Allocating test-time compute with one shared price

Four LLM requests share a budget of B compute units. Request i minimizes its toy loss wᵢ/(1+xᵢ) plus the price λxᵢ. The master only sees total usage and adjusts λ.

Master price
λ = 2.500
Compute requested
—
Budget
17.0
Usage − budget
—
17 0.05 2.5
total compute requested current multiplier clearing multiplier λ★
iteration k
0
price λk
2.500
compute used
—
dual bound
—
optimal loss
—