pwc-archive/papers-with-abstracts huggingface dataset:
Evaluating interventions for Plasmodium vivax forest malaria using a three-scale mathematical model
Authors: Shoshana Elgart, Mark B. Flegg, Jennifer A. Flegg
Date: 2025-06-10 00:00:00

The rising proportion of Plasmodium vivax cases concentrated in forest-fringe areas across the Greater Mekong Subregion highlights the importance of pharmaceutical and mosquito control techniques specifically targeted towards forest-going populations. To mathematically assess best-possible antimalarial interventions in the context of hypnozoite reactivation and seasonal forest migration, we extend a previously developed three-scale integro-differential equations model of P. vivax transmission. In particular, we fit the model to data gathered over a four-year period in Vietnam to gain insight into local P. vivax dynamics and validate the model's ability to capture epidemiological trends. The calibrated model is then used to generate optimal schedules for mass-drug administration (MDA) in forest-goers and gauge the efficacy of vector control techniques (such as long-lasting insecticide nets and indoor residual spraying) in forest-adjacent areas. Our results highlight the dependence of optimal MDA timing on the demographics of the human population, the importance of interventions targeting the mosquito bite rate, and the need for efficacy in hypnozoite-targeting antimalarial drugs.
Cancer model with moving extinction threshold reproduces real cancer data
Authors: Frank Bastian, Hassan Alkhayuon, Kieran Mulchrone, Micheal O'Riordain, Sebastian Wieczorek
Date: 2025-06-06 00:00:00

We propose a simple dynamic model of cancer development that captures carcinogenesis and subsequent cancer progression. A central idea of the model is to include the immune system as an extinction threshold, similar to the strong Allee effect in population biology. We first identify the limitations of commonly used Allee effect models in reproducing typical cancer progression. We then address these limitations by deriving a new model that incorporates: (i) random mutations of stem cells at a rate that increases with age and (ii) immune response whose strength may also vary over time. Our model accurately reproduces a wide range of real-world cancer data: the typical age-specific cumulative risk of most human cancers, the progression of breast cancer in mice, and the unusual age-specific cumulative risk of breast cancer in women. In the last case, we use a moving extinction threshold to reflect the different immune response at different phases of the menstrual cycle and menopausal treatment. This provides new insights into the effects of hormone replacement therapy and menstrual cycle length. This moving threshold approach can be applied to a variety of other cancer scenarios where the immune response or other important factors may vary over time.
Age-Structured Population Dynamics
Authors: Odo Diekmann, Francesca Scarabel
Date: 2025-06-03 00:00:00

This chapter reviews some aspects of the theory of age-structured models of populations with finite maximum age. We formulate both the renewal equation for the birth rate and the partial differential equation for the age density, and show their equivalence. Next, we define and discuss central concepts in population dynamics, like the basic reproduction number $R_0$, the Malthusian parameter $r$, and the stable age distribution. We briefly review the sun-star theory that turns the birth term into a bounded additive perturbation, thus allowing to develop stability and bifurcation theory along standard lines. Finally, we review the pseudospectral approximation of the infinite-dimensional age-structured models by means of a finite system of ordinary differential equations, which allows to perform numerical bifurcation analysis with existing software tools. Here, Nicholson's blowfly equation serves as a worked example.
Signature Maximum Mean Discrepancy Two-Sample Statistical Tests
Authors: Andrew Alden, Blanka Horvath, Zacharia Issa
Date: 2025-06-02 00:00:00
Tasks: Two-sample testing

Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a kernel-based method, the MMD can be extended to path space valued distributions using the signature kernel. The resulting signature MMD (sig-MMD) can be used to define a metric between distributions on path space. Similarly to the original use case of the MMD as a test statistic within a two-sample testing framework, the sig-MMD can be applied to determine if two sets of paths are drawn from the same stochastic process. This work is dedicated to understanding the possibilities and challenges associated with applying the sig-MMD as a statistical tool in practice. We introduce and explain the sig-MMD, and provide easily accessible and verifiable examples for its practical use. We present examples that can lead to Type 2 errors in the hypothesis test, falsely indicating that samples have been drawn from the same underlying process (which generally occurs in a limited data setting). We then present techniques to mitigate the occurrence of this type of error.
The Boundary Reproduction Number for Determining Boundary Steady State Stability in Chemical Reaction Systems
Authors: Matthew D. Johnston, Florin Avram
Date: 2025-06-02 00:00:00

