When to Escalate: A Cost-Aware Belief Policy for Conversational Agents Under Hidden Intent

Abstract

A conversational agent replying to inbound sales leads must choose an action before it knows the lead’s intent. It can answer, ask a qualifying question, hold, or escalate to a human, but the true buying-readiness and whether a human is actually needed are hidden. The two ways of being wrong are not equally costly. A missed escalation, where a lead who needed a person did not get one, is far more expensive than a needless one, and some wrong answers are not a cost to trade off at all but a line the agent must not cross. We build a small agent that makes this trade-off explicit. It holds a belief over the hidden state, split into readiness (hot, warm, cold) and a separate probability that the case needs a human, and at each message it picks the action with the lowest expected cost under a cost matrix that encodes the asymmetry. Escalation is split into notify, where a human is told while the conversation continues, and pause, where the agent stops, because the two carry different costs. The hardest wrong answers, such as false legal or land claims, are enforced as a hard constraint rather than a priced term. We test on 100 synthetic cases with cached language-model beliefs, comparing the cost-aware policy against the same policy with a uniform cost matrix and against three fixed-action baselines. Two of those baselines give opposite answers, so both are named wherever the cost result appears. Against the uniform-cost version of the same rule — same belief, same feasible set, only the asymmetry removed — the cost-aware policy reaches 1.72 against 2.58 over all 100 cases, a reduction of a third; that gap is what cost-awareness buys, and it is against that baseline and no other. Against always-notify, which escalates every message, there is no cost win: 1.72 against 1.74 over the same 100 cases is a near-tie, a total of 172 against 174, so the cost-aware policy is not the cheaper policy and is not claimed to be. What it buys there is human load rather than cost — over all 100 cases it reaches the same cost while escalating 43 times rather than 100, at an escalation precision of 0.605 against 0.420. The uniform-baseline gap is also not all machinery: that baseline selects the same action as a plain 0.5 threshold on all 100 cases, and reweighting the case set toward the design’s own readiness prior moves the gap from 0.86 to 1.07 rather than closing it, so the direction is robust to reweighting even as the magnitude shifts. Every missed escalation traces to one cause: the belief under-estimated the needs-human probability rather than misreading readiness. Expected calibration error on that marginal is 0.142 (bootstrap 95% CI [0.100, 0.249]), concentrated in the bins adjacent to the escalation threshold rather than the bin containing it; recalibrating that marginal on the same 100 cases is an in-sample ceiling, and the body reports it as one. Held out, the result is different in kind. Re-eliciting bh from the model’s digit logprobs, fitting a map on 50 development cases and scoring the other 50, improves all three calibration measures named in advance — on those 50 test cases expected calibration error falls from 0.1526 to 0.0696, cross-entropy from 0.8546 to 0.8136 bits, and Brier from 0.2063 to 0.1962. Better calibration does not buy a better decision. The fitted map is isotonic, and the lowest block it pools sets a reachable-score floor of 6/23 ≈ 0.2609, above the 3/13 ≈ 0.2308 a belief must fall below for answering to be cheapest, so the threshold sits inside an interval the map cannot emit: on those same 50 cases the policy stops choosing answer at all, escalation precision falls from 0.667 to 0.463, and recall rises from 0.667 to 0.905. The cause is the map’s range rather than the scores it produced, and a calibration-quality gain that the range prevents from becoming a decision gain is the finding. We also report a failure the test set cannot produce by construction, a high-cost message dropped when it arrived batched with a routine one, observed in a live run. Code and data are available.