Adaptive methods refer to experimental procedures in which the stimulus presented on each trial depends on the observer’s responses on previous trials. In psychophysics, these methods efficiently estimate perceptual thresholds by concentrating stimulus presentations near the threshold region. In educational testing, the same principle drives Computerized Adaptive Testing (CAT), where item selection is tailored to the examinee’s estimated ability.
Stochastic approximation
At the core of many adaptive methods lies stochastic approximation, originally introduced by Robbins and Monro (1951). The Robbins-Monro process provides a general framework for finding the root of an unknown function using noisy observations. In psychophysics, this translates to iteratively adjusting stimulus intensity to converge on the threshold where the observer’s detection probability reaches a target level.
My research in adaptive methods
Adaptive methods have been a central theme of my research since my master’s thesis:
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Generalized Robbins-Monro process. For my master’s thesis, I proposed a generalization of the classical Robbins-Monro process by incorporating additional response variables—response time and response confidence—into the stochastic approximation procedure. This enriched process can leverage the information carried by these auxiliary variables to improve the efficiency of threshold estimation. This work was published in the Journal of Mathematical Psychology (2024).
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Stochastic approximation for CAT. I demonstrated that the stochastic approximation framework naturally extends to item selection in Computerized Adaptive Testing. Under this perspective, ability estimation after each item response can be viewed as a Robbins-Monro update. I showed that certain stochastic approximation-based methods can outperform the classical maximum information method in short-test scenarios, published in Behaviormetrika (2024).
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Online Convex Optimization for adaptive testing. My dissertation takes the connection between adaptive methods and online learning further. I formalize adaptive testing within the Online Convex Optimization (OCO) framework, which provides finite-sample performance guarantees (regret bounds) rather than relying solely on asymptotic theory. This framework reveals that the maximum information method is a no-regret algorithm and enables the construction of anytime-valid confidence intervals using martingale concentration inequalities.
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Robustness via exploration-exploitation. Drawing on multi-armed bandit theory, I developed item selection strategies based on the Upper Confidence Bound (UCB) algorithm. These methods explicitly balance exploration (testing items at diverse difficulty levels) with exploitation (selecting items near the current ability estimate), addressing the premature commitment problem that arises when early ability estimates are unreliable.
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Comparison of psychophysical methods. With collaborators, I conducted a systematic comparison of bisection-based and adaptive psychophysical methods for eliciting indifference points in loss aversion research, evaluating the practical trade-offs between different adaptive procedures (manuscript submitted, 2025).