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Jinyang Zheng

Publications and source records attributed to Jinyang Zheng.

3 recordsLinked to original sources

Generative AI and Two-Tiered Online Mental Health Communities

Online mental health communities (OMHCs) are tiered platforms that connect patients with licensed counselors through public Q&A forums and paid private consultations. Their two-tier structure creates a strategic dilemma for genAI integration. Conversational agents can provide scalable and timely responses to a broader set of patients, alleviating persistent supply shortages, but their large-scale presence may also reshape counselors' participation in providing nuanced expertise, emotionally sensitive support, and paid consultations, which are central to platform revenue and long-run sustainability. Leveraging a quasi-natural experiment from the integration of a genAI-based conversational agent in a leading OMHC, we examine how AI entry affects counselor participation. Using multiple identification strategies, we find that posting intensity increases significantly after AI integration, while average response length remains unchanged and per-post social recognition declines. Mechanism analyses show that AI improves responsiveness and expands patient engagement, enlarging counselors' opportunity sets, with activity partially reallocated from a nearby non-AI subforum. Counselors respond heterogeneously: intrinsically motivated counselors reduce participation, whereas economically motivated counselors intensify competitive effort. These dynamics generate cross-tier spillovers: inactive counselors experience declines in paid consultations, while those who increase public participation preserve or expand downstream demand. Overall, our findings show that in tiered professional platforms, demand expansion and competitive incentives can outweigh intrinsic crowding-out.

cs.CY

On globally solving nonconvex trust region subproblem via projected gradient method

The trust region subproblem (TRS) is to minimize a possibly nonconvex quadratic function over a Euclidean ball. There are typically two cases for (TRS), the so-called ``easy case'' and ``hard case''. Even in the ``easy case'', the sequence generated by the classical projected gradient method (PG) may converge to a saddle point at a sublinear local rate, when the initial point is arbitrarily selected from a nonzero measure feasible set. To our surprise, when applying (PG) to solve a cheap and possibly nonconvex reformulation of (TRS), the generated sequence initialized with {\it any} feasible point almost always converges to its global minimizer. The local convergence rate is at least linear for the ``easy case'', without assuming that we have possessed the information that the ``easy case'' holds. We also consider how to use (PG) to globally solve equality-constrained (TRS).

math.OC

Comment on "First-order methods almost always avoid strict saddle points"

The analysis on the global stability of Riemannian gradient descent method in manifold optimization (i.e., it avoids strict saddle points for almost all initializations) due to Lee et al. (Math. Program. 176:311-337) is corrected. Moreover, an explicit bound on the step-size is presented by the newly introduced retraction L-smooth property.

math.OC