We introduce the boundary reproduction number, adapted from the next generation matrix method, to assess whether an infusion of species will persist or become exhausted in a chemical reaction system. Our main contributions are as follows: (a) we show how the concept of a siphon, prevalent in Petri nets and chemical reaction network theory, identifies sets of species that may become depleted at steady state, analogous to a disease-free boundary steady state; (b) we develop an approach for incorporating biochemically motivated conservation laws, which allows the stability of boundary steady states to be determined within specific compatibility classes; and (c) we present an effective heuristic for decomposing the Jacobian of the system that reduces the computational complexity required to compute the stability domain of a boundary steady state. The boundary reproduction number approach significantly simplifies existing parameter-dependent methods for determining the stability of boundary steady states in chemical reaction systems and has implications for the capacity of critical metabolites and substrates in metabolic pathways to become exhausted.
A condensing approach to multiple shooting neural ordinary differential equation
Authors: Siddharth Prabhu, Srinivas Rangarajan, Mayuresh Kothare
Date: 2025-05-31 00:00:00
Tasks: parameter estimation

Multiple-shooting is a parameter estimation approach for ordinary differential equations. In this approach, the trajectory is broken into small intervals, each of which can be integrated independently. Equality constraints are then applied to eliminate the shooting gap between the end of the previous trajectory and the start of the next trajectory. Unlike single-shooting, multiple-shooting is more stable, especially for highly oscillatory and long trajectories. In the context of neural ordinary differential equations, multiple-shooting is not widely used due to the challenge of incorporating general equality constraints. In this work, we propose a condensing-based approach to incorporate these shooting equality constraints while training a multiple-shooting neural ordinary differential equation (MS-NODE) using first-order optimization methods such as Adam.
Schauder Bases for $C[0, 1]$ Using ReLU, Softplus and Two Sigmoidal Functions
Authors: Anand Ganesh, Babhrubahan Bose, Anand Rajagopalan
Date: 2025-06-09 00:00:00

We construct four Schauder bases for the space $C[0,1]$, one using ReLU functions, another using Softplus functions, and two more using sigmoidal versions of the ReLU and Softplus functions. This establishes the existence of a basis using these functions for the first time, and improves on the universal approximation property associated with them.
Stability of Mean-Field Variational Inference
Authors: Shunan Sheng, Bohan Wu, Alberto González-Sanz, Marcel Nutz
Date: 2025-06-09 00:00:00
Tasks: Bayesian Inference, Variational Inference

Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. This paper studies the stability properties of the mean-field approximation when the target distribution varies within the class of strongly log-concave measures. We establish dimension-free Lipschitz continuity of the MFVI optimizer with respect to the target distribution, measured in the 2-Wasserstein distance, with Lipschitz constant inversely proportional to the log-concavity parameter. Under additional regularity conditions, we further show that the MFVI optimizer depends differentiably on the target potential and characterize the derivative by a partial differential equation. Methodologically, we follow a novel approach to MFVI via linearized optimal transport: the non-convex MFVI problem is lifted to a convex optimization over transport maps with a fixed base measure, enabling the use of calculus of variations and functional analysis. We discuss several applications of our results to robust Bayesian inference and empirical Bayes, including a quantitative Bernstein--von Mises theorem for MFVI, as well as to distributed stochastic control.
S-shaped Utility Maximization with VaR Constraint and Partial Information
Authors: Dongmei Zhu, Ashley Davey, Harry Zheng
Date: 2025-06-11 00:00:00

We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determines if the constrained problem admits a unique optimal solution and Lagrange multiplier or is infeasible. We also propose three algorithms (Lagrange, simulation, deep neural network) to solve the problem and compare their performances with numerical examples.
Optimal hedging of an informed broker facing many traders
Authors: Philippe Bergault, Pierre Cardaliaguet, Wenbin Yan
Date: 2025-06-10 00:00:00

This paper investigates the optimal hedging strategies of an informed broker interacting with multiple traders in a financial market. We develop a theoretical framework in which the broker, possessing exclusive information about the drift of the asset's price, engages with traders whose trading activities impact the market price. Using a mean-field game approach, we derive the equilibrium strategies for both the broker and the traders, illustrating the intricate dynamics of their interactions. The broker's optimal strategy involves a Stackelberg equilibrium, where the broker leads and the traders follow. Our analysis also addresses the mean field limit of finite-player models and shows the convergence to the mean-field solution as the number of traders becomes large.
Reliable Critics: Monotonic Improvement and Convergence Guarantees for Reinforcement Learning
Authors: Eshwar S. R., Gugan Thoppe, Aditya Gopalan, Gal Dalal
Date: 2025-06-08 00:00:00
Tasks: Reinforcement Learning (RL)

