Budget Feasible Mechanisms for Experimental Design

We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant (approximate to 12.98) factor approximation for the Experimental Design Problem (EDP). By applying previous work on budget feasible mechanisms with a submodular objective, one could only have derived either an exponential time deterministic mechanism or a randomized polynomial time mechanism. We also establish that no truthful, budget-feasible mechanism is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression.