Approximating Drift-Diffusion Models for User Decisions under Nudging and External Information

Gustavo Grivol, Hanna Halaburda, Alexander Tuzhilin
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:36705-36723, 2026.

Abstract

Modeling decision-making outside of controlled environments requires accounting for asynchronous, exogenous signals, such as notifications or algorithmic feeds, that dynamically alter user response times. Standard Drift-Diffusion Models (DDM) become analytically intractable when drift rates vary continuously with time. In this paper, we derive a closed-form analytical approximation for the first-passage time distribution of a single-boundary DDM with time-dependent drift, valid in the high-threshold regime. The main result allows us to analytically study the optimal timing of external signals to maximize the probability of a user response within our approximation framework. To evaluate our response time model, we conduct an extensive empirical comparison with state-of-the-art methods for user watch-time prediction and evaluation in simulated environments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-grivol26a, title = {Approximating Drift-Diffusion Models for User Decisions under Nudging and External Information}, author = {Grivol, Gustavo and Halaburda, Hanna and Tuzhilin, Alexander}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {36705--36723}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/grivol26a/grivol26a.pdf}, url = {https://proceedings.mlr.press/v306/grivol26a.html}, abstract = {Modeling decision-making outside of controlled environments requires accounting for asynchronous, exogenous signals, such as notifications or algorithmic feeds, that dynamically alter user response times. Standard Drift-Diffusion Models (DDM) become analytically intractable when drift rates vary continuously with time. In this paper, we derive a closed-form analytical approximation for the first-passage time distribution of a single-boundary DDM with time-dependent drift, valid in the high-threshold regime. The main result allows us to analytically study the optimal timing of external signals to maximize the probability of a user response within our approximation framework. To evaluate our response time model, we conduct an extensive empirical comparison with state-of-the-art methods for user watch-time prediction and evaluation in simulated environments.} }
Endnote
%0 Conference Paper %T Approximating Drift-Diffusion Models for User Decisions under Nudging and External Information %A Gustavo Grivol %A Hanna Halaburda %A Alexander Tuzhilin %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-grivol26a %I PMLR %P 36705--36723 %U https://proceedings.mlr.press/v306/grivol26a.html %V 306 %X Modeling decision-making outside of controlled environments requires accounting for asynchronous, exogenous signals, such as notifications or algorithmic feeds, that dynamically alter user response times. Standard Drift-Diffusion Models (DDM) become analytically intractable when drift rates vary continuously with time. In this paper, we derive a closed-form analytical approximation for the first-passage time distribution of a single-boundary DDM with time-dependent drift, valid in the high-threshold regime. The main result allows us to analytically study the optimal timing of external signals to maximize the probability of a user response within our approximation framework. To evaluate our response time model, we conduct an extensive empirical comparison with state-of-the-art methods for user watch-time prediction and evaluation in simulated environments.
APA
Grivol, G., Halaburda, H. & Tuzhilin, A.. (2026). Approximating Drift-Diffusion Models for User Decisions under Nudging and External Information. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:36705-36723 Available from https://proceedings.mlr.press/v306/grivol26a.html.

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