Despite decades of research, it remains challenging to correctly use Reinforcement Learning (RL) algorithms with function approximation. A prime example is policy iteration, whose fundamental guarantee of monotonic improvement collapses even under linear function approximation. To address this issue, we introduce Reliable Policy Iteration (RPI). It replaces the common projection or Bellman-error minimization during policy evaluation with a Bellman-based constrained optimization. We prove that not only does RPI confer textbook monotonicity on its value estimates but these estimates also lower bound the true return. Also, their limit partially satisfies the unprojected Bellman equation, emphasizing RPI's natural fit within RL. RPI is the first algorithm with such monotonicity and convergence guarantees under function approximation. For practical use, we provide a model-free variant of RPI that amounts to a novel critic. It can be readily integrated into primary model-free PI implementations such as DQN and DDPG. In classical control tasks, such RPI-enhanced variants consistently maintain their lower-bound guarantee while matching or surpassing the performance of all baseline methods.
Distributionally Robust Learning in Survival Analysis
Authors: Yeping Jin, Lauren Wise, Ioannis Ch. Paschalidis
Date: 2025-06-02 00:00:00
Tasks: regression, Survival Analysis

We introduce an innovative approach that incorporates a Distributionally Robust Learning (DRL) approach into Cox regression to enhance the robustness and accuracy of survival predictions. By formulating a DRL framework with a Wasserstein distance-based ambiguity set, we develop a variant Cox model that is less sensitive to assumptions about the underlying data distribution and more resilient to model misspecification and data perturbations. By leveraging Wasserstein duality, we reformulate the original min-max DRL problem into a tractable regularized empirical risk minimization problem, which can be computed by exponential conic programming. We provide guarantees on the finite sample behavior of our DRL-Cox model. Moreover, through extensive simulations and real world case studies, we demonstrate that our regression model achieves superior performance in terms of prediction accuracy and robustness compared with traditional methods.
Similarity Matching Networks: Hebbian Learning and Convergence Over Multiple Time Scales
Authors: Veronica Centorrino, Francesco Bullo, Giovanni Russo
Date: 2025-06-06 00:00:00
Tasks: Dimensionality Reduction

A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biological interpretation, successful application in several domains, and experimental validation, a formal complete convergence analysis remains elusive. Building on this framework, we consider and analyze a continuous-time neural network, the \emph{similarity matching network}, for principal subspace projection. Derived from a min-max-min objective, this biologically-plausible network consists of three coupled dynamics evolving at different time scales: neural dynamics, lateral synaptic dynamics, and feedforward synaptic dynamics at the fast, intermediate, and slow time scales, respectively. The feedforward and lateral synaptic dynamics consist of Hebbian and anti-Hebbian learning rules, respectively. By leveraging a multilevel optimization framework, we prove convergence of the dynamics in the offline setting. Specifically, at the first level (fast time scale), we show strong convexity of the cost function and global exponential convergence of the corresponding gradient-flow dynamics. At the second level (intermediate time scale), we prove strong concavity of the cost function and exponential convergence of the corresponding gradient-flow dynamics within the space of positive definite matrices. At the third and final level (slow time scale), we study a non-convex and non-smooth cost function, provide explicit expressions for its global minima, and prove almost sure convergence of the corresponding gradient-flow dynamics to the global minima. These results rely on two empirically motivated conjectures that are supported by thorough numerical experiments. Finally, we validate the effectiveness of our approach via a numerical example.
Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Games
Authors: Philipp Plank, Yufei Zhang
Date: 2025-06-06 00:00:00
Tasks: Bilevel Optimization, Multi-agent Reinforcement Learning

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating such games while capturing heterogeneity among players. In this paper, we propose and analyze a policy optimization framework for continuous-time, finite-horizon linear-quadratic GMFGs. Exploiting the structural properties of GMFGs, we design an efficient policy parameterization in which each player's policy is represented as an affine function of their private state, with a shared slope function and player-specific intercepts. We develop a bilevel optimization algorithm that alternates between policy gradient updates for best-response computation under a fixed population distribution, and distribution updates using the resulting policies. We prove linear convergence of the policy gradient steps to best-response policies and establish global convergence of the overall algorithm to the Nash equilibrium. The analysis relies on novel landscape characterizations over infinite-dimensional policy spaces. Numerical experiments demonstrate the convergence and robustness of the proposed algorithm under varying graphon structures, noise levels, and action frequencies.
Optimized projection-free algorithms for online learning: construction and worst-case analysis
Authors: Julien Weibel, Pierre Gaillard, Wouter M. Koolen, Adrien Taylor
Date: 2025-06-06 00:00:00

