A memo from the administrators at Metropolis Health System, in response to a nationwide blood shortage, asked the care teams and doctors at all of their hospitals to be particularly conservative and judicious in how they used blood products because of the critical shortage. Phoebe, a 17-year-old girl, is being treated for leukemia at Metro Hospital, which is part of the health system. She has gone through several rounds of chemotherapy, but has not responded to the treatment.

Background

1. originally, multi-agent team pre-assigns roles
2. LLMs are heterogeneous, but they are treated homogeneously
3. problem decomposition is hard

Eval

synergy

• weak synergy: team >= average member
• strong synergy: team >= best member

Human teams reliably achieve strong synergy IFF when expert identity is given (e.g., the teams easily know who is the expert).

Dataset

NASA moon survival / lost at seay

Rank 15 items by importance

Student body president

Different people are given different information + shared info. Hidden-profile (shared info + unique info must be paired to reveal the right one.)

convex-concave problems

Heuristic method for solving a specific type of non-convex problem. Solves a small sequence of convex problems.

difference-of-convex function

For:

\begin{equation} h\qty(x) = f\qty(x) - g\qty(x) \end{equation}

for convex \(f\qty(x)\) and \(g\qty(x)\).

some examples

• a convex quadratic, except the \(P\) in \(\qty(\frac{1}{2}) x^{T}Px\) is not PSD; we express this in terms of \(P = P_{\text{psd}} - P_{\text{nsd}}\). And thus we can get: \(\qty(\frac{1}{2})x^{T}P_{\text{psd}} x - \qty(\frac{1}{2})x^{T}P_{\text{nsd}}x\)

majorization

Taylor approximation: