Cellular protein homeostasis requires continuous monitoring of stress in the endoplasmic reticulum (ER). Stress-detection networks control protein homeostasis by mitigating the deleterious effects of protein accumulation, such as aggregation and misfolding, with precise modulation of chaperone production. Here, we develop a coarse model of the unfolded protein response in yeast and use multi-objective optimization to determine which sensing and activation strategies optimally balance the trade-off between unfolded protein accumulation and chaperone production. By comparing a stress-sensing mechanism that responds directly to the level of unfolded protein in the ER to a mechanism that is negatively regulated by unbound chaperones, we show that chaperone-mediated sensors are more efficient than sensors that detect unfolded proteins directly. This results from the chaperone-mediated sensor having separate thresholds for activation and deactivation. Finally, we demonstrate that a sensor responsive to both unfolded protein and unbound chaperone does not further optimize homeostatic control. Our results suggest a strategy for designing stress sensors and may explain why BiP-mitigated ER stress-sensing networks have evolved.