This paper presents an efficient preference elicitation framework for uncertain matroid optimization, where precise weight information is unavailable, but insights into possible weight values are accessible. The core innovation of our approach lies in its ability to systematically elicit user preferences, aligning the optimization process more closely with decision-makers' objectives. By incrementally querying preferences between pairs of elements, we iteratively refine the parametric uncertainty regions, leveraging the structural properties of matroids. Our method aims to achieve the exact optimum by reducing regret with a few elicitation rounds. Additionally, our approach avoids the computation of Minimax Regret and the use of Linear programming solvers at every iteration, unlike previous methods. Experimental results on four standard matroids demonstrate that our method reaches optimality more quickly and with fewer preference queries than existing techniques.

The proliferation of the Internet has led to the emergence of online advertising, driven by the mechanics of online auctions. In these repeated auctions, software agents participate on behalf of aggregated advertisers to optimize for their long-term utility. To fulfill the diverse demands, bidding strategies are employed to optimize advertising objectives subject to different spending constraints. Existing approaches on constrained bidding typically rely on i.i.d. train and test conditions, which contradicts the adversarial nature of online ad markets where different parties possess potentially conflicting objectives. In this regard, we explore the problem of constrained bidding in adversarial bidding environments, which assumes no knowledge about the adversarial factors. Instead of relying on the i.i.d. assumption, our insight is to align the train distribution of environments with the potential test distribution meanwhile minimizing policy regret. Based on this insight, we propose a practical Minimax Regret Optimization (MiRO) approach that interleaves between a teacher finding adversarial environments for tutoring and a learner meta-learning its policy over the given distribution of environments. In addition, we pioneer to incorporate expert demonstrations for learning bidding strategies. Through a causality-aware policy design, we improve upon MiRO by distilling knowledge from the experts. Extensive experiments on both industrial data and synthetic data show that our method, MiRO with Causality-aware reinforcement Learning (MiROCL), outperforms prior methods by over 30%.

In this paper, we consider learning scenarios where the learned model is evaluated under an unknown test distribution which potentially differs from the training distribution (i.e. distribution shift). The learner has access to a family of weight functions such that the test distribution is a reweighting of the training distribution under one of these functions, a setting typically studied under the name of Distributionally Robust Optimization (DRO). We consider the problem of deriving regret bounds in the classical learning theory setting, and require that the resulting regret bounds hold uniformly for all potential test distributions. We show that the DRO formulation does not guarantee uniformly small regret under distribution shift. We instead propose an alternative method called Minimax Regret Optimization (MRO), and show that under suitable conditions this method achieves uniformly low regret across all test distributions. We also adapt our technique to have stronger guarantees when the test distributions are heterogeneous in their similarity to the training data. Given the widespead optimization of worst case risks in current approaches to robust machine learning, we believe that MRO can be a strong alternative to address distribution shift scenarios.