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This paper proposes AdaTest, a novel adaptive test pattern generation framework for efficient and reliable Hardware Trojan (HT) detection. HT is a backdoor attack that tampers with the design of victim integrated circuits (ICs). AdaTest improves the existing HT detection techniques in terms of scalability and accuracy of detecting smaller Trojans in the presence of noise and variations. To achieve high trigger coverage, AdaTest leverages Reinforcement Learning (RL) to produce a diverse set of test inputs. Particularly, we progressively generate test vectors with high reward values in an iterative manner. In each iteration, the test set is evaluated and adaptively expanded as needed. Furthermore, AdaTest integrates adaptive sampling to prioritize test samples that provide more information for HT detection, thus reducing the number of samples while improving the sample quality for faster exploration. We develop AdaTest with a Software/Hardware co-design principle and provide an optimized on-chip architecture solution. AdaTest's architecture minimizes the hardware overhead in two ways:(i) Deploying circuit emulation on programmable hardware to accelerate reward evaluation of the test input; (ii) Pipelining each computation stage in AdaTest by automatically constructing auxiliary circuit for test input generation, reward evaluation, and adaptive sampling. We evaluate AdaTest's performance on various HT benchmarks and compare it with two prior works that use logic testing for HT detection. Experimental results show that AdaTest engenders up to two orders of test generation speedup and two orders of test set size reduction compared to the prior works while achieving the same level or higher Trojan detection rate.