Convergence Dynamics of Agent-to-Agent Interactions with Misaligned Objectives

This paper develops a theoretical framework to study agent-to-agent interactions in a simplified in-context linear regression setting, where each agent is a single-layer transformer with linear self-attention. The authors analyze the coupled dynamics when two such agents update from each other's outputs under potentially misaligned fixed objectives.

Details

The paper develops a theoretical framework to study agent-to-agent interactions in a simplified in-context linear regression setting. Each agent is modeled as a single-layer transformer with linear self-attention, trained to implement gradient-descent-like updates on a quadratic regression objective from in-context examples. The authors then analyze the coupled dynamics when two such agents alternately update from each other's outputs under potentially misaligned fixed objectives. They find that misalignment leads to a biased equilibrium where neither agent reaches its target, with residual errors predictable from the objective gap and the prompt-induced geometry. The paper contrasts this fixed objective regime with an adaptive multi-agent setting, where a helper agent updates a turn-based objective to implement a Newton-like step for the main agent, eliminating the plateau and accelerating its convergence. Experiments with trained LSA agents and GPT-5-mini runs on in-context linear regression tasks are consistent with the theoretical predictions.