This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an online Frank-Wolfe algorithm along with its conceptually simple potential-based proof, and (ii) shows how to leverage semidefinite programming to jointly design and analyze online Frank-Wolfe-type algorithms numerically in a variety of settings-that include the design of the variant (i). Based on the semidefinite technique, we conclude with strong numerical evidence suggesting that no pure online Frank-Wolfe algorithm within our model class can have a regret guarantee better than O(T^3/4) (T is the time horizon) without additional assumptions, that the current algorithms do not have optimal constants, that the algorithm benefits from similar anytime properties O(t^3/4) not requiring to know T in advance, and that multiple linear optimization rounds do not generally help to obtain better regret bounds.
Exploiting Similarity for Computation and Communication-Efficient Decentralized Optimization
Authors: Yuki Takezawa, Xiaowen Jiang, Anton Rodomanov, Sebastian U. Stich
Date: 2025-06-06 00:00:00

Reducing communication complexity is critical for efficient decentralized optimization. The proximal decentralized optimization (PDO) framework is particularly appealing, as methods within this framework can exploit functional similarity among nodes to reduce communication rounds. Specifically, when local functions at different nodes are similar, these methods achieve faster convergence with fewer communication steps. However, existing PDO methods often require highly accurate solutions to subproblems associated with the proximal operator, resulting in significant computational overhead. In this work, we propose the Stabilized Proximal Decentralized Optimization (SPDO) method, which achieves state-of-the-art communication and computational complexities within the PDO framework. Additionally, we refine the analysis of existing PDO methods by relaxing subproblem accuracy requirements and leveraging average functional similarity. Experimental results demonstrate that SPDO significantly outperforms existing methods.
Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming
Authors: Fuat Can Beylunioglu, Mehrdad Pirnia, P. Robert Duimering
Date: 2025-06-05 00:00:00
Tasks: energy management

Neural Networks (NN) with ReLU activation functions are used to model multiparametric quadratic optimization problems (mp-QP) in diverse engineering applications. Researchers have suggested leveraging the piecewise affine property of deep NN models to solve mp-QP with linear constraints, which also exhibit piecewise affine behaviour. However, traditional deep NN applications to mp-QP fall short of providing optimal and feasible predictions, even when trained on large datasets. This study proposes a partially-supervised NN (PSNN) architecture that directly represents the mathematical structure of the global solution function. In contrast to generic NN training approaches, the proposed PSNN method derives a large proportion of model weights directly from the mathematical properties of the optimization problem, producing more accurate solutions despite significantly smaller training data sets. Many energy management problems are formulated as QP, so we apply the proposed approach to energy systems (specifically DC optimal power flow) to demonstrate proof of concept. Model performance in terms of solution accuracy and speed of predictions was compared against a commercial solver and a generic Deep NN model based on classical training. Results show KKT sufficient conditions for PSNN consistently outperform generic NN architectures with classical training using far less data, including when tested on extreme, out-of-training distribution test data. Given its speed advantages over traditional solvers, the PSNN model can quickly produce optimal and feasible solutions within a second for millions of input parameters sampled from a distribution of stochastic demands and renewable generator dispatches, which can be used for simulations and long term planning.
Zeroth-Order Optimization Finds Flat Minima
Authors: Liang Zhang, Bingcong Li, Kiran Koshy Thekumparampil, Sewoong Oh, Michael Muehlebach, Niao He
Date: 2025-06-05 00:00:00
Tasks: Binary Classification, Language Modeling, Language Modelling

Zeroth-order methods are extensively used in machine learning applications where gradients are infeasible or expensive to compute, such as black-box attacks, reinforcement learning, and language model fine-tuning. Existing optimization theory focuses on convergence to an arbitrary stationary point, but less is known on the implicit regularization that provides a fine-grained characterization on which particular solutions are finally reached. We show that zeroth-order optimization with the standard two-point estimator favors solutions with small trace of Hessian, which is widely used in previous work to distinguish between sharp and flat minima. We further provide convergence rates of zeroth-order optimization to approximate flat minima for convex and sufficiently smooth functions, where flat minima are defined as the minimizers that achieve the smallest trace of Hessian among all optimal solutions. Experiments on binary classification tasks with convex losses and language model fine-tuning support our theoretical findings.