Bernd Heidergott

Jinyang Jiang, Bernd Heidergott, Jiaqiao Hu et al. · pku

Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the Distortion-Measure (DM) form and Quantile-Function (QF) form. The DM-form employs a three-timescale algorithm to track quantiles, compute their gradients, and update decision variables, utilizing the Generalized Likelihood Ratio and kernel-based density estimation. The QF-form provides a simpler two-timescale approach that avoids the need for complex quantile gradient estimation. A hybrid form integrates both approaches, applying the DM-form for robust performance around distortion function jumps and the QF-form for efficiency in smooth regions. Proofs of strong convergence and convergence rates for the proposed algorithms are provided. In particular, the DM-form achieves an optimal rate of $O(k^{-4/7})$, while the QF-form attains a faster rate of $O(k^{-2/3})$. Numerical experiments confirm their effectiveness and demonstrate substantial improvements over baselines in robust portfolio selection tasks. The method's scalability is further illustrated through integration into deep reinforcement learning. Specifically, a DRM-based Proximal Policy Optimization algorithm is developed and applied to multi-echelon dynamic inventory management, showcasing its practical applicability.

Christian Franssen, Iman van Lelyveld, Bernd Heidergott

Understanding the functional roles of financial institutions within interconnected markets is critical for effective supervision, systemic risk assessment, and resolution planning. We propose an interpretable role-based clustering approach for multi-layer financial networks, designed to identify the functional positions of institutions across different market segments. Our method follows a general clustering framework defined by proximity measures, cluster evaluation criteria, and algorithm selection. We construct explainable node embeddings based on egonet features that capture both direct and indirect trading relationships within and across market layers. Using transaction-level data from the ECB's Money Market Statistical Reporting (MMSR), we demonstrate how the approach uncovers heterogeneous institutional roles such as market intermediaries, cross-segment connectors, and peripheral lenders or borrowers. The results highlight the flexibility and practical value of role-based clustering in analyzing financial networks and understanding institutional behavior in complex market structures.

Christian Franssen, Jinyang Jiang, Yijie Peng et al. · pku

Pruning encompasses a range of techniques aimed at increasing the sparsity of neural networks (NNs). These techniques can generally be framed as minimizing a loss function subject to an $L_0$ norm constraint. This paper introduces CoNNect, a novel differentiable regularizer for sparse NN training that ensures connectivity between input and output layers. We prove that CoNNect approximates $L_0$ regularization, guaranteeing maximally connected network structures while avoiding issues like layer collapse. Moreover, CoNNect is easily integrated with established structural pruning strategies. Numerical experiments demonstrate that CoNNect can improve classical pruning strategies and enhance state-of-the-art one-shot pruners, such as DepGraph and LLM-pruner.