The Value of Human Expertise

We prove that no single rank ordered adversary strategy is globally optimal for the prediction with expert advice problem with six or more experts, in both the geometric stopping and finite time horizon settings. The proof is based on establishing a leading order correction when one expert moves far ahead of the others. This allows us to connect optimal strategies between $n$ and $j<n$ experts and utilize recent results on the exact optimality set for the five expert problem.

Human-in-the-loop Bayesian optimization (HITL BO) methods utilize human expertise to improve the sample-efficiency of BO. Most HITL BO methods assume that a domain expert can quantify their knowledge, for instance by pinpointing query locations or specifying their prior beliefs about the location of the maximum as a probability distribution. However, since human expertise is often tacit and cannot be explicitly quantified, we consider a setting where domain knowledge of an expert is elicited via pairwise comparisons of designs. We interpret the expert's pairwise judgements as noisy evidence about the values of the observable objective function and develop a principled method for combining the information obtained via direct observations and pairwise queries. Specifically, we derive a cost-aware value-of-information acquisition function that balances direct observations against pairwise queries. The proposed method approaches the convex hull of the trajectories of the individual information sources: when pairwise queries are cheap it substantially improves sample-efficiency over observation-only BO, and when pairwise queries are costly or noisy, it recovers the performance of standard BO by relying on direct observations alone.

Reducing the number of focal elements of a mass function is classically driven by an intrinsic distance, such as Jaccard or Jousselme, that keeps the approximation close to the original as a body of evidence. We consider instead the case where the mass function feeds a linear combinatorial optimisation problem with evidential costs. What should then be preserved is not the closeness of the two mass functions, but the quality of the decision they induce. We introduce a decision-aware approximation that targets the regret of the decision: one decides with the cheaper approximation and is evaluated under the true mass function. On a minimal shortest path, the distance-optimal approximation flips the decision while a decision-aware merge preserves it, and this occurs on a non-negligible fraction of random instances. We prove a one-point bound that localises the regret at the true optimum, turn it into an exact dynamic program for the scalar case, and extend it to an online version that prunes focal elements before the final cost is known. In experiments the decision-aware compressor flips the decision less often than representation-aware compression, for both the linear criterion and a non-linear proxy read-out.