Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Games

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.

A Long Short-Term Memory for AI Applications in Spike-based Neuromorphic Hardware

In spite of intensive efforts it has remained an open problem to what extent current Artificial Intelligence (AI) methods that employ Deep Neural Networks (DNNs) can be implemented more energy-efficiently on spike-based neuromorphic hardware. This holds in particular for AI methods that solve sequence processing tasks, a primary application target for spike-based neuromorphic hardware. One difficulty is that DNNs for such tasks typically employ Long Short-Term Memory (LSTM) units. Yet an efficient emulation of these units in spike-based hardware has been missing. We present a biologically inspired solution that solves this problem. This solution enables us to implement a major class of DNNs for sequence processing tasks such as time series classification and question answering with substantial energy savings on neuromorphic hardware. In fact, the Relational Network for reasoning about relations between objects that we use for question answering is the first example of a large DNN that carries out a sequence processing task with substantial energy-saving on neuromorphic hardware.