multi-Agent Performative Prediction
Stability fails when the spectral radius of the reflexivity matrix crosses one, with linear excess loss above it.
The paper studies repeated retraining when many learners' predictions change the data other agents train on. It defines a reflexivity matrix from per-agent gradient sensitivities and curvature, and says the spectral radius crossing one separates stable learning from obstruction. Below the threshold, retraining converges geometrically to a unique performatively stable equilibrium. Above it, constructed noisy instances make every local-information learner's expected cumulative excess loss grow linearly.
- The threshold is the spectral radius of the reflexivity matrix crossing one.
- Below it, cumulative excess loss is bounded uniformly in the time horizon.
- Above it, excess loss grows linearly for horizons up to order 1 over rho(Gamma) minus 1.
- The single-agent scalar threshold from prior work is recovered as a special case.
From the original article
1 min read at arxiv.orgMany learning systems are performative: once deployed, their predictions change the data distribution on which future models are trained. In multi-agent settings, this feedback is routed through a network of interacting learners, so stability depends not only on the strength of performativity but also on who affects whom.
By Ahmed Mahrous · arxiv.org
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