arXiv subjects

Ahmed Rashwan

Publications and source records attributed to Ahmed Rashwan.

5 recordsLinked to original sources

arXiv2026

Refined outer-approximation algorithms for monotonic optimisation

Monotonic optimisation is a broad class of non-convex problems formulated in terms of monotone functions. Such problems are commonly solved via the polyblock outer-approximation algorithm (POA), a branch-and-bound method that iteratively refines a rectangular outer-approximation of the feasible set. POA scales poorly, however: the number of vertices needed to describe the approximation can grow exponentially, leading to large memory requirements and increasingly expensive subroutines. To address these limitations, we propose three algorithmic improvements: a generalised anchor selection that yields an optimal balanced monotonicity cut, a relaxed optimality condition that guarantees finite termination without continuity assumptions, and a vectorised variant that processes multiple nodes concurrently. We further develop an efficient tree-based implementation, which accelerates POA's core subroutines while storing the outer-approximation compactly. Numerical experiments show that these improvements yield order-of-magnitude speed-ups over standard POA and solve problems on which existing variants fail. Finally, we introduce polyblocks, an open-source Python package implementing the proposed algorithms alongside a framework for developing new POA variants, available at https://github.com/RashwanA/polyblocks.

math.OC↗

arXiv2026

Monotone Optimisation with Learned Projections

Monotone optimisation problems admit specialised global solvers such as the Polyblock Outer Approximation (POA) algorithm, but these methods typically require explicit objective and constraint functions. In many applications, these functions are only available through data, making POA difficult to apply directly. We introduce an algorithm-aware learning approach that integrates learned models into POA by directly predicting its projection primitive via the radial inverse, avoiding the costly bisection procedure used in standard POA. We propose Homogeneous-Monotone Radial Inverse (HM-RI) networks, structured neural architectures that enforce key monotonicity and homogeneity properties, enabling fast projection estimation. We provide a theoretical characterisation of radial inverse functions and show that, under mild structural conditions, a HM-RI predictor corresponds to the radial inverse of a valid set of monotone constraints. To reduce training overhead, we further develop relaxed monotonicity conditions that remain compatible with POA. Across multiple monotone optimisation benchmarks (indefinite quadratic programming, multiplicative programming, and transmit power optimisation), our approach yields substantial speed-ups in comparison to direct function estimation while maintaining strong solution quality, outperforming baselines that do not exploit monotonic structure.

cs.LG↗

arXiv2026

Factored Value Functions for Graph-Based Multi-Agent Reinforcement Learning

Credit assignment is a core challenge in multi-agent reinforcement learning (MARL), especially in large-scale systems with structured, local interactions. Graph-based Markov decision processes (GMDPs) capture such settings via an influence graph, but standard critics are poorly aligned with this structure: global value functions provide weak per-agent learning signals, while existing local constructions can be difficult to estimate and ill-behaved in infinite-horizon settings. We introduce the Diffusion Value Function (DVF), a factored value function for GMDPs that assigns to each agent a value component by diffusing rewards over the influence graph with temporal discounting and spatial attenuation. We show that DVF is well-defined, admits a Bellman fixed point, and decomposes the global discounted value via an averaging property. DVF can be used as a drop-in critic in standard RL algorithms and estimated scalably with graph neural networks. Building on DVF, we propose Diffusion A2C (DA2C) and a sparse message-passing actor, Learned DropEdge GNN (LD-GNN), for learning decentralised algorithms under communication costs. Across the firefighting benchmark and three distributed computation tasks (vector graph colouring and two transmit power optimisation problems), DA2C consistently outperforms local and global critic baselines, improving average reward by up to 11%.

cs.LG↗

arXiv2025

Enforcing convex constraints in Graph Neural Networks

Many machine learning applications require outputs that satisfy complex, dynamic constraints. This task is particularly challenging in Graph Neural Network models due to the variable output sizes of graph-structured data. In this paper, we introduce ProjNet, a Graph Neural Network framework which satisfies input-dependant constraints. ProjNet combines a sparse vector clipping method with the Component-Averaged Dykstra (CAD) algorithm, an iterative scheme for solving the best-approximation problem. We establish a convergence result for CAD and develop a GPU-accelerated implementation capable of handling large-scale inputs efficiently. To enable end-to-end training, we introduce a surrogate gradient for CAD that is both computationally efficient and better suited for optimization than the exact gradient. We validate ProjNet on four classes of constrained optimisation problems: linear programming, two classes of non-convex quadratic programs, and radio transmit power optimization, demonstrating its effectiveness across diverse problem settings.

cs.LG↗

arXiv2025

A neural drift-plus-penalty algorithm for network power allocation and routing

The drift-plus-penalty method is a Lyapunov optimisation technique commonly applied to network routing problems. It reduces the original stochastic planning task to a sequence of greedy optimizations, enabling the design of distributed routing algorithms which stabilize data queues while simultaneously optimizing a specified penalty function. While drift-plus-penalty methods have desirable asymptotic properties, they tend to incur higher network delay than alternative control methods, especially under light network load. In this work, we propose a learned variant of the drift-plus-penalty method that can preserve its theoretical guarantees, while being flexible enough to learn routing strategies directly from a model of the problem. Our approach introduces a novel mechanism for learning routing decisions and employs an optimal transport-based method for link scheduling. Applied to the joint task of transmit-power allocation and data routing, the method achieves consistent improvements over common baselines under a broad set of scenarios.

eess.SY↗