Phase-transition materials such as vanadium dioxide (VO2) inherently exhibit non-linear and hysteretic behavior, which limits their applicability in devices like infrared bolometric sensors that require linear and non-hysteretic responses. To circumvent this issue, nonstoichiometric VOx has been widely used in infrared bolometers despite its degraded phase transitions and resultant lower temperature coefficient of resistance (TCR) compared to stoichiometric VO2. Achieving both a high TCR and a linear, non-hysteretic response has therefore remained a major bottleneck in advancing microbolometer technology. In this study, we present a multilayer approach using machine-learning-optimized WxV1-xOy thin films with varying doping ratios to address these challenges. By stacking layers with different W doping levels and employing genetic algorithm optimization, we achieve tailored linear/flat TCR profiles and significantly reduced hysteresis. These multilayer systems simultaneously achieve a high TCR and low electrical noise even under complementary metal-oxide semiconductor (CMOS)-compatible growth conditions, resulting in a universal bolometric performance 23.6 times greater than that of commercial materials. This work demonstrates a general methodology for achieving both a large and linear response to external stimuli, which can be widely adopted not only for microbolometers but also for other technologies.