Which Model for Which Role? Cost-Aware Pareto Search over LLM Agent Configurations

LLM agents increasingly assign different models to specialized roles. Choosing these assignments must balance task performance against deployment API cost while limiting the cost of end-to-end search. We formulate static role-level assignment as cost-aware Pareto search and introduce radial-Gittins, a multi-objective cost-aware Gittins policy for discovering compact, high-value configuration sets. For each configuration, it maintains one vector posterior over both objectives, shared across radial scalarizations, and uses direction-specific indices to decide whether another batch is worth its monetary search cost. AgentOpt, our client-side implementation, measures role-attributed outcomes, token usage, monetary cost, and latency and recommends Pareto configurations. We evaluate radial-Gittins on HotpotQA planner--solver and MathQA answer--critic workflows using exhaustive $9 \times 9=81$ assignment matrices as replay data and ground truth. Across 20 matched replay seeds, it stops after spending, on average, only $5.9\%$ and $5.7\%$ of exhaustive-evaluation API cost, respectively, while returning compact sets with low hypervolume regret and generational distance.