Biases with respect to socially-salient attributes of individuals have been well documented in evaluation processes used in settings such as admissions and hiring. We view such an evaluation process as a transformation of a distribution of the true utility of an individual for a task to an observed distribution and model it as a solution to a loss minimization problem subject to an information constraint. Our model has two parameters that have been identified as factors leading to biases: the resource-information trade-off parameter in the information constraint and the risk-averseness parameter in the loss function. We characterize the distributions that arise from our model and study the effect of the parameters on the observed distribution. The outputs of our model enrich the class of distributions that can be used to capture variation across groups in the observed evaluations. We empirically validate our model by fitting real-world datasets and use it to study the effect of interventions in a downstream selection task. These results contribute to an understanding of the emergence of bias in evaluation processes and provide tools to guide the deployment of interventions to mitigate biases.

Let ϑ Rd1 and µ Rd2 be the dual variables corresponding to the d1 equality constraints and the d2 inequality constraints respectively. Let X? be an optimal solution to (SDP) and let X?FW be an optimal solution to (SDP-LSE). For ease of notation, let u= A(1)(X) b(1) andv = b(2) A(2)(X), (1) and define (bu,bv), (uFW,vFW) and (u?,v?) by substituting bX, XFW and X? respectively in (1). Upper bound on the objective. Rearranging the terms, using the duality of the `1 and ` norms, and the fact that µ? 0, gives hC, bX i hC,X?i+

A.1 For LEHD model467 In Table 5, we explore the effects of eliminating normalization from the attention layer in our LEHD468 model. We train three LEHD models with the same training scheme and training budget, differing469 solely in the attention layer: one with batch normalization (BN), one with instance normalization470 (IN), and one without normalization (w/o). We train all three POMO models with the same reinforcement learning method477 with POMO strategy and training budget (1000 epochs). The results show that different types of478 normalization have few effects on the POMO model.479 The results in Table 6 show that removing normalization from attention layer has little impact on the480 model with a heavy encoder and a light decoder.

Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that combines a penalty formulation, a surrogate model, and a trust region strategy. The constrained problem is converted to an unconstrained form by penalizing constraint violations, which provides a unified modeling framework. A trust region restricts the search to a local region around the current best solution, which improves stability and efficiency in high dimensions. Within this region, we use the Expected Improvement acquisition function to select evaluation points by balancing improvement and uncertainty. The proposed Trust Region method integrates penalty-based constraint handling with local surrogate modeling. This combination enables efficient exploration of feasible regions while maintaining sample efficiency. We compare the proposed method with state-of-the-art methods on synthetic and real-world high-dimensional constrained optimization problems. The results show that the method identifies high-quality feasible solutions with fewer evaluations and maintains stable performance across different settings.

We study the cost function for hierarchical clusterings introduced by [16] where hierarchies are treated as first-class objects rather than deriving their cost from projections into flat clusters. It was also shown in [16] that a top-down algorithm returns a hierarchical clustering of cost at most O(αnlog n) times the cost of the optimal hierarchical clustering, where αn is the approximation ratio of the Sparsest Cut subroutine used. Thus using the best known approximation algorithm for Sparsest Cut due to Arora-Rao-Vazirani, the top-down algorithm returns a hierarchical clustering of cost at most O log3/2 ntimes the cost of the optimal solution. We improve this by giving an O(log n)-approximation algorithm for this problem. Our main technical ingredients are a combinatorial characterization of ultrametrics induced by this cost function, deriving an Integer Linear Programming (ILP) formulation for this family of ultrametrics, and showing how to iteratively round an LP relaxation of this formulation by using the idea of sphere growing which has been extensively used in the context of graph partitioning. We also prove that our algorithm returns an O(log n)-approximate hierarchical clustering for a generalization of this cost function also studied in [16]. We also give constant factor inapproximability results for this problem.

In these processes, an evaluator estimates an individual's value to an